Frequency characteristics analysis method of power system with wind power based on double grid difference method

Abstract

A frequency characteristic analysis method for a wind power system based on a double-grid difference method includes the following steps: S1, establishing a power fluctuation model of a wind power system; S2, establishing a random dynamics model of the power system; S3, establishing a primary frequency regulation model of a wind power system; S4, analyzing the characteristics of the primary frequency regulation model of the wind power system, and obtaining the FPK equation of the random dynamics model of the wind power system; S5, solving the frequency probability distribution density function of the wind power system. This design establishes a primary frequency regulation model of a wind power system, and then obtains the FPK equation of the system frequency probability distribution density function, and adopts a double-grid difference iterative numerical algorithm, combined with the advantages of the finite element method and the finite difference method, to accurately and quickly obtain the probability distribution function of the system frequency, providing a reference for the power grid frequency regulation capability analysis, frequency regulation parameter optimization, and unit economic operation.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a frequency characteristic analysis method of a wind power system based on a double-grid difference method, which is mainly suitable for improving analysis accuracy and analysis efficiency. Background Art

[0002] The frequency of the power system is one of the important criteria for measuring the quality of electric energy, and is also an important parameter for describing the balance of power generation and consumption in the power grid. The proportion of renewable energy output in the new power system is increasing, and conventional units are being replaced in large numbers, which has changed the inertial support capacity and frequency regulation capacity of the power system. In addition, the randomness of renewable energy output has increased the complexity of power fluctuations in the power system, and the analysis of the probability distribution characteristics of system frequency has become more difficult.

[0003] In general, since load fluctuations present a normal distribution, the probability distribution of the power system frequency also presents a normal distribution. In the actual operation of the power grid, there are a large number of nonlinear factors in the frequency regulation link of the power system, such as the dead zone link of the speed regulator, the characteristics of the gas valve, and the unit output limit link. Under the influence of the above series of factors, the probability distribution of the system frequency is no longer a simple normal distribution. There are two common research methods for the probability distribution of power system frequency: one is to use the random signal analysis method for research, but the system frequency probability distribution curve obtained by segmented analysis is discontinuous and has a certain deviation from the actual situation of the power grid; the other is to obtain a series of frequency data through time domain simulation and conduct statistical analysis on it. Long-term time domain simulation has universal applicability, but the amount of calculation is huge and the mechanism is unclear. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects and problems of low analysis accuracy and low analysis efficiency in the prior art, and to provide a frequency characteristic analysis method of a wind power system based on a double-grid difference method with high analysis accuracy and high analysis efficiency.

[0005] To achieve the above objectives, the technical solution of the present invention is: a frequency characteristic analysis method of a wind power system based on a double-grid difference method, comprising the following steps:

[0006] S1. Establish a power fluctuation model for wind power system;

[0007] S2. Establish a stochastic dynamics model of the power system;

[0008] S3. Establish a primary frequency regulation model for the power system including wind power;

[0009] S4. Analyze the characteristics of the primary frequency regulation model of the power system containing wind power, and obtain the FPK equation of the stochastic dynamics model of the power system containing wind power;

[0010] S5. Solve the frequency probability distribution density function of the power system containing wind power.

[0011] Step S1 specifically includes the following steps:

[0012] S11. Calculate the corrected standard deviation of wind power fluctuation

[0013]

[0014] In the above formula, a is the wind power fluctuation time scale coefficient, which indicates the law of wind power output variation with time scale; z α1 is the α1 quantile of the standard normal distribution, indicating the wind power fluctuation distribution characteristics; η is the wind power output ratio; b is the wind power fluctuation smoothing effect index, indicating the spatial smoothing effect of wind power;

[0015] S12. Calculate the total power fluctuation X of the power system including wind power:

[0016] X=X W +X L ~N(0,σ *2 ) (2)

[0017]

[0018] In the above formula, load power fluctuation X L 、Wind power fluctuation X W are independent of each other and follow a normal distribution, where σ * is the fluctuation intensity after wind power access, and σ1 is the standard deviation of load power fluctuation.

