Wind power virtual inertia parameter optimization method and medium for improving the probabilistic stability of power systems

Abstract

The present invention discloses a method for optimizing the virtual inertia parameters of wind power for improving the probabilistic stability of a power system, which includes the following steps: 1) Establish an optimization model for the virtual inertia parameters of wind power considering the probabilistic stability of the system with the goal of maximizing the probability of meeting the frequency and small-signal stability of the power system; 2) Analyze the optimization model for the virtual inertia parameters of wind power to establish an analytical optimization model for the virtual inertia parameters of wind power that coordinately considers the probabilistic stability of the system; 3) Solve the analytical optimization model for the virtual inertia parameters of wind power using a probabilistic stability optimization algorithm based on sensitivity analysis to obtain the virtual inertia parameters of wind power that meet the requirements of the probabilistic stability of the power system. The present invention simultaneously considers the requirements of the frequency stability and small-signal stability of the system, and can effectively improve the system stability through the optimization of the virtual inertia parameters.

Description

Technical Field

[0001] The present invention relates to the field of power systems and their automation, and specifically to a method and medium for optimizing wind power virtual inertia parameters for improving the probabilistic stability of power systems. Background Art

[0002] To make up for the lack of inertia caused by the reduction of synchronous units, alternative solutions for providing virtual inertia by new energy units have been proposed both at home and abroad. Utilizing the mechanical energy stored in the rotor, wind turbines can provide inertia response for the system, and wind turbines with virtual inertia control are gradually being commercialized.

[0003] Virtual inertia parameters are closely related to the frequency stability and small-signal stability of the system. Increasing virtual inertia can improve the total inertia level of the system, thereby improving the frequency stability of the system. However, due to factors such as the rapid development of ultra-high voltage AC power transmission and the popularization of renewable energy, the small-signal stability problem has become increasingly prominent, and there is even a risk of inducing large-scale power outages. Unreasonable setting of virtual inertia parameters may lead to the instability of small-signal stability, and increasing virtual inertia may make the already prominent small-signal stability problem worse.

[0004] Therefore, when setting virtual inertia parameters, it is necessary to optimize each virtual inertia parameter while considering the requirements of system frequency stability and small-signal stability. The virtual inertia optimization method considering small-signal stability generally takes small-signal stability indexes such as system eigenvalues or damping ratios as the optimization objectives, and establishes an optimization model considering parameter self-constraints.

[0005] Existing research mainly focuses on stability optimization for a single stability requirement, and it is difficult to effectively meet the system stability requirements. Existing research has proposed a method for optimizing wind power virtual inertia parameters by coordinately considering system frequency stability and small-signal stability. However, due to the fact that low-inertia systems contain a high proportion of renewable energy and the system has strong uncertainties, optimizing only considering the system stability under the determined operating conditions is still difficult to ensure the safe and stable operation of the system, and the application scenarios have certain limitations. Summary of the Invention

[0006] The object of the present invention is to provide a method for optimizing wind power virtual inertia parameters for improving the probabilistic stability of power systems, including the following steps:

[0007] 1) Establish an optimization model for wind power virtual inertia parameters considering system probabilistic stability with the goal of maximizing the probability of meeting the frequency and small-signal stability of the power system;

[0008] Furthermore, the wind power virtual inertia parameter optimization model is as follows:

[0009] (maxP f )∩(maxPζ )(1)

[0010] Among them, the probability \(P\) of meeting the system frequency stability constraint f , the probability \(P\) of meeting the small-signal stability ζ are respectively as follows:

[0011]

[0012] \(P\) ζ =P(ζ > ζ c )(3)

[0013] In the formula, \(P(*)\) is the probability of meeting the constraint condition; ζ is the system damping ratio; ζ c is the threshold for meeting the small-signal stability of the system; Δf is the system frequency deviation; |Δf| max is the maximum value of the frequency deviation; RoCoF thr , Δf thr are the stability thresholds of the rate of frequency change and the frequency deviation respectively.

[0014] 2) Analyze the optimization model of wind power virtual inertia parameters, and establish an analytical optimization model of wind power virtual inertia parameters that coordinately considers the system probability stability;

[0015] Furthermore, the analytical optimization model of wind power virtual inertia parameters that coordinately considers the system probability stability includes the small-signal probability stability optimal objective function, the minimum virtual inertia demand constraint condition under the maximum allowable disturbance of the system, and the self-constraint condition of the virtual inertia parameters;

[0016] The small-signal probability stability optimal objective function maxG is as follows:

[0017]

[0018] In the formula, \(N\) m is the number of system modes; l is the mode serial number; represents the probability distribution function of the damping ratio ζ l ; ζ c is the threshold for meeting the small-signal stability of the system;

[0019] The minimum virtual inertia demand constraint condition under the maximum allowable disturbance of the system is as follows:

[0020]

[0021] In the formula, \(M\) ω,max is the minimum virtual inertia demand under the maximum allowable disturbance of the system; \(K\) ωi is the virtual inertia parameter of wind farm \(i\); \(N\) W is the number of wind farms.

[0022] The self - constraint conditions of the virtual inertia parameter are as follows:

[0023] K ωimin ≤K ωi ≤K ωimax i = 1, 2,..., N W (6)

[0024] Wherein, K ωjmax and K ωjmin are the upper and lower limits of the virtual inertia parameter respectively.

[0025] Furthermore, the steps to establish the minimum demand constraint condition of the virtual inertia under the maximum allowable disturbance of the system include:

[0026] a) Establish an expression for the frequency response process of the power system under active power disturbance, that is:

[0027]

[0028] Wherein, M is the system inertia; Δf is the system frequency deviation; D is the system damping factor; ΔP m is the change in generator mechanical power; ΔP is the active power disturbance of the system;

[0029] b) Establish the frequency change rate constraint (8) and the frequency deviation constraint (9), that is:

[0030]

[0031]

[0032] Wherein, |dΔf / dt| max is the maximum value of the frequency change rate; |Δf| max is the maximum value of the frequency deviation; F g is the aggregation parameter of the high - pressure turbine coefficient of the synchronous unit; R g is the aggregation parameter of the governor regulation coefficient of the synchronous unit; T g is the time constant of the generator governor of the synchronous unit; ω n is the natural oscillation frequency corresponding to the frequency dynamic process; is the damping ratio corresponding to the frequency dynamic process; t nadir is the time when the lowest frequency occurs; RoCoF thr and Δf thr are the stability thresholds of the frequency change rate and the frequency deviation respectively;

[0033] c) Establish an expression for the virtual inertia of a single wind farm, that is:

[0034]

[0035] Where, ΔP ω is the virtual inertia response output: K ω is the virtual inertia parameter of the wind farm;

[0036] d) Calculate the system inertia M, that is:

[0037]

[0038] Where, M gj is the inertia parameter of the synchronous generator set j; N SG is the number of synchronous generator sets; K ωi is the virtual inertia parameter of the wind farm i; N W is the number of wind farms;

[0039] e) Convert the probabilistic objective function maxP f into a deterministic constraint for system frequency stability under the maximum allowable disturbance of the system, and obtain:

[0040]

[0041]

[0042] Where, ΔP max is the maximum allowable disturbance amount of the system.

