An analytical method for probabilistic estimation of the frequency minimum point in a power system containing new energy sources after disturbance.

Abstract

This invention provides an analytical method for probabilistic estimation of the frequency minimum point after a disturbance in a power system containing renewable energy sources, belonging to the field of power system frequency stability analysis. The analytical method first analyzes the influencing factors of the frequency minimum point of the power system after the disturbance and extracts the probabilistic characteristics of each influencing factor; then, it establishes an analytical expression relating the influencing factors to the frequency minimum point; finally, it performs a specific nonlinear function transformation on the analytical expression to quickly and accurately calculate the probability distribution of the frequency minimum point of the power system containing renewable energy sources after the disturbance. This invention can consider the probabilistic characteristics of the power system in terms of initial frequency, number of disturbances, and unit status, and calculates the probability distribution of the frequency minimum point of the power system after the disturbance through analytical methods, thus providing a more reliable basis for power system frequency stability analysis and control both quickly and accurately.

Description

Technical Field

[0001] This invention belongs to the field of power system frequency stability analysis, and relates to an analytical method for probabilistic estimation of the frequency minimum point after a disturbance in a power system containing new energy sources. Background Technology

[0002] After a power system experiences a significant disturbance, its frequency undergoes a drastic and complex dynamic process. It may recover to a quasi-steady-state frequency and remain stable after several oscillations, or it may lose control and deviate significantly from its rated value through oscillations or monotonically increasing / decreasing, ultimately leading to instability. In system operation and management, it is necessary to analyze future or anticipated operating scenarios to obtain the frequency dynamics after the disturbance, thereby enabling a rapid and accurate assessment of the frequency safety level and providing a basis and reference for planning and operation.

[0003] The frequency dynamics process can be described by differential equations (rotor motion equations), and the current solution methods include three categories: time-domain simulation, model analysis, and machine learning. Among them, model analysis can provide analytical relationships between the system's frequency dynamics and related influencing factors, has good interpretability and generalization ability, and can better coordinate the analysis precision and accuracy. Therefore, it has been widely explored and has yielded relatively rich research results.

[0004] The factors influencing frequency dynamics, i.e., the boundary conditions for solving differential equations, mainly include: the active power deficit caused by the disturbance (referred to as power deficit), the initial frequency deviation at the time of the disturbance (referred to as initial frequency difference), and the system's frequency response capability at the time of the disturbance (referred to as response capability, including inertia and primary frequency regulation capability). In actual power system operation, these three influencing factors all change randomly at all times; that is, these influencing factors are random variables. This means that the frequency dynamics affected by them are probabilistic quantities that change randomly.

[0005] Previously, due to the relatively stable system operation and sufficient frequency regulation resources, the system operation analysis based on the deterministic frequency dynamic process analysis results had small deviations and could fully meet the analytical accuracy requirements of system safety operation planning, program formulation, and control strategy design. Therefore, the deterministic analysis method has been adopted in actual power grid operation.

[0006] If deterministic analysis is used, the probabilistic characteristics of the above three boundary conditions are ignored and all are determined values, namely: 1) The power deficit is set to the maximum value: only the most severe disturbance in the expected fault concentration is analyzed; 2) The initial frequency difference is 0: it is assumed that the frequency of the system at the moment of disturbance is the rated value; 3) The unit response capability is the nameplate nominal value, that is, the response capability is the sum of the rated values ​​of the regulation capabilities of all control elements and remains unchanged.

[0007] With the increasing proportion of renewable energy capacity, frequency regulation resources are becoming increasingly scarce, frequency stability is becoming more strained, the uncertainty of operating parameters is increasing, the fluctuation range of operating conditions is widening, and the system's operating state is approaching its limits. The adjustment capability of frequency regulation resources is also gradually increasing in amplitude as operating conditions change. This leads to increasingly significant probabilistic characteristics of the frequency dynamic process after the system is disturbed. At this point, if existing deterministic analysis methods are still used, the obtained frequency dynamic process may not accurately and comprehensively characterize the system's frequency security status and evolution trend. This could lead to loopholes in the three lines of defense for security based on the analysis results, thus creating potential security risks.

[0008] Current research indicates that the probabilistic analysis of frequency dynamics after system disturbance is still in its exploratory stage. Some studies employing a probabilistic perspective either fail to adequately consider system uncertainties (e.g., treating only wind power output fluctuations as the disturbance source and describing them using a Weibull distribution) or suffer from low computational efficiency (e.g., using time-domain simulation to obtain the frequency minimum / high point after disturbance). Therefore, it is necessary to conduct research on analytical methods for probabilistic estimation of the frequency minimum point in power systems containing renewable energy sources after disturbance.

[0009] This invention proposes an analytical method for probabilistic estimation of the frequency minimum point after a disturbance in a power system containing renewable energy sources. The method provides a framework: first, it analyzes the influencing factors in the frequency dynamic process and extracts the probabilistic characteristics of each factor; then, it establishes an analytical expression for the influencing factors and the frequency minimum point; finally, it uses a specific nonlinear function transformation to calculate the probability density function of each parameter at the minimum point. The proposed method can quickly and accurately calculate the probability distribution of the frequency minimum point after a disturbance in a power system containing renewable energy sources. Summary of the Invention