[0019] In step S2, the stochastic dynamics model of the power system is:

[0020]

[0021] In the above formula, p is the power fluctuation deviation; γ is the mean recovery coefficient of load fluctuation, which indicates the ability to make the random process of load fluctuation close to the mean μ over a long period of time; σ is the fluctuation intensity, and ξ(t) is the Gaussian white noise process;

[0022] Assuming μ is 0, equation (4) is:

[0023]

[0024] In step S3, the Ito stochastic differential equations of the power system frequency regulation model are:

[0025]

[0026] In the above formula, ω is the system frequency deviation, δ is the adjustment coefficient, and H is the system inertia time constant;

[0027] The unit adjustment coefficient δ after wind power access * for:

[0028]

[0029] System inertia time constant H after wind power access * for:

[0030] H * =(1-η)H(8)

[0031] The primary frequency regulation model of the power system containing wind power is expressed by the Ito stochastic differential equations as follows:

[0032]

[0033] In the above formula, ε(ω) is the dead zone function. There are two types of dead zones, namely, ordinary dead zone ε1(ω) and enhanced dead zone ε2(ω). The expression is:

[0034]

[0035]

[0036] Step S4 specifically includes the following steps:

[0037] S41. Write the primary frequency regulation model of the power system containing wind power into vector form;

[0038] For equation (9), let x = [x1, x2] = [ω, p], and write it in vector form as:

[0039]

[0040] in:

[0041]

[0042]

[0043] In the above formula, f(x) is the drift term, which is the deterministic part of the dynamic process of the power system and is a nonlinear function of the state variable x; g(x)ξ is the diffusion term, g(x) is the diffusion coefficient of the equation, and ξ is the white noise vector;

[0044] S42, the FPK equation of the stochastic dynamics model of the wind power system is obtained:

[0045]

[0046] In the above formula, Gi =[G1, ..., Gn] is:

[0047]

[0048] In the above formula, a is the drift coefficient and b is the diffusion coefficient;

[0049]

[0050]

[0051] The FPK equation of formula (9) about the probability density function Γ(x, t) is:

[0052]

[0053] make:

[0054] Thus we get:

[0055]

[0056] In step S5, the frequency probability distribution density function of the wind power system without considering the dead zone is solved by the following steps:

[0057] For equation (21), without considering the dead zone function, the expression of Γ(ω, p) is obtained as follows:

[0058]

[0059] in:

[0060]

[0061]

[0062] By integrating over p, we can obtain the probability density function F(ω) of the system frequency deviation ω:

[0063]

[0064] The frequency probability distribution density function of the power system containing wind power is obtained by analytical method;

[0065] The frequency probability distribution density function of the wind power system considering the dead zone is solved by the following steps:

[0066] Formula (21) can be expressed by the following partial differential equation:

[0067]

[0068] In the above formula, x and y are variables, L is a differential operator, and Ω is a boundary value;

[0069] Divide the plane area into fine grid areas Ω using grid steps of d and D respectively. d and the coarse mesh region Ω D ;

[0070] At a certain grid node, the five-point difference method is used to obtain the difference equation of formula (24):

[0071]

[0072] It can be expressed in matrix form as:

[0073]

[0074]

[0075] In the above formula, L d is an N×N dimensional matrix, L D is an M×M dimensional matrix, is an N-dimensional column vector consisting of the fine grid node degrees of freedom, is the M-dimensional column vector consisting of the degrees of freedom of the coarse grid nodes, is the N-dimensional column vector of generalized loads on fine mesh nodes, is the M-dimensional column vector of generalized loads on the coarse grid nodes;

[0076] When a coarse grid node coincides with a fine grid node, a direct mapping method is used, that is, the coarse grid node value takes the fine grid node value of the node:

[0077]

[0078] In the above formula, is the transfer operator of the grid function from the coarse grid to the fine grid;

[0079] The linear interpolation method is used to distribute the coarse grid node values ​​to the adjacent fine grid nodes according to the weight:

[0080]

[0081] In the above formula, is the transfer operator of the grid function from the fine grid to the coarse grid;

[0082] Solve the equation using dual-grid finite difference iterations. Perform the calculations as follows:

[0083] (1) Set the initial value

[0084] (2) Perform an iterative relaxation operation κ1 times in the fine grid area to obtain the approximate value

[0085] (3) Calculation of fine grid loss Transfer operator of mesh functions from coarse to fine grids

[0086] (4) Calculate the exact solution in the coarse grid area And correct the fine mesh node values;

[0087] (5) The initial value is the iterative relaxation operation κ2 times in the fine grid area to obtain the approximate value Return to step (2) and perform n operations to obtain the frequency probability distribution density function of the wind power system.

[0088] Compared with the prior art, the present invention has the following beneficial effects:

[0089] In a frequency characteristic analysis method of a wind power system based on a double-grid difference method, the present invention establishes a primary frequency regulation model of a wind power system and obtains an FPK equation about the system frequency probability distribution density function. A double-grid difference iterative numerical algorithm is adopted. By relaxing in a fine grid area and correcting in a coarse grid area, the advantages of a finite element method and a finite difference method are combined to quickly and accurately obtain the system frequency probability distribution function, effectively shortening the numerical solution time, thereby providing an analysis tool for power grid frequency regulation capability analysis, frequency regulation parameter optimization, unit economic operation, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 It is a flow chart of the frequency characteristic analysis method of a wind power system based on a double-grid difference method of the present invention.