[0043] f) Calculate the system inertia

[0044] when the system frequency stability constraint reaches the limit and the system inertia That is:

[0045]

[0046]

[0047] Where, the natural oscillation frequency ω n , damping ratio and the time t nadir when the lowest frequency point occurs are functions of

[0048] g) Obtain the unique solutions of the system inertia and the system inertia according to formulas (14) and (15), and establish the system inertia M constraint, that is:

[0049]

[0050]

[0051] h) Let the system inertia Then:

[0052] M ≥ M sys,max (18)

[0053] i) Substitute Equation (11) into Equation (18), thereby transforming the system inertia constraint into a virtual inertia constraint (19), that is:

[0054]

[0055] j) Let the minimum required value of virtual inertia Thereby, the system frequency stability constraint can be transformed into a minimum required value constraint of virtual inertia (5).

[0056] The steps to establish the optimal objective function for small-signal probabilistic stability include:

[0057] I) Establish the linear relationship between Δζ l and ΔP w in the small-signal stability analysis, and obtain:

[0058]

[0059] In the formula, Δζ l = ζ l - ζ 0l is the change in damping ratio; ζ 0l is the damping ratio corresponding to the mode l under the system base state; ΔP wi is the active power perturbation of the i-th wind farm;

[0060] Among them, the sensitivity s 0l of the damping ratio ζ w0i to the frequency P 0l,i is as follows:

[0061]

[0062] In the formula, λ 0l = σ 0l ± jω 0l is the eigenvalue under the system base state; σ 0l , ω 0l respectively represent the real part and the imaginary part of the eigenvalue λ 0l ; A s0 is the system state matrix under the system base state; v 0l is the left eigenvector of the eigenvalue λ 0l ; u 0l is the right eigenvector of the eigenvalue λ 0l ;

[0063] II) The damping ratio variation Δζ in the small disturbance analysis obtained according to formula (20) l and active power disturbance ΔP wi The linear relationship between the damping ratio change Δζ in small disturbance analysis is established l and active power disturbance ΔP wi The n-order semi-invariant relation is:

[0064]

[0065] In the formula, is the damping ratio change Δζ l The nth order parameter of ; ΔP wi The nth-order parameter of

[0066] III) According to the parameters Determine the damping ratio change Δζ l The nth order central moment For the n-th order central moment Perform Gram-Charlier series expansion to obtain the normalized damping ratio change The probability distribution function of Right now:

[0067]

[0068] Among them, the standardized damping ratio change As shown below:

[0069]

[0070] In the formula, is the normalized damping ratio change Δζ l The mean of is the normalized damping ratio change Δζ l The standard deviation of Φ(x) is the probability distribution function of the standard normal distribution. The superscript n represents the nth derivative of Φ(x) with respect to x. The coefficients g0, g3, g4, and g5 are about and Function of

[0071] IV) According to formula (23) and formula (24), calculate the damping ratio change Δζ l The probability distribution function of Right now:

[0072]

[0073] V) According to the damping ratio change Δζ l =ζ l -ζ 0l , calculate the damping ratio ζl Probability distribution function That is:

[0074]

[0075] VI) According to formula (26), establish the probability distribution of small-signal stability of the system That is:

[0076]

[0077] VII) Convert the small-signal probability stability objective function maxP ζ into the small-signal probability stability optimal objective function (4).

[0078] 3) Use the probability stability optimization algorithm based on sensitivity analysis to solve the analytical optimization model of wind power virtual inertia parameters, and obtain the wind power virtual inertia parameters that meet the probability stability requirements of the power system.

[0079] Furthermore, the steps of using the probability stability optimization algorithm based on sensitivity analysis to solve the analytical optimization model of wind power virtual inertia parameters include:

[0080] 3.1) Set the initial value of the virtual inertia that meets the minimum demand constraint condition of the virtual inertia under the maximum allowable disturbance of the system and the self-constraint condition of the virtual inertia parameter Initialize the iteration number k←0.

[0081] 3.2) Calculate the objective function of the analytical optimization model of wind power virtual inertia parameters, and the sensitivity of the objective function value with respect to the virtual inertia;

[0082] The steps of calculating the sensitivity of the objective function value with respect to the virtual inertia include:

[0083] 3.2.1) Calculate the analytical expressions of the objective function with respect to the damping ratio ζ 0l The sensitivity of the damping ratio with respect to the virtual inertia parameter K with respect to the virtual inertia parameter K ω The sensitivity of the objective function with respect to the sensitivity s The analytical expression of the sensitivity s 0l,i with respect to the virtual inertia parameter K The sensitivity of the sensitivity s 0l,i with respect to the virtual inertia parameter K ω The sensitivity of That is:

[0084]

[0085]

[0086]

[0087]

[0088] In the formula, the parameter

[0089] 3.2.2) Calculate the objective function with respect to the virtual inertia parameter K ω sensitivity, that is:

[0090]

[0091] 3.2.3) Calculate the sensitivity of the objective function with respect to the virtual inertia parameter K ω sensitivity That is:

[0092]

[0093] 3.3) Determine whether the termination condition is satisfied. If so, the iteration ends and the virtual inertia parameter is output. Otherwise, let the iteration number k = k + 1 and return to step 3.2).

[0094] The termination condition includes a first termination condition and a second termination condition;

[0095] When the first termination condition or the second termination condition is satisfied, the iteration ends;

[0096] The first termination condition is: when k ≥ 1, the difference between the objective function values of two iterations satisfies the convergence gap ε, that is:

[0097] |G(K ω ) (k+1) -G(K ω ) (k) | ≤ ε (34)

[0098] In the formula, G(K ω ) (k+1) , G(K ω ) (k) respectively represent the objective function values of the (k + 1)-th iteration and the k-th iteration;

[0099] The second termination condition is: that is, the virtual inertia parameter can ensure the small-signal stability of the system in all expected scenarios, that is:

[0100] G(K ω ) (k+1) = N m (35)

[0101] N m is the number of system modes;

[0102] A computer medium stores a computer program;

[0103] wherein, the computer program can be executed by a processor to implement the steps of the above method.

[0104] It should be noted that the present invention first considers the uncertainty of wind power, and aims to maximize the probability of meeting the frequency and small-signal stability of the power system, and establishes an optimization model for the virtual inertia parameters of wind power. Aiming at the problem that the probabilistic optimization objective is difficult to solve, by considering the maximum allowable disturbance of the system, the frequency probability stability objective is transformed into an analytical frequency stability constraint; at the same time, the analytical expression of small-signal probabilistic stability is derived by using the analytical cumulant method, and an analytical optimization model for the virtual inertia parameters of wind power that coordinately considers the probabilistic stability of the system is established. Then, the sensitivity of the probabilistic stability objective and the virtual inertia parameters is derived with the damping ratio as the intermediate variable, and the sensitivity is used as the Newton gradient, and a probabilistic stability optimization algorithm based on sensitivity analysis is proposed to solve the model. Finally, simulations are carried out on the IEEE 39-bus system in the Digsilent / PowerFactory and Matlab software environments, which proves that the present invention can greatly improve the probability of meeting the small-signal stability of the system on the premise of meeting the frequency stability of the system.

[0105] The technical effect of the present invention is beyond doubt. The present invention proposes an optimization method for the virtual inertia parameters of wind power that coordinately considers the frequency and small-signal probabilistic stability of the system, and this method can greatly reduce the stable operation risk of the power system.

[0106] The present invention simultaneously considers the frequency stability and small-signal stability requirements of the system, and can effectively improve the system stability through the optimization of the virtual inertia parameters.