[0091] Figure 2 It is a schematic diagram of the dead zone function of the ordinary and enhanced speed regulators in the present invention.

[0092] Figure 3 It is a diagram of the grid node distribution in the double grid difference method of the present invention.

[0093] Figure 4 It is an algorithm flow chart of the dual-grid finite difference iterative method in the present invention.

[0094] Figure 5 is a system frequency probability distribution density function curve under different dead zones in the embodiment of the present invention.

[0095] Figure 6 It is a comparison diagram of system frequency probability distribution density function curves obtained by different methods in the embodiments of the present invention.

[0096] Figure 7It is a schematic diagram of a 3-machine 9-node power system modified in an embodiment of the present invention.

[0097] Figure 8 It is a statistical diagram of the probability distribution of power system frequency under different dead zones in an embodiment of the present invention.

[0098] Fig. 9 It is a system frequency probability distribution density function curve under different wind power penetration rates in the embodiment of the present invention.

[0099] Fig.10 It is a statistical diagram of the probability distribution of power system frequency under different new energy penetration rates in an embodiment of the present invention.

[0100] Fig.11 It is a system frequency probability distribution density function curve under different frequency modulation parameters in the embodiment of the present invention.

[0101] Fig.12 It is a statistical diagram of the probability distribution of power system frequency under different frequency modulation parameters in an embodiment of the present invention. DETAILED DESCRIPTION

[0102] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0103] See also Figures 1 to 4 A frequency characteristic analysis method of a wind power system based on a double-grid difference method comprises the following steps:

[0104] S1. Establish a power fluctuation model for wind power system;

[0105] S2. Establish a stochastic dynamics model of the power system;

[0106] S3. Establish a primary frequency regulation model for the power system including wind power;

[0107] S4. Analyze the characteristics of the primary frequency regulation model of the power system containing wind power, and obtain the FPK equation of the stochastic dynamics model of the power system containing wind power;

[0108] S5. Solve the frequency probability distribution density function of the power system containing wind power.

[0109] Step S1 specifically includes the following steps:

[0110] S11. Calculate the corrected standard deviation of wind power fluctuation

[0111]

[0112] In the above formula, a is the wind power fluctuation time scale coefficient, which indicates the law of wind power output variation with time scale; z α1is the α1 quantile of the standard normal distribution, indicating the wind power fluctuation distribution characteristics; η is the wind power output ratio; b is the wind power fluctuation smoothing effect index, indicating the spatial smoothing effect of wind power;

[0113] S12. Calculate the total power fluctuation X of the power system including wind power:

[0114] X=X W +X L ~N(0,σ *2 ) (2)

[0115]

[0116] In the above formula, load power fluctuation X L 、Wind power fluctuation X W are independent of each other and follow a normal distribution, where σ * is the fluctuation intensity after wind power access, and σ1 is the standard deviation of load power fluctuation.

[0117] In step S2, the stochastic dynamics model of the power system is:

[0118]

[0119] In the above formula, p is the power fluctuation deviation; γ is the mean recovery coefficient of load fluctuation, which indicates the ability to make the random process of load fluctuation close to the mean μ over a long period of time; σ is the fluctuation intensity, and ξ(t) is the Gaussian white noise process;

[0120] Assuming μ is 0, equation (4) is:

[0121]

[0122] In step S3, the Ito stochastic differential equations of the power system frequency regulation model are:

[0123]

[0124] In the above formula, ω is the system frequency deviation, δ is the adjustment coefficient, and H is the system inertia time constant;

[0125] The unit adjustment coefficient δ after wind power access * for:

[0126]

[0127] System inertia time constant H after wind power access * for:

[0128] H * =(1-η)H (8)

[0129] The primary frequency regulation model of the power system containing wind power is expressed by the Ito stochastic differential equations as follows:

[0130]

[0131] In the above formula, ε(ω) is the dead zone function. There are two types of dead zones, namely, ordinary dead zone ε1(ω) and enhanced dead zone ε2(ω). The expression is:

[0132]

[0133]

[0134] Step S4 specifically includes the following steps:

[0135] S41. Write the primary frequency regulation model of the power system containing wind power into vector form;

[0136] For equation (9), let x = [x1, x2] = [ω, p], and write it in vector form as:

[0137]

[0138] in:

[0139]

[0140]

[0141] In the above formula, f(x) is the drift term, which is the deterministic part of the dynamic process of the power system and is a nonlinear function of the state variable x; g(x)ξ is the diffusion term, g(x) is the diffusion coefficient of the equation, and ξ is the white noise vector;

[0142] S42, the FPK equation of the stochastic dynamics model of the wind power system is obtained:

[0143]

[0144] In the above formula, G i =[G1, ..., G n ]for:

[0145]

[0146] In the above formula, a is the drift coefficient and b is the diffusion coefficient;

[0147]

[0148]

[0149] The FPK equation of formula (9) about the probability density function Γ(x, t) is:

[0150]

[0151] make:

[0152] Thus we get:

[0153]

[0154] In step S5, the frequency probability distribution density function of the wind power system without considering the dead zone is solved by the following steps:

[0155] For equation (21), without considering the dead zone function, the expression of Γ(ω, p) is obtained as follows:

[0156]

[0157] in:

[0158]

[0159]

[0160] By integrating over p, we can obtain the probability density function F(ω) of the system frequency deviation ω:

[0161]

[0162] The frequency probability distribution density function of the power system containing wind power is obtained by analytical method;

[0163] The frequency probability distribution density function of the wind power system considering the dead zone is solved by the following steps:

[0164] Formula (21) can be expressed by the following partial differential equation:

[0165]

[0166] In the above formula, x and y are variables, L is a differential operator, and Ω is a boundary value;

[0167] Divide the plane area into fine grid areas Ω using grid steps of d and D respectively. d and the coarse mesh region Ω D ;

[0168] At a certain grid node, the five-point difference method is used to obtain the difference equation of formula (24):

[0169]

[0170] It can be expressed in matrix form as:

[0171]

[0172]

[0173] In the above formula, L d is an N×N dimensional matrix, L D is an M×M dimensional matrix, is an N-dimensional column vector consisting of the fine grid node degrees of freedom, is the M-dimensional column vector consisting of the degrees of freedom of the coarse grid nodes, is the N-dimensional column vector of generalized loads on fine mesh nodes, is the M-dimensional column vector of generalized loads on the coarse grid nodes;

[0174] When a coarse grid node coincides with a fine grid node, a direct mapping method is used, that is, the coarse grid node value takes the fine grid node value of the node:

[0175]

[0176] In the above formula, is the transfer operator of the grid function from the coarse grid to the fine grid;

[0177] The linear interpolation method is used to distribute the coarse grid node values ​​to the adjacent fine grid nodes according to the weight:

[0178]

[0179] In the above formula, is the transfer operator of the grid function from the fine grid to the coarse grid;

[0180] Solve the equation using dual-grid finite difference iterations. Perform the calculations as follows:

[0181] (1) Set the initial value

[0182] (2) Perform an iterative relaxation operation κ1 times in the fine grid area to obtain the approximate value

[0183] (3) Calculation of fine grid loss Transfer operator of mesh functions from coarse to fine grids

[0184] (4) Calculate the exact solution in the coarse grid area And correct the fine mesh node values;

[0185] (5) The initial value is the iterative relaxation operation κ2 times in the fine grid area to obtain the approximate value Return to step (2) and perform n operations to obtain the frequency probability distribution density function of the wind power system.

[0186] The principle of the present invention is described as follows:

[0187] At present, the research on power grid frequency mainly focuses on system frequency regulation and evaluation indicators, and there are fewer studies on power grid frequency distribution. If we can quickly and accurately obtain the frequency probability distribution function curve, explore the power grid frequency control information contained in the frequency probability distribution characteristics and its evolution, and understand the key factors affecting the frequency regulation capability and frequency probability distribution in the system, it can provide a reference for the capacity analysis, parameter optimization, and economic operation of power grid frequency regulation control.

[0188] The FPK equation is a distribution function that describes the position or velocity of a particle that evolves over time after being subjected to random forces in a potential energy field. It can be used to calculate the solution of the distribution function of a variable in a random differential equation. By applying the FPK equation to a random dynamic system such as a power system, the probability density function of the variable system frequency can be studied.