[0107] The present invention considers the uncertainty of wind power. Compared with the stability co-optimization model that only considers the deterministic operating state, the obtained optimization results, on the premise of meeting the frequency stability constraint of the maximum allowable disturbance of the system, increase the probability of meeting the small-signal stability constraint of the system from 15.25% to 99.57%. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 is the algorithm flowchart;

[0109] Figure 2 is the frequency response under different example systems;

[0110] Figure 3 is the probability density of the key mode damping ratio;

[0111] Figure 4 is the distribution of the key mode eigenvalues;

[0112] Figure 5 It is the time-domain simulation diagram of the rotational speed of the synchronous unit in Case 2;

[0113] Figure 6 It is the time-domain simulation diagram of the rotational speed of the synchronous unit in Case 4;

[0114] Figure 7 It is the time-domain simulation diagram of the rotational speed of the synchronous unit in Case 5. Specific implementation manners

[0115] The present invention will be further described below in conjunction with embodiments, but it should not be understood that the above-mentioned subject scope of the present invention is limited to the following embodiments. Without departing from the above technical idea of the present invention, various substitutions and changes made according to the common general knowledge and conventional means in the art should be included within the protection scope of the present invention.

[0116] Embodiment 1:

[0117] A wind power virtual inertia parameter optimization method for improving the probabilistic stability of a power system includes the following steps:

[0118] 1) Taking the maximum probability of satisfying the power system frequency and small-signal stability as the objective, establish a wind power virtual inertia parameter optimization model considering the probabilistic stability of the system;

[0119] The wind power virtual inertia parameter optimization model is as follows:

[0120] (maxP f ) ∩ (maxP ζ )(1)

[0121] Among them, the probability P f of satisfying the system frequency stability constraint and the probability P ζ of satisfying the small-signal stability are respectively as follows:

[0122]

[0123] P ζ = P(ζ > ζ c )(3)

[0124] In the formula, P(*) is the probability of satisfying the constraint condition; ζ is the system damping ratio; ζ c is the threshold for satisfying the small-signal stability of the system; Δf is the system frequency deviation; |Δf| max is the maximum value of the frequency deviation; RoCoF thr , Δf thr are respectively the stability thresholds of the frequency change rate and the frequency deviation.

[0125] 2) Analyze the optimization model of wind power virtual inertia parameters, and establish an analytical optimization model of wind power virtual inertia parameters that coordinately considers the probabilistic stability of the system;

[0126] The analytical optimization model of wind power virtual inertia parameters that coordinately considers the probabilistic stability of the system includes a small-signal probabilistic stability optimal objective function, a minimum virtual inertia demand constraint condition under the maximum allowable disturbance of the system, and a self-constraint condition of the virtual inertia parameters;

[0127] The small-signal probabilistic stability optimal objective function maxG is as follows:

[0128]

[0129] In the formula, N m is the number of system modes; l is the mode number; represents the probability distribution function of the damping ratio ζ l ; ζ c is the threshold value to meet the small-signal stability of the system;

[0130] The minimum virtual inertia demand constraint condition under the maximum allowable disturbance of the system is as follows:

[0131]

[0132] In the formula, M ω,max is the minimum virtual inertia demand under the maximum allowable disturbance of the system; K ωi is the virtual inertia parameter of wind farm i; NW is the number of wind farms.

[0133] The self-constraint condition of the virtual inertia parameters is as follows:

[0134] K ωimin ≤K ωi ≤K ωimax i = 1, 2,..., N W (6)

[0135] In the formula, K ωjmax and K ωjmin are the upper and lower limits of the virtual inertia parameter respectively.

[0136] The steps to establish the minimum virtual inertia demand constraint condition under the maximum allowable disturbance of the system include:

[0137] a) Establish an expression for the frequency response process of the power system under active power disturbance, that is:

[0138]

[0139] In the formula, M is the system inertia; Δf is the system frequency deviation; D is the system damping factor; ΔP mΔPm is the change in the mechanical power of the generator; ΔP is the active power disturbance of the system;

[0140] b) Establish the frequency change rate constraint (8) and the frequency deviation constraint (9), i.e.:

[0141]

[0142]

[0143] In the formula, |dΔf / dt| max is the maximum value of the frequency change rate; |Δf| max is the maximum value of the frequency deviation; F g is the aggregated parameter of the high-pressure turbine coefficient of the synchronous unit; R g is the aggregated parameter of the governor regulation coefficient of the synchronous unit; T g is the time constant of the generator governor of the synchronous unit; ω n is the natural oscillation frequency corresponding to the frequency dynamic process; is the damping ratio corresponding to the frequency dynamic process; t nadir is the time when the lowest frequency occurs; RoCoF thr , Δf thr are the stability thresholds of the frequency change rate and the frequency deviation respectively;

[0144] c) Establish the virtual inertia expression of a single wind farm, i.e.:

[0145]

[0146] In the formula, ΔP ω is the output of the virtual inertia response: K ω is the virtual inertia parameter of the wind farm;

[0147] d) Calculate the system inertia M, i.e.:

[0148]

[0149] In the formula, M gj is the inertia parameter of the synchronous generator set j; N SG is the number of synchronous generator sets; K ωi is the virtual inertia parameter of the wind farm i; N W is the number of wind farms;

[0150] e) Convert the probabilistic objective function maxP f into a deterministic constraint for system frequency stability under the maximum allowable disturbance of the system, and obtain:

[0151]

[0152]

[0153] where ΔP max is the maximum allowable disturbance of the system.

[0154] f) Calculate the system inertia when the system frequency stability constraint reaches the limit under the maximum allowable disturbance of the system and the system inertia That is:

[0155]

[0156]

[0157] where the natural oscillation frequency ω n , damping ratio and the time t when the lowest frequency point occurs nadir are functions of ;

[0158] g) Obtain the unique solutions of the system inertia and the system inertia according to formulas (14) and (15), and establish the system inertia M constraint, that is:

[0159]

[0160]

[0161] h) Let the system inertia Then:

[0162] M ≥ M sys,max (18)

[0163] i) Substitute formula (11) into formula (18) to convert the system inertia constraint into the virtual inertia constraint (19), that is:

[0164]

[0165] j) Let the minimum required value of the virtual inertia Thus, the system frequency stability constraint can be converted into the minimum required value constraint of the virtual inertia (5).

[0166] The steps to establish the optimal objective function for small disturbance probability stability include:

[0167] I) Establish the linear relationship between Δζ l and ΔP w in the small disturbance stability analysis, and obtain:

[0168]

[0169] where Δζ l = ζ l - ζ 0l is the change in damping ratio; ζ 0l is the damping ratio corresponding to mode l in the system's ground state; ΔP wi is the active power perturbation of the i-th wind farm;

[0170] Among them, the sensitivity s 0l of the damping ratio ζ w0i to the frequency P 0l,i is as follows:

[0171]

[0172] where λ 0l = σ 0l ± jω 0l is the eigenvalue of the system in the ground state; σ 0l , ω 0l represent the real part and the imaginary part of the eigenvalue λ 0l respectively; A s0 is the system state matrix in the ground state of the system; v 0l is the left eigenvector of the eigenvalue λ 0l ; u 0l is the right eigenvector of the eigenvalue λ 0l ;

[0173] II) Establish an n-th order semi-invariant relationship between the change in damping ratio Δζ l and the active power perturbation ΔP wi obtained from the small-signal analysis according to formula (20), that is: l wi l where,

[0174]

[0175] is the n-th order parameter of the change in damping ratio Δζ ; l is the n-th order parameter of ΔP ; wi ;