[0189] Example:

[0190] See also Figure 1 A frequency characteristic analysis method of a wind power system based on a double-grid difference method comprises the following steps:

[0191] S1. Establish a power fluctuation model for a wind power system; specifically, the following steps are included:

[0192] S11, wind power fluctuation standard deviation σ2 is closely related to the output proportion of wind turbines in the whole system. Calculate the corrected wind power fluctuation standard deviation

[0193]

[0194] In the above formula, a is the wind power fluctuation time scale coefficient, which indicates the law of wind power output variation with time scale; z α1 is the α1 quantile of the standard normal distribution, indicating the wind power fluctuation distribution characteristics; η is the wind power output ratio; b is the wind power fluctuation smoothing effect index, indicating the spatial smoothing effect of wind power; the above coefficients can be obtained through historical data statistics;

[0195] S12. When considering wind power output, the probability function of the net power fluctuation of the power system is a composite probability function of the load power fluctuation and the wind power output fluctuation. The data statistics of engineering practice confirm that the load power fluctuation law conforms to the normal distribution. Calculate the total power fluctuation X of the power system including wind power:

[0196] X=X W +X L~N(0,σ *2 ) (2)

[0197]

[0198] In the above formula, load power fluctuation X L 、Wind power fluctuation X W are independent of each other and follow a normal distribution, where σ * is the fluctuation intensity after wind power access, σ1 is the standard deviation of load power fluctuation (obtained from historical data statistics);

[0199] S2. The power system model considering the random fluctuation of system power is often represented by a set of stochastic differential equations (SDE). The random process that can reflect the load power fluctuation is the Ornstein-Uhlenbeck (OU) process. Compared with the standard Wiener process, the OU process is more suitable for modeling random disturbances in dynamic systems. The random dynamic model of the power system is established as follows:

[0200]

[0201] In the above formula, p is the power fluctuation deviation; γ is the mean recovery coefficient of load fluctuation, which indicates the ability to make the random process of load fluctuation close to the mean μ over a long period of time; σ is the fluctuation intensity, and ξ(t) is the Gaussian white noise process;

[0202] Assuming μ is 0, equation (4) is:

[0203]

[0204] S3. Without considering the time lag characteristics, dead zone characteristics, prime mover time constant and secondary frequency regulation of the speed regulator, a primary frequency regulation model of the power system containing wind power is established;

[0205] The Ito stochastic differential equations of the power system frequency regulation model are:

[0206]

[0207] In the above formula, ω is the system frequency deviation, δ is the adjustment coefficient, and H is the system inertia time constant;

[0208] Since wind turbines can only provide limited virtual inertia and the technology for wind turbines to participate in primary frequency regulation control is not yet mature, the frequency regulation task in the power system is still undertaken by conventional synchronous generators. As the output proportion of wind turbines in the system increases, the primary frequency regulation characteristics of the power system also change accordingly.

[0209] The total unit regulation power of the power system generator set is reduced, and the unit regulation coefficient δ after wind power access can be obtained. * for:

[0210]

[0211] System inertia time constant H after wind power access * for:

[0212] H * =(1-η)H (8)

[0213] The primary frequency regulation model of the power system with wind power considering the dead zone is expressed by the Ito stochastic differential equations:

[0214]

[0215] In the above formula, ε(ω) is the dead zone function. There are two types of dead zones, namely, ordinary dead zone ε1(ω) and enhanced dead zone ε2(ω), as shown in Figure 2 As shown, the expression is:

[0216]

[0217]

[0218] S4. Analyze the characteristics of the primary frequency regulation model of the power system containing wind power, and obtain the FPK equation of the stochastic dynamics model of the power system containing wind power; specifically, the following steps are included:

[0219] S41. Write the primary frequency regulation model of the power system containing wind power into vector form;

[0220] For equation (9), let x = [x1, x2] = [ω, p], and write it in vector form as:

[0221]

[0222] in:

[0223]

[0224]

[0225] In the above formula, f(x) is the drift term, which is the deterministic part of the dynamic process of the power system and is a nonlinear function of the state variable x; g(x)ξ is the diffusion term, g(x) is the diffusion coefficient of the equation, and ξ is the white noise vector;

[0226] S42, the FPK equation of the stochastic dynamics model of the wind power system is obtained:

[0227]

[0228] In the above formula, Γ represents the probability density function Γ(x, y), x represents ω, and t is time; G i =[G1, ..., G n ]for:

[0229]

[0230] In the above formula, a is the drift coefficient, b is the diffusion coefficient; n is the dimension, which is 2 in this design;

[0231]

[0232]

[0233] The FPK equation of formula (9) about the probability density function Γ(x, t) is:

[0234]

[0235] To get the probability density over a long period of time, let:

[0236] Thus we get:

[0237]

[0238] S5. Solve the frequency probability distribution density function of the power system containing wind power;

[0239] The frequency probability distribution density function of the power system containing wind power without considering the dead zone is solved by the following steps:

[0240] For equation (21), without considering the dead zone function, the expression of Γ(ω, p) is obtained as follows:

[0241]

[0242] in:

[0243]

[0244]

[0245] By integrating over p, we can obtain the probability density function F(ω) of the system frequency deviation ω:

[0246]

[0247] The frequency probability distribution density function of the power system containing wind power is obtained by analytical method;

[0248] The frequency probability distribution density function of the wind power system considering the dead zone is solved by the following steps:

[0249] The FPK equation in formula (21) is an elliptic variable coefficient partial differential equation, which can be expressed by the following partial differential equation:

[0250]

[0251] In the above formula, x and y are variables, L is a differential operator, and Ω is a boundary value;

[0252] Divide the plane area into fine grid areas Ω using grid steps of d and D respectively. d and the coarse mesh area ΩD ， And D = 2d; the distribution of fine grid nodes and coarse grid nodes is as follows Figure 3 As shown;

[0253] At a certain grid node, the five-point difference method is used to obtain the difference equation of formula (24):

[0254]

[0255] In the above formula, Δ d Represents the discretized differential operator, that is, the discretization of Lu is Δ d u i，j ;f ij represents f(x, y); g i，j represents g(x, y); i, j represent horizontal and vertical discrete points;

[0256] It can be expressed in matrix form as:

[0257]

[0258]

[0259] In the above formula, L d is an N×N dimensional matrix, L D is an M×M dimensional matrix, is an N-dimensional column vector consisting of the fine grid node degrees of freedom, is the M-dimensional column vector consisting of the degrees of freedom of the coarse grid nodes, is the N-dimensional column vector of generalized loads on fine mesh nodes, is the M-dimensional column vector of generalized loads on the coarse grid nodes;

[0260] When a coarse grid node coincides with a fine grid node, a direct mapping method is used, that is, the coarse grid node value takes the fine grid node value of the node:

[0261]

[0262] In the above formula, is the transfer operator of the grid function from the coarse grid to the fine grid, u d For vector Specific values ​​in ;

[0263] The linear interpolation method is used to distribute the coarse grid node values ​​to the adjacent fine grid nodes according to the weight:

[0264]

[0265] In the above formula, is the transfer operator of the grid function from the fine grid to the coarse grid;

[0266] See also Figure 4 , use the dual-grid finite difference iterative method to solve the equation, and perform the calculations as follows:

[0267] (1) Set the initial value

[0268] (2) Perform an iterative relaxation operation κ1 times in the fine grid area to obtain the approximate value

[0269] (3) Calculation of fine grid loss Transfer operator of mesh functions from coarse to fine grids

[0270] (4) Calculate the exact solution in the coarse grid area And correct the fine mesh node values;

[0271] (5) The initial value is the iterative relaxation operation κ2 times in the fine grid area to obtain the approximate value Return to step (2) and perform n operations to obtain the frequency probability distribution density function of the wind power system.

[0272] The initial conditions and infinite boundary conditions adopted are:

[0273]

[0274]

[0275] During the calculation process, the coarse grid accuracy is 40×40, and the fine grid accuracy is 80×80. The numerical solution of the equation is obtained, thereby obtaining the probability density curve of the frequency deviation.

[0276] In the stochastic dynamics model of a single-machine system, the probability distribution density (PDF) function curves of the system frequency are obtained under three conditions: not considering the dead zone, considering the ordinary dead zone, and considering the enhanced dead zone, as shown in Figure 5 Compared with the frequency probability distribution statistics obtained by Monte Carlo simulation method, it is shown in Figure 6. Figure 6 In (a), the simulation time of the Monte Carlo simulation method is 1×10 5 s, the simulation step is 0.05s, and the actual running time of the computer is 12.6s; Figure 6 In (b), the simulation time is 5×10 5 s, the simulation step is 0.01s, and the actual running time is 43.2s; Figure 6 In (c), the simulation time is 1.5×10 6 s, the simulation step is 0.01s, and the actual running time is 383.3s; the numerical solution calculation time of this design is 40.1s. Figure 6 (a) Figure 6 (b) and Figure 6 (c) The Monte Carlo method can only obtain a discrete and non-smooth grid frequency probability distribution density function curve. The smaller the sample size, the worse the double hump effect of the frequency probability distribution reflected in the statistical diagram of the system frequency probability distribution. If the same smooth result is required, the number of simulations in the Monte Carlo method needs to be increased by an order of magnitude, so that the calculation time also needs to be increased by an order of magnitude.