[0176] III) Determine the n-th order central moment of the change in damping ratio Δζ l according to the parameter Perform a Gram-Charlier series expansion on the n-th order central moment to obtain the probability distribution function of the standardized change in damping ratio That is:

[0177]

[0178] Among them, the standardized damping ratio change amount is as follows:

[0179]

[0180] In the formula, is the mean value of the standardized damping ratio change amount Δζ l ; is the standard deviation of the standardized damping ratio change amount Δζ l ; Φ(x) is the probability distribution function of the standard normal distribution; the superscript n represents the nth derivative of Φ(x) with respect to x; the coefficients g0, g3, g4, g5 are functions of and ;

[0181] IV) According to formulas (23) and (24), calculate the probability distribution function of the damping ratio change amount Δζ l That is: Namely:

[0182]

[0183] V) According to the damping ratio change amount Δζ l = ζ l - ζ 0l , calculate the probability distribution function of the damping ratio ζ l That is: Namely:

[0184]

[0185] VI) According to formula (26), establish the probability distribution of the small-signal stability of the system That is:

[0186]

[0187] VII) According to formula (27), convert the small-signal probability stability objective function maxP ζ into the small-signal probability stability optimal objective function (4).

[0188] 3) Use the probability stability optimization algorithm based on sensitivity analysis to solve the analytical optimization model of the wind power virtual inertia parameter, and obtain the wind power virtual inertia parameter that meets the probability stability requirements of the power system.

[0189] The steps of using the probability stability optimization algorithm based on sensitivity analysis to solve the analytical optimization model of the wind power virtual inertia parameter include:

[0190] 3.1) Set the initial value of the virtual inertia that meets the minimum demand constraint condition of the virtual inertia under the maximum disturbance allowed by the system and the self-constraint condition of the virtual inertia parameter Initialize the iteration number k ← 0.

[0191] 3.2) Calculate the objective function of the analytical optimization model of the wind power virtual inertia parameter and the sensitivity of the objective function value with respect to the virtual inertia;

[0192] The steps for calculating the sensitivity of the objective function value with respect to the virtual inertia include:

[0193] 3.2.1) Calculate the objective function with respect to the damping ratio ζ 0l analytical expression The sensitivity of the damping ratio with respect to the virtual inertia parameter K ω sensitivity Objective function with respect to the sensitivity s 0l,i analytical expression Sensitivity s 0l,i with respect to the virtual inertia parameter K ω sensitivity That is:

[0194]

[0195]

[0196]

[0197]

[0198] In the formula, the parameter

[0199] 3.2.2) Calculate the sensitivity of the objective function with respect to the virtual inertia parameter K ω That is:

[0200]

[0201] 3.2.3) Calculate the sensitivity of the objective function with respect to the virtual inertia parameter K ω sensitivity That is:

[0202]

[0203] 3.3) Judge whether the termination condition is met. If so, the iteration ends and the virtual inertia parameter is output. Otherwise, let the iteration number k = k + 1 and return to step 3.2).

[0204] The termination conditions include a first termination condition and a second termination condition;

[0205] When the first termination condition or the second termination condition is satisfied, the iteration ends;

[0206] The first termination condition is: when k≥1, the difference between the objective function values of two consecutive iterations satisfies the convergence gap ε, that is:

[0207] |G(K ω ) (k+1) -G(K ω ) (k) |≤ε (34)

[0208] In the formula, G(K ω ) (k+1) and G(K ω ) (k) respectively represent the objective function values of the (k + 1)-th iteration and the k-th iteration;

[0209] The second termination condition is: that is, the virtual inertia parameter can ensure the small-signal stability of the system in all expected scenarios, that is:

[0210] G(K ω ) (k+1) =N m (35)

[0211] N m is the number of system modes;

[0212] A computer medium, the computer-readable medium stores a computer program;

[0213] Wherein, the computer program can be executed by a processor to implement the steps of the above method.

[0214] Embodiment 2:

[0215] A method for optimizing the virtual inertia parameter of a wind power generation system for improving the probabilistic stability of a power system, comprising the following steps:

[0216] 1. Establish an optimization model for the virtual inertia parameter of a wind power generation system considering the probabilistic stability of the system

[0217] The probability P f that satisfies the system frequency stability constraint can be expressed as Equation (1):

[0218]

[0219] In the formula, P(*) is the probability that satisfies the constraint condition.

[0220] According to the principle of small-signal analysis, when the damping ratio ζ > 0, it can be considered that the system satisfies small-signal stability, and the larger the damping ratio, the more stable the system. To ensure system safety, a certain safety margin is generally reserved. Therefore, the damping ratio of each mode of the system should be greater than its threshold ζ c (3%-5%). The probability P ζ of satisfying small-signal stability can be expressed as Equation (2):

[0221] P ζ = P(ζ > ζ c ) (2)

[0222] where ζ is the system damping ratio; ζ c is the threshold for satisfying the small-signal stability of the system.

[0223] To maximize the probability of the system satisfying frequency stability and the probability of small-signal stability, the objective function can be established as Equation (3):

[0224] (maxP f ) ∩ (maxP ζ ) (3)

[0225] To solve this optimization objective, first, an analytical expression of this optimization objective with respect to the virtual inertia parameter needs to be obtained. Therefore, it is necessary to first analyze the analytical expression of probability stability, and then establish an analytical optimization model for the wind power virtual inertia parameter that coordinately considers the system probability stability.

[0226] 2 Analytical Modeling of System Frequency Probability Stability

[0227] The expression of the frequency response process of the power system under active power disturbance is shown in Equation (4):

[0228]

[0229] where M is the system inertia; Δf is the system frequency deviation; D is the system damping factor; ΔP m is the change in generator mechanical power; ΔP is the active power disturbance of the system.

[0230] The general idea of the virtual inertia parameter optimization method considering frequency stability is to transform the frequency stability index into a constraint and add it to the optimization model as a limiting condition. Commonly used constraints are the frequency change rate constraint and the frequency deviation (lowest point) constraint, as shown in Equations (5) and (6) respectively:

[0231]

[0232]

[0233] where |dΔf / dt| maxis the maximum value of the rate of change of frequency; |Δf| max is the maximum value of the frequency deviation; F g is the aggregated parameter of the high-pressure turbine coefficient of the synchronous unit; R g is the aggregated parameter of the governor regulation coefficient of the synchronous unit; T g is the time constant of the generator governor of the synchronous unit; ω n is the natural oscillation frequency corresponding to the frequency dynamic process; is the damping ratio corresponding to the frequency dynamic process; t nadir is the time when the lowest frequency occurs; RoCoF thr and Δf thr are the stability thresholds of the frequency change rate and the frequency deviation respectively.

[0234] The virtual inertia of a single wind farm can be expressed as Equation (7):

[0235]

[0236] In the formula, ΔP ω is the output of the virtual inertia response: K ω is the virtual inertia parameter of the wind farm.

[0237] According to Equation (4) and the virtual inertia expression (7), after considering the virtual inertia response control, the system inertia M is provided by the synchronous generator inertia and the wind power virtual inertia. The system inertia M is shown in Equation (8):

[0238]

[0239] In the formula, M gj is the inertia parameter of the synchronous generator set j; N SG is the number of synchronous generator sets; K ωi is the virtual inertia parameter of the wind farm i; N W is the number of wind farms.