[0277] In order to further prove the rapidity and accuracy of this design method, Table 1 shows the time consumption comparison of Monte Carlo simulation method, finite element method and dual-grid finite difference iteration method of this design under the same solution accuracy. -5 The probability density function obtained by the segmentation accuracy calculation is taken as the standard solution, and the absolute value of the difference between the numerical solution of the probability density function and the standard solution is taken as the accuracy standard. Among them, all simulations and numerical calculations are performed on a 64-bit Windows 10 computer with a 2.9GHz AMD R7-4800H and 16GB memory, and the software platform is Mathematica.

[0278] Table 1 Comparison of time consumption of different methods

[0279]

[0280] By comparison, it can be seen that the method of this design can obtain the system frequency probability distribution density function curve more quickly and accurately. Table 2 shows the percentage of time reduction of this design method compared with the finite element method under different accuracy. Under different solution accuracy, this design can reduce the solution time, and as the solution accuracy continues to improve, the percentage of time reduced by this design is also increasing.

[0281] Table 2. Reduction time percentage under different precisions

[0282]

[0283]

[0284] In order to verify the rationality of this design algorithm, the following Figure 7 The 3-machine 9-node power system with wind and thermal power shown in the figure. The system contains 3 thermal power units G1, G2 and G3, and 1 wind turbine unit. The total installed capacity of the frequency regulation units G1-G3 are 1000MW, 600MW and 800MW respectively; the wind turbine unit does not participate in the primary frequency regulation of the power system, and the installed capacity is 450MW. Gaussian white noise is injected into the load L1-L3 and the wind turbine output end to simulate the power fluctuation of the load end and the wind turbine output. The simulation time is 80000s, the frequency of node B5 is selected as the adopted data, and the sampling interval is 1s. In the simulation model, no dead zone, ordinary dead zone, and enhanced dead zone are set for G1-G3 respectively. The probability distribution statistics of power frequency are as follows Figure 8 As shown in Figure 2, different wind power output ratios are used, and the system frequency probability distribution density function curve is shown in Figure 2. Fig. 9 As shown. When the proportion of wind power output gradually increases from 10% to 30%, the system equivalent inertia time constant continues to decrease, the equivalent differential system continues to increase, and the standard deviation of the total power fluctuation also increases. The primary frequency regulation capability of the entire system continues to decline, and the hump top and the saddle between the double hump of the probability density distribution curve continue to become lower. In the simulation model, the capacity of the thermal power units in the system is reduced, the capacity of the wind power units is increased, and the wind power output is increased or decreased proportionally to change the proportion of wind power in the system. The probability distribution statistics of the grid frequency under three different wind power output ratios are shown in the figure below. Fig.10 shown.

[0285] Using different system parameters, the system frequency probability distribution density function curve is as follows: Fig.11 As shown in the figure. When different inertia time constants H are used, the system frequency probability distribution density function curve does not change much, so the influence of inertia time constant H is small. Fig.11In (b), when the load mean grayscale value changes from 0.06 to 0.04, the hump top and the saddle between the double humps of the probability density distribution curve become lower and lower. Fig.11 In (c), when the dead zone of the speed regulator changes from 1.5r / min to 2.5r / min, the hump top of the probability density distribution curve does not decrease, the width of the saddle between the two humps increases, and the lowest point of the saddle decreases. The time when the system frequency is outside the dead zone changes from 85.3% to 78.4%. As the dead zone increases, the double hump phenomenon becomes more and more detailed. Fig.11 In (d), when the speed regulation rate changes from 0.06 to 0.04, the primary frequency regulation capability of the system continues to increase, the hump top of the probability density distribution curve continues to increase, and the saddle between the double humps remains basically unchanged. Fig.12 The influence of different system parameters on the system frequency probability distribution in the simulation model is given.

[0286] The above comparison reflects the rationality of the design algorithm. This design establishes a primary frequency regulation model of the wind power system, obtains the FPK equation of the system frequency probability distribution density function, and uses a double-grid difference iterative numerical algorithm that combines the advantages of the finite element method and the finite difference method to quickly and accurately obtain the frequency probability distribution function, thereby providing a reference target for the power grid frequency regulation capacity analysis, frequency regulation parameter optimization, and unit economic operation.