[0240] For frequency stability, it can be seen from Equations (5) and (6) that the randomness of wind power mainly affects the active power disturbance amount ΔP of the system when a disturbance occurs. The active power disturbance amount ΔP of the system is proportional to both the maximum value of the rate of change of frequency |dΔf / dt| max and the maximum value of the frequency change amount |Δf| max Considering the maximum allowable disturbance amount of the system (for example, the maximum disturbance amount of the UK power grid is 1000 MW), the frequency index will reach the maximum value. Based on the idea of robust optimization, if the frequency stability can still be satisfied under the maximum allowable disturbance of the system, it is considered that the system can satisfy the frequency stability with a probability of 100%, that is, the probability of satisfying the frequency stability reaches the maximum. Therefore, the probabilistic objective function maxP fIt can be transformed into the deterministic constraints for the system frequency stability under the maximum allowable disturbance of the system, as shown in Eqs. (9) and (10):

[0241]

[0242]

[0243] In the formula, ΔP max is the maximum allowable disturbance of the system.

[0244] Since Eq. (10) contains transcendental functions and it is difficult to directly substitute it into the optimization model for solution, the present invention transforms Eq. (10) into a linear constraint through derivation to reduce the solution difficulty. The specific derivation process is as follows: Under the maximum allowable disturbance of the system, the system inertia and when the system frequency stability constraint reaches the limit can be obtained from Eqs. (11) and (12):

[0245]

[0246]

[0247] In the formula, ω n , and t nadir are functions of . Generally, the maximum frequency change rate and the maximum frequency deviation of the frequency stability index are monotonically decreasing with respect to M. From this, it can be known that the unique solutions of and can be obtained through Eqs. (11) and (12).

[0248] Therefore, the system inertia M needs to satisfy the constraints (13) and (14) simultaneously:

[0249]

[0250]

[0251] That is Let Then the system inertia M should satisfy Eq. (15):

[0252] M≥M sys,max (15)

[0253] Substituting Eq. (8) into Eq. (15) can transform the system inertia constraint into the virtual inertia constraint (16):

[0254]

[0255] Let M ω,maxis the minimum required virtual inertia under the maximum allowable disturbance of the system. Then, the system frequency stability constraint can be transformed into the minimum required virtual inertia constraint (17):

[0256]

[0257] When the system virtual inertia satisfies Equation (17), it can be considered that the probability of meeting the system frequency stability constraint reaches the maximum value, that is, 100%. Therefore, the goal of maximizing the probability of meeting the system frequency stability constraint is transformed into the minimum required virtual inertia constraint under the maximum allowable disturbance of the system. Through the above analysis, it can be seen that the probabilistic goal of meeting the system frequency stability constraint can be transformed into a definite minimum required virtual inertia constraint and substituted into the optimization model for solution.

[0258] 3 Analytical Modeling of Small Disturbance Probability Stability of the System

[0259] An important factor for the frequency probability stability to be transformed into a deterministic constraint is that the frequency stability index has a clear proportional relationship with the power disturbance. However, the influence of wind power on small disturbance stability has no general rule, that is, the increase in wind power of a certain wind farm may lead to better small disturbance stability or may also lead to worse small disturbance stability. Since the relationship between power fluctuation and small disturbance stability is not clear, it is difficult to transform small disturbance stability into a deterministic analytical constraint like frequency stability. In the analysis of small disturbance probability stability, the analytical cumulant method has good efficiency and accuracy. Therefore, the present invention uses the analytical cumulant method to establish an analytical expression for small disturbance probability stability. When the fan parameters (such as cut-in wind speed, rated wind speed, cut-out wind speed, rated power) and the wind speed probability distribution parameters (such as wind speed mean and standard deviation) are known, the wind power-related probability distribution parameters, such as the nth moment w of the wind power change ΔP and the nth semi-invariant

[0260] In the small disturbance stability analysis, a linear relationship between Δζ l and ΔP w is established, as shown in Equation (18):

[0261]

[0262] where Δζ l = ζ l - ζ 0l is the change in damping ratio; ζ 0l is the damping ratio corresponding to the mode l under the system base state; is the sensitivity of ζ 0l to P w0i , and its value is shown in Equation (19):

[0263]

[0264] where λ 0l = σ 0l ± jω 0l is the eigenvalue at the system's ground state;

[0265] A s0 is the system state matrix at the system's ground state; v 0l is the left eigenvector of λ 0l ; u 0l is the right eigenvector of λ 0l .

[0266] According to the linear relationship between Δζ l and ΔP w obtained from Equation (18), it can be known from probability theory that there is also a linear relationship between their n-th semi-invariants. Then, the relationship of the n-th semi-invariants of Δζ l and ΔP w is shown in Equation (20):

[0267]

[0268] where is the n-th order of Δζ l .

[0269] From , the n-th central moment of Δζ l can be directly derived through probability theory. Based on the n-th central moment , the probability distribution function of obtained by Gram-Charlier series expansion is shown in Equation (21): where the normalized damping ratio change

[0270]

[0271] can be expressed as: where

[0272]

[0273] where is the mean value of Δζ l , and its value is is the standard deviation of Δζ l , and its value is Φ(x) is the probability distribution function of the standard normal distribution; the superscript n represents the n-th derivative of Φ(x) with respect to x; the coefficients g0 - g5 are and functions of.

[0274] Through equations (21) and (22), Δζ l 's probability distribution function can be obtained from 's probability distribution function is as shown in equation (23):

[0275]

[0276] Since Δζ l = ζ l - ζ 0l , therefore, ζ l 's probability distribution function can be obtained from equation (23):

[0277]

[0278] Based on equation (24), the probability distribution of the system's small-signal stability is as shown in equation (25):

[0279]

[0280] In the above analysis, it can be seen from equation (20) that the probability satisfying small-signal stability is a function of the sensitivity s 0l,i . At the same time, it can be seen from equation (24) that the probability satisfying small-signal stability is a function of the damping ratio ζ 0l . And the eigenvalue λ 0l and the damping ratio ζ 0l are implicit functions of the virtual inertia parameter K ω . Based on the analysis of equation (19), it can be known that the sensitivity s 0l,i is also a function of the virtual inertia parameter K ω . Thus, it can be seen that equation (25) can be expressed as an analytical function relationship between small-signal probability stability and the virtual inertia parameter. The original small-signal probability stability objective function maxP ζ can be transformed into the analytical function expressed by equation (26):

[0281]

[0282] where N m is the number of system modes.

[0283] So far, the probability stability optimization problem expressed by equation (3) can be transformed into an optimization problem with the optimal small-signal probability stability as the goal (represented by equation (26)), considering the constraint of the minimum required virtual inertia under the maximum allowable disturbance of the system (represented by equation (17)). Considering the safe operation and output limit of the wind farm, the constraint of the virtual inertia parameter itself should also be considered, and the constraint expression is as shown in (27):

[0284] K ωimin ≤ Kωi ≤K ωimax i = 1, 2, ..., N W (27)

[0285] In the formula, K ωjmax and K ωjmin are the upper and lower limits of the virtual inertia parameter respectively.