Claims

1. A frequency characteristic analysis method for a wind power system based on a double-grid difference method, characterized in that: The following steps are involved: S1. Establish a power fluctuation model for a wind power system; specifically, the following steps are included: S11. Calculate the corrected standard deviation of wind power fluctuation In the above formula, a is the wind power fluctuation time scale coefficient, which indicates the law of wind power output variation with time scale; z α1 is the α1 quantile of the standard normal distribution, indicating the distribution characteristics of wind power fluctuation; η is the proportion of wind power output; b is the wind power fluctuation smoothing effect index, indicating the spatial smoothing effect of wind power; S12. Calculate the total power fluctuation X of the power system including wind power: X=X W +X L ~N(0,σ *2 ) (2) In the above formula, load power fluctuation X L 、Wind power fluctuation X W are independent of each other and follow a normal distribution, where σ * is the fluctuation intensity after wind power access, σ1 is the standard deviation of load power fluctuation; S2. Establish a stochastic dynamics model of the power system; In the above formula, p is the power fluctuation deviation; γ is the mean recovery coefficient of load fluctuation, which indicates the ability to make the random process of load fluctuation close to the mean μ over a long period of time; σ is the fluctuation intensity, and ξ(t) is the Gaussian white noise process; Assuming μ is 0, equation (4) is: S3. Establish a primary frequency regulation model for the power system including wind power; The Ito stochastic differential equations of the power system frequency regulation model are: In the above formula, ω is the system frequency deviation, δ is the adjustment coefficient, and H is the system inertia time constant; The unit adjustment coefficient δ after wind power access * for: System inertia time constant H after wind power access * for: H * =(1-η)H (8) The primary frequency regulation model of the power system containing wind power is expressed by the Ito stochastic differential equations as follows: In the above formula, ε(ω) is the dead zone function. There are two types of dead zones, namely, ordinary dead zone ε1(ω) and enhanced dead zone ε2(ω). The expression is: S4. Analyze the characteristics of the primary frequency regulation model of the power system containing wind power, and obtain the FPK equation of the stochastic dynamics model of the power system containing wind power; specifically, the following steps are included: S41. Write the primary frequency regulation model of the power system containing wind power into vector form; For equation (9), let x = [x1, x2] = [ω, p] and write it in vector form as: in: In the above formula, f(x) is the drift term, which is the deterministic part of the dynamic process of the power system and is a nonlinear function of the state variable x; g(x)ξ is the diffusion term, g(x) is the diffusion coefficient of the equation, and ξ is the white noise vector; S42, the FPK equation of the stochastic dynamics model of the wind power system is obtained: In the above formula, G i =[G1,...,G n ]for: In the above formula, a is the drift coefficient and b is the diffusion coefficient; The FPK equation of formula (9) about the probability density function Γ(x, t) is: make: Thus we get: S5. Solve the frequency probability distribution density function of the power system containing wind power; The frequency probability distribution density function of the power system containing wind power without considering the dead zone is solved by the following steps: For equation (21), without considering the dead zone function, the expression of Γ(ω,p) is: in: By integrating over p, we can obtain the probability density function F(ω) of the system frequency deviation ω: The frequency probability distribution density function of the power system containing wind power is obtained by analytical method; The frequency probability distribution density function of the wind power system considering the dead zone is solved by the following steps: Formula (21) can be expressed by the following partial differential equation: In the above formula, x and y are variables, L is a differential operator, and Ω is a boundary value; Divide the plane area into fine grid areas Ω using grid steps of d and D respectively. d and the coarse mesh region Ω D ; At a certain grid node, the five-point difference method is used to obtain the difference equation of formula (24): It can be expressed in matrix form as: In the above formula, L d is an N×N dimensional matrix, L D is an M×M dimensional matrix, is an N-dimensional column vector consisting of the fine grid node degrees of freedom, is the M-dimensional column vector consisting of the degrees of freedom of the coarse grid nodes, is the N-dimensional column vector of generalized loads on fine mesh nodes, is the M-dimensional column vector of generalized loads on the coarse grid nodes; When a coarse grid node coincides with a fine grid node, a direct mapping method is used, that is, the coarse grid node value takes the fine grid node value of the node: In the above formula, is the transfer operator of the grid function from the coarse grid to the fine grid; The linear interpolation method is used to distribute the coarse grid node values ​​to the adjacent fine grid nodes according to the weight: In the above formula, is the transfer operator of the grid function from the fine grid to the coarse grid; Solve the equation using dual-grid finite difference iterations. Perform the calculations as follows: (1) Set the initial value (2) Perform an iterative relaxation operation κ1 times in the fine grid area to obtain the approximate value (3) Calculation of fine grid loss Transfer operator of mesh functions from coarse to fine grids (4) Calculate the exact solution in the coarse grid area And correct the fine mesh node values; (5) The initial value is the iterative relaxation operation κ2 times in the fine grid area to obtain the approximate value Return to step (2) and perform n operations to obtain the frequency probability distribution density function of the wind power system.

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