[0286] 4 Power System Probability Stability Optimization Algorithm Based on Sensitivity Analysis

[0287] The sensitivity of the objective function with respect to the virtual inertia parameter K ω is shown in Equation (28):

[0288]

[0289] Since the calculation of the damping ratio needs to be based on the calculation of the eigenvalues of the differential equation, it is difficult to directly write the relationship between the virtual inertia parameter K ω in the objective function, and it is relatively difficult to directly solve the sensitivity with respect to the virtual inertia parameter K ω . Based on the analysis of Equations (20)-(24), the analytical expressions for the damping ratio ζ 0l and the sensitivity s 0l,i can be obtained. Taking the partial derivative of this analytical expression can relatively easily obtain the sensitivity of the objective function with respect to the damping ratio ζ 0l and the sensitivity s 0l,i . Then, based on the eigenvalue sensitivity analysis, the damping ratio ζ 0l and the sensitivity s 0l,i with respect to the virtual inertia parameter K ω are further solved. Thus, the sensitivity with respect to the virtual inertia parameter K ω is shown in Equation (29):

[0290]

[0291] First, solve the sensitivity of the objective function with respect to the damping ratio ζ 0l and the sensitivity s 0l,i .

[0292] From Equations (22)-(24), we can get:

[0293]

[0294] Let Taking the partial derivative with respect to ζ 0l gives:

[0295]

[0296] Similarly, for s 0l,i taking the partial derivative gives:

[0297]

[0298] The specific derivation process can be found in Appendix B.

[0299] Similar to the first-order sensitivity of Equation (19) The expression is as shown in Equation (33):

[0300]

[0301] where

[0302] the sensitivity can be expressed as:

[0303]

[0304] have all been obtained, substituting them into Equation (29) can obtain According to Equation (28), the sensitivity between the objective function and the virtual inertia parameter can be further calculated to obtain the value.

[0305] The algorithm flow of the present invention is as Figure 1 shown.

[0306] Step 0: Data preparation

[0307] ① Set the initial value of the virtual inertia which needs to satisfy Equation (17) and Equation (27).

[0308] ② k ← 0.

[0309] Step 1: Calculate the small-signal probability stability objective function value and its sensitivity with respect to the virtual inertia

[0310] ① Calculate the objective function value G(K ω ) (k) .

[0311] ② Calculate the sensitivity of the objective function with respect to the virtual inertia parameter K ω through Equation (28)

[0312] ③ Judge the termination condition:

[0313] 1) Termination condition 1: When k ≥ 1, the difference between the objective function values of two iterations satisfies the convergence gap ε, that is:

[0314] |G(K ω ) (k+1) -G(K ω ) (k) |≤ε (35)

[0315] 2) Termination condition 2: The small-signal stability probabilities of all modes reach 100%, that is, the system small-signal stability can be guaranteed in all expected scenarios:

[0316] G(K ω ) (k+1) =N m (36)

[0317] Stop the iteration and output the optimization result when any termination condition is met. If none of the termination conditions are met, go to step 2 to iteratively update the virtual inertia parameters.

[0318] Example 3:

[0319] An experiment on the optimization method of wind power virtual inertia parameters for improving the probabilistic stability of power systems includes the following steps:

[0320] (1) Test system

[0321] The New England 39-bus test system with 3 wind farms will be used to prove the effectiveness of the proposed method. This system includes 9 synchronous generators, and the connection nodes are nodes 30 - 38. The total inertia of the synchronous generators is 985 MWs / Hz. There are 3 wind farms in total, and each wind farm contains 1000 doubly-fed wind turbines with a capacity of 1.5 MW. The connection nodes of the wind farms are nodes 16, 18, and 28 respectively, and the wind power penetration rate is 42%. In this invention, the built-in modal analysis module of DIgSILENT / PowerFactory is used to analyze the small-signal stability, and MATLAB is used for the optimization calculation.

[0322] The parameters related to frequency stability are: the nominal frequency of the system is 50 Hz. Considering that the maximum allowable disturbance of the system is the disconnection of the synchronous unit with the largest capacity, that is, the generator output is reduced by 1000 MW. Set the stability threshold of the frequency change rate as RoCoF thr =0.5 Hz / s, and the stability threshold of the frequency deviation is Δf thr =0.5 Hz. To meet the frequency stability constraint, at least M ω，max =1015 MWs / Hz of virtual inertia needs to be provided by the wind farm. The parameters related to small-signal stability are: set the small-signal stability threshold as ζ c =5%. The parameters related to the wind turbine are: the cut-in wind speed v c =4.8 m / s, the rated wind speed vr = 11.59 m / s, the cut-out wind speed v f = 22 m / s, the rated power P of the wind turbine r = 1 p.u., the parameters related to the wind speed probability distribution are: the mean wind speed μ = 10 m / s, and the standard deviation of the wind speed σ = 1 m / s. The base-state wind power of the system is set to the wind power output P corresponding to the mean wind speed w0,1 = P w0,2 = P w0,3 = 0.7662 p.u. Set the upper and lower limits of the virtual inertia constraint to K ωmax = 0.6 p.u., K ωmin = 0 p.u. Set the optimization step size to τ = 5 p.u.

[0323] Generally, the small-signal stability of the system is determined by only a few key modes. If the eigenvalues or damping ratios of the key modes meet the requirements of the system's small-signal stability, the system is considered to be able to maintain stability. In this paper, the mode corresponding to the minimum damping ratio of the system is used as the key mode. Through modal analysis, in the process of power fluctuation and virtual inertia optimization, the mode corresponding to the minimum damping ratio is mode 68. Therefore, the present invention determines the key mode as mode 68.

[0324] The following 5 cases are compared to verify that the proposed method can effectively improve the probabilistic stability of the system.

[0325] Case 1: The system before optimization, ignoring the system frequency stability, and the system has no virtual inertia;

[0326] Case 2: The system before optimization, considering the system frequency stability constraint, and the virtual inertia demand is evenly distributed to three wind farms;

[0327] Case 3: Based on Case 1, ignoring the frequency stability constraint, and optimizing the virtual inertia parameters considering the system probabilistic stability;

[0328] Case 4: Based on Case 2, considering the frequency stability constraint, and optimizing the virtual inertia parameters considering the stability of the determined state system;

[0329] Case 5: Based on Case 2, considering the frequency stability constraint, and optimizing the virtual inertia parameters considering the system probabilistic stability, that is, the method proposed in the present invention.

[0330] (2) Frequency stability verification

[0331] Table 1 The maximum values of the virtual inertia and RoCoF provided by the wind farms in Case 1, Case 3, and Case 5

[0332]

[0333] As can be observed from Table 1, when the wind farm does not provide virtual inertia, the maximum value of RoCoF in Case 1 is 1.015 Hz / s, far exceeding the threshold RoCoF thr = 0.5 Hz / s. For the cases considering virtual inertia (i.e., Case 3 and Case 5), the maximum value of RoCoF decreases compared to Case 1. However, in Case 3, due to the lack of consideration of frequency stability constraints, the virtual inertia provided by the optimized wind farm is insufficient, and the maximum value of RoCoF still exceeds its constraint limit, which may lead to the disconnection of equipment and cannot meet the system frequency stability requirements. In Case 5, due to the effective consideration of frequency stability constraints, the proposed method can provide sufficient virtual inertia for the system, and the maximum value of its RoCoF is equal to its constraint limit RoCoF thr = 0.5 Hz / s, indicating that the proposed method can effectively ensure the system frequency stability. In addition, the time-domain simulation of the system frequency is as Figure 2 shown. The frequency drop rate in Case 5 is slower than that in Case 1 and Case 3, providing more sufficient response time for other frequency responses, indicating that the proposed method can meet the system frequency stability constraints under the maximum allowable disturbance conditions of the system, that is, it is considered that the system can meet the frequency stability by 100%.

[0334] (3) Verification of small-signal stability

[0335] In this subsection, the small-signal stability of Case 2, Case 4, and Case 5 is compared. The probability distributions of the minimum damping ratio of the system are obtained through 10,000 Monte Carlo samplings for each example. The critical mode damping ratios and the probabilities of meeting the small-signal stability requirements under the system base state of Case 2, Case 4, and Case 5 are shown in Table 3. The minimum damping ratio under the base state in Case 2 is 3.79% < 5%, that is, the system before optimization cannot meet the small-signal stability requirements. If only the small-signal stability under the determined state is considered, the minimum damping ratio of the system in Case 4 can reach 5.04% under the determined state, meeting the small-signal stability requirements. However, when considering the randomness of wind power, the probability of meeting the small-signal stability is only 15.25%, which means that the setting of this virtual inertia parameter may lead to the system being unable to meet the small-signal stability requirements with a high probability (more than 80% of the scenarios). The proposed method in this paper, with probability stability as the optimization goal in Case 5, can increase the probability of the system meeting the small-signal stability to 99.57%, which can greatly improve the probability of the system meeting the small-signal stability compared to Case 2 and Case 4. Ensure the stable operation of the system considering the random characteristics of wind power.

[0336] Table 3 Critical mode damping ratios and probabilities of meeting the small-signal stability requirements under the system base state of Case 2, Case 4, and Case 5

[0337] Case 2 Case 4 Case 5 Critical modal damping ratio in the ground state 3.79％ 5.04％ 6.36％ Probability of meeting small disturbance stability 2.89％ 15.25％ 99.57％

[0338] The probability distributions of the system's critical modal damping ratios for Case 2, Case 4, and Case 5 are as follows Figure 3 shown. For Case 2, the critical modal damping ratios are concentrated in the range of 1.7% to 3.4%, and the minimum value of the critical modal damping ratio is 0.26%. For Case 4, the critical modal damping ratios are concentrated in the range of 3% to 4.2%, and the minimum value of the critical modal damping ratio is 1.13%. Therefore, it is also proven that it is difficult for Case 2 and Case 4 to meet the system's small-signal stability requirements under a large number of scenarios. For Case 5, the critical modal damping ratios are concentrated in the range of 5% to 6.5%, which can ensure the stable operation of the system with a high probability. The minimum value of the critical modal damping ratio is 3.1%. Although it does not reach 5%, there is still a certain margin. Compared with Case 2 and Case 4, the small-signal stability of the system is effectively improved.

[0339] The distributions of the system's critical modal eigenvalues for Case 2, Case 4, and Case 5 are as follows Figure 4 shown. Compared with Case 2 and Case 4, the eigenvalue distributions of the critical modes in Case 5 are significantly shifted to the left. The real parts of the eigenvalues are all negative and far from zero, which can effectively ensure the small-signal stability of the system. For Case 2 and Case 4, the real parts of the critical modal eigenvalues are closer to zero, and the system may oscillate for a longer time in this scenario. In the most severe scenario of small-signal stability, the time-domain simulations of the synchronous generator rotor speeds for Case 2 and Case 4, and Case 5 are further carried out. The time-domain simulation results are as follows Figure 5 shown. This simulation verifies that Case 5 can converge relatively quickly after small disturbances and has better small-signal stability compared with Case 2 and Case 4. Especially in the most severe scenario, Case 2 needs to experience oscillations for a long time, which is not conducive to the stable operation of the system.

[0340] It can be seen from the experimental results that the proposed method can improve the probability of meeting the system's small-signal stability constraints while ensuring the system frequency stability constraints under the maximum allowable disturbance of the system, thereby reducing the risk of the system's stable operation.

[0341] In summary, the present invention proposes a method for optimizing the parameters of wind power virtual inertia. First, considering the randomness of wind power, an optimization model of wind power virtual inertia parameters is established with the goal of maximizing the probability of meeting the system frequency stability constraint and the small-signal stability constraint. Then, an analytical analysis and modeling of the probabilistic stability objective are carried out: the frequency probabilistic stability is transformed into a system frequency stability constraint under the maximum allowable disturbance of the system; an analytical expression of small-signal probabilistic stability is obtained by the analytical cumulative distribution function method, and an analytical optimization model for improving the system probabilistic stability is established. Taking the damping ratio as an intermediate variable, the sensitivity between the objective function and the virtual inertia parameters is derived, and the model is solved by the Newton method with the sensitivity as the gradient. The simulation analysis shows that: although the stability co-optimization model considering only the deterministic operating state can meet the stability requirements of the current state, the optimization result may still have a high probability of making the system in an unstable state, and it may be difficult to apply in a low-inertia system with a high proportion of new energy. Since the method proposed in this paper directly aims at the probability of meeting the system frequency stability constraint and the small-signal stability constraint, the obtained optimization result, on the premise of meeting the system frequency stability constraint under the maximum allowable disturbance of the system, improves the probability of meeting the system small-signal stability constraint from 15.25% to 99.57%.

Claims

1. A method for optimizing the virtual inertia parameters of wind power for improving the probabilistic stability of power systems, characterized in that, It includes the following steps: 1) Taking the maximum probability of meeting the power system frequency and small-signal stability as the goal, establish an optimization model for wind power virtual inertia parameters considering the probabilistic stability of the system; 2) Analyze the optimization model for wind power virtual inertia parameters, and establish an analytical optimization model for wind power virtual inertia parameters considering the probabilistic stability of the system in a coordinated manner; 3) Use the probabilistic stability optimization algorithm based on sensitivity analysis to solve the analytical optimization model for wind power virtual inertia parameters, and obtain the wind power virtual inertia parameters that meet the requirements of the probabilistic stability of the power system; The optimization model for wind power virtual inertia parameters is as follows: (maxP f )∩(maxP ζ )(1) Among them, the probabilities \(P\) f that satisfy the system frequency stability constraint and \(P\) ζ that satisfy small-signal stability are respectively as follows: P ζ = P(ζ > ζ c ) (3) Wherein, P(*) is the probability of satisfying the constraint condition; ζ is the system damping ratio; ζ c is the threshold value for satisfying the small-signal stability of the system; Δf is the system frequency deviation; |Δf| max is the maximum value of the frequency deviation; RoCoF thr and Δf thr are the stability thresholds of the rate of frequency change and the frequency deviation respectively.

2. The optimization method for wind power virtual inertia parameters for improving the probabilistic stability of a power system according to claim 1, wherein The analytical optimization model for wind power virtual inertia parameters considering the probabilistic stability of the system in a coordinated manner includes an optimal objective function for small-signal probabilistic stability, a minimum demand constraint condition for virtual inertia under the maximum allowable disturbance of the system, and a self-constraint condition for virtual inertia parameters; The optimal objective function maxG for small-signal probabilistic stability is as follows: Where N m is the number of system modes; l is the mode number; represents the probability distribution function of the damping ratio ζ l ; ζ c is the threshold for meeting the small-signal stability of the system; The minimum demand constraint condition for virtual inertia under the maximum allowable disturbance of the system is as follows: Where, M ω,max is the minimum demand for virtual inertia under the maximum disturbance allowed by the system; K ωi is the virtual inertia parameter of wind farm i; N W is the number of wind farms; The self-constraint condition for virtual inertia parameters is as follows: K ωimin ≤K ωi ≤K ωimax i = 1, 2, ..., N W (6) where K ωimax and K ωimin are the upper and lower limits of the virtual inertia parameter, respectively.

3. The method for optimizing the virtual inertia parameters of wind power for improving the probabilistic stability of power systems according to claim 2, wherein The steps of establishing the minimum demand constraint condition for virtual inertia under the maximum allowable disturbance of the system include: 1) Establish an expression for the frequency response process of the power system under active power disturbance, that is: where M is the system inertia; Δf is the system frequency deviation; D is the system damping factor; ΔP m is the change in generator mechanical power; ΔP is the active power disturbance of the system; 2) Establish a frequency change rate constraint (8) and a frequency deviation constraint (9), that is: where |dΔf / dt| max is the maximum value of the rate of change of frequency; |Δf| max is the maximum value of the frequency deviation; F g is the aggregated parameter of the high-pressure turbine coefficient of the synchronous unit; R g is the aggregated parameter of the governor regulation coefficient of the synchronous unit; T g is the time constant of the generator governor of the synchronous unit; ω n is the natural oscillation frequency corresponding to the frequency dynamic process; ζ is the damping ratio corresponding to the frequency dynamic process; t nadir is the time when the lowest frequency occurs; RoCoF thr , Δf thr are the stability thresholds of the rate of change of frequency and the frequency deviation respectively; 3) Establish an expression for the virtual inertia of a single wind farm, that is: where ΔP ω is the virtual inertia response output: K ω is the virtual inertia parameter of the wind farm; 4) Calculate the system inertia M, that is: where, M gj is the inertia parameter of synchronous generator set j; N SG is the number of synchronous generator sets; K ωi is the virtual inertia parameter of wind farm i; N W is the number of wind farms; 5) Convert the probabilistic objective function maxP f into a deterministic constraint for system frequency stability under the maximum disturbance allowed by the system, obtaining: where ΔP max is the maximum allowable disturbance amount of the system; 6) Calculate the system inertia when the system frequency stability constraint reaches its limit under the maximum disturbance allowed by the system and the system inertia That is: where the natural oscillation frequency ω n , damping ratio and the time t nadir when the lowest frequency point occurs are functions of ; 7) Obtain the system inertia according to formula (14) and formula (15) and the system inertia to get the unique solution, and establish the system inertia M constraint, that is: 8) Let the system inertia Then: M≥M sys,max (18) 9) Substitute formula (11) into formula (18), so as to transform the system inertia constraint into a virtual inertia constraint (19), that is: 10) Let the minimum required value of virtual inertia Therefore, the system frequency stability constraint can be transformed into the minimum required value constraint of virtual inertia (5).

4. The method for optimizing the virtual inertia parameters of wind power for improving the probabilistic stability of a power system according to claim 2, characterized in that, The steps of establishing the optimal objective function for small-signal probabilistic stability include: 1) Establish the linear relationship between Δζ l and ΔP w to obtain: where Δζ l = ζ l - ζ 0l is the change in damping ratio; ζ 0l is the damping ratio corresponding to mode l in the system's ground state; ΔP wi is the active power perturbation of the i-th wind farm; Among them, the damping ratio ζ 0l and the sensitivity s w0i to the frequency P 0l,i are as follows: where λ 0l = σ 0l ± jω 0l are the characteristic roots in the system's ground state; σ 0l , ω 0l represent the real part and the imaginary part of the characteristic root λ 0l respectively; A s0 is the system state matrix in the system's ground state; v 0l is the left eigenvector of the characteristic root λ 0l ; u 0l is the right eigenvector of the characteristic root λ 0l ; 2) The change in damping ratio Δζ in the small-signal analysis obtained according to Equation (20) l and the active power perturbation ΔP wi to establish the relationship between the change in damping ratio Δζ l and the active power perturbation ΔP wi of the n-th order semi-invariant relationship, that is: In the formula, is the change amount of damping ratio Δζ l of the nth order parameter; is ΔP wi of the nth order parameter; 3) Determine the change in damping ratio Δζ according to the parameter and the nth-order central moment of l Perform a Gram-Charlier series expansion on the nth-order central moment to obtain the probability distribution function of the standardized change in damping ratio That is: the probability distribution function of Namely: Among them, the standardized damping ratio change amount is as follows: In the formula, is the mean value of the standardized damping ratio change amount Δζ l ; is the standard deviation of the standardized damping ratio change amount Δζ l ; Φ(x) is the probability distribution function of the standard normal distribution; the superscript n represents the nth derivative of Φ(x) with respect to x; the coefficients g0, g3, g4, g5 are functions of and ; 4) Calculate the change in damping ratio Δζ according to Equation (23) and Equation (24). l Probability distribution function That is: 5) Calculate the probability distribution function of the damping ratio ζ according to the change amount of damping ratio Δζ l = ζ l - ζ 0l , that is: l The probability distribution function of Namely: 6) Establish the probability distribution of the small-signal stability of the system according to formula (26). That is: 7) Convert the small-signal probability stability objective function maxP according to formula (27). ζ Convert it into the small-signal probability stability optimal objective function (4).

5. The optimization method for wind power virtual inertia parameters for improving the probabilistic stability of a power system according to claim 2, characterized in that The steps of using the probabilistic stability optimization algorithm based on sensitivity analysis to solve the analytical optimization model for wind power virtual inertia parameters include: 1) Set the initial value of virtual inertia that satisfies the minimum demand constraint condition of virtual inertia under the maximum disturbance allowed by the system and the self-constraint condition of virtual inertia parameters Initialize the iteration number k ← 0; 2) Calculate the objective function of the analytical optimization model for wind power virtual inertia parameters, and the sensitivity of the objective function value with respect to virtual inertia; 3) Judge whether the termination condition is satisfied. If so, the iteration ends and the virtual inertia parameters are output. Otherwise, let the iteration number k = k + 1, and return to step 2).

6. The optimization method of wind power virtual inertia parameters for improving the probabilistic stability of power systems according to claim 5, characterized in that The steps of calculating the sensitivity of the objective function value with respect to virtual inertia include: 1) Calculate the objective function separately with respect to the damping ratio ζ 0l for the analytical expression The sensitivity of the damping ratio with respect to the virtual inertia parameter K ω for the sensitivity The objective function with respect to the sensitivity s 0l,i for the analytical expression The sensitivity s 0l,i with respect to the virtual inertia parameter K ω for the sensitivity That is: In the formula, the parameter 2) Calculate the objective function with respect to the virtual inertia parameter K ω sensitivity, i.e.: 3) Calculate the sensitivity of the objective function with respect to the virtual inertia parameter K ω That is Namely:

7. The method for optimizing the virtual inertia parameters of wind power for improving the probabilistic stability of power systems according to claim 5, characterized in that: The termination condition includes a first termination condition and a second termination condition; When the first termination condition or the second termination condition is satisfied, the iteration ends; The first termination condition is: when k ≥ 1, the difference between the objective function values of two consecutive iterations satisfies the convergence gap ε, that is: |G(K ω ) (k+1) -G(K ω ) (k) |≤ε (34) where G(K ω ) (k+1) and G(K ω ) (k) represent the objective function values of the (k + 1)-th iteration and the k-th iteration, respectively; The second termination condition is: the virtual inertia parameter can ensure the small-signal stability of the system in all expected scenarios, that is: G(K ω ) (k+1) = N m (35) where N m is the number of system modes.

8. A computer medium, characterized in that, The computer-readable medium stores a computer program; Wherein, the computer program can be executed by a processor to implement the steps of the method described in any one of claims 1 to 7.

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