[0010] The frequency fluctuations in new power systems are becoming increasingly complex. Currently, the stability model of a power system after power electronization can still be abstracted into rotor motion equations. The essence of analyzing the frequency dynamics after disturbance remains solving a system of differential equations, but explicit solutions are difficult to obtain analytically. Therefore, for the goal of finding the minimum frequency point, this invention transforms the time-domain problem into a non-time-domain problem and constructs a method for probabilistic analytical estimation of the minimum frequency point: The first step involves classifying and describing the influencing factors of the minimum frequency point (hereinafter referred to as the minimum point) of the power system after disturbance. For factors that can be directly obtained through data, the probability density function (PDF) is calculated using a Gaussian mixture model (GMM). The proposed method uses a function to describe the factors. For factors requiring model description, a model is first constructed. Then, parameters exhibiting uncertainty are calculated using a Geometric Model (GMM) to determine the probability distribution (PDF). The PDF and model are then combined to describe the factors. The second step involves simplifying the model, solving for loops, and fitting the output curves using polynomials to construct an analytical expression between the influencing factors and the minimum point parameters. Finally, a specific nonlinear function transformation is applied to the analytical expression to establish the relationship between the PDF of the influencing factors and the PDF of the minimum point. The PDF of the minimum point is then calculated using the PDF of the influencing factors. This method can quickly and accurately calculate the probability distribution of frequency minimum points in a power system containing new energy sources after disturbance.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0012] An analytical method for probabilistic estimation of the frequency minimum point in a power system containing renewable energy sources after disturbance includes the following steps:

[0013] S1: This invention uses the initial frequency at the time of disturbance, the number of disturbances, and the system frequency response capability as influencing factors on the lowest frequency point of the power system after disturbance. The initial frequency and the number of disturbances are described using a probability model (PDF) calculated by the Gaussian Mixture Model (GMM). For the system frequency response capability, a model is first constructed, and then the wind speed and thermal power unit status are calculated using the GMM. The probabilistic characteristics are described by combining the model and the PDF. The specific steps are as follows:

[0014] S1-1: The uncertainties in the initial frequency and the number of disturbances are caused by numerous factors, and their formation process is complex and difficult to analyze. Based on probability and statistics theory, this invention describes the probabilistic characteristics of these two factors using PDF extraction from GMM.

[0015] S1-2: Regarding the uncertainty of the system's frequency response capability, this invention only considers two energy sources: wind power and thermal power. First, it constructs models for the inertial response link and the primary frequency regulation link for each of them.

[0016] In terms of inertial response modeling, the inertial time constant is used to describe inertia. In this invention, the inertial time constant of thermal power is taken as a fixed value, and the inertial time constant of wind power is calculated by equation (1).

[0017]

[0018] In the formula, H wg Let λ be the wind turbine inertial time constant, λ be the tip speed ratio, and v be the blade tip rotation speed ratio. w For wind speed, K G R is the gearbox ratio, R is the rotor radius, and J is the rotor radius. wr J is the moment of inertia of the wind turbine generator. t Let S be the moment of inertia of the wind turbine. wg This refers to the capacity of the wind turbine generator set.

[0019] By weighted aggregation of the inertial time constants of wind power and thermal power, the system inertial time constant can be obtained, as shown in equation (2).

[0020]

[0021] In the formula, H total H is the total inertial time constant of the system. wg_i H gt_j Let S be the inertial time constant of the i-th wind turbine and the j-th thermal power unit. wg_i S gt_j Let n be the capacity of the i-th wind turbine and the j-th thermal power unit, and m be the number of wind turbines and thermal power units.

[0022] Therefore, the probabilistic characteristics of the system inertia can be described based on equation (2) and the PDF of wind speed, which is obtained from GMM.

[0023] S1-3: Regarding the modeling of the primary frequency regulation stage, for the primary frequency regulation stage of thermal power plants, the IEEE G1 governor model can be used, such as... Figure 1 As shown, the governor gain coefficient K in the governor model can reflect the frequency regulation capability of the unit. The uncertainty of the frequency response capability of the thermal power unit comes from the heat storage state of the unit. Therefore, the analytical expression shown in equation (3) is established.

[0024]

[0025] In the formula, K fr C is a fixed parameter within the unit. E Where P0 is the heat storage coefficient, V0 is the main steam pressure, and R is the valve opening. t This is the unit's droop coefficient.

[0026] At this point, the probabilistic characteristics of primary frequency regulation of thermal power plants can be described based on the PDF of main steam pressure and valve opening and the IEEE G1 governor model. The PDF of main steam pressure and valve opening is obtained from GMM.

[0027] S1-4: For the primary frequency regulation stage of wind power, the speed governor model in Figure (3) can be used to describe it, and the parameters are calculated as shown in equations (4)-(7).

[0028] J wg =J wr ·K G 2 +J t (4)

[0029]

[0030] P MPPT =k opt ω 3 (6)

[0031] λ=K G Rω / v (7)

[0032] In the formula, J wg Let ω be the fan inertia, ρ be the rotor speed, and C be the air density. p Where is the wind energy utilization coefficient, v is the wind speed, λ is the tip speed ratio, and K is the tip speed ratio. G P is the gearbox ratio. MPPT To control the output power of the fan in MPPT mode, k opt This represents the control coefficient for the wind turbine.

[0033] Furthermore, in S1-4, the speed governor model is specifically as follows: the input is the system frequency difference Δf, firstly based on the virtual droop coefficient K... dr Generate the wind turbine power increment signal ΔP set Based on the power signal, via 1 / J wg The change in fan rotor speed is calculated using ω0s. The change in rotor speed is then subtracted from the initial speed ω0 to obtain the frequency-adjusted rotor speed ω. This ω is then substituted into equation (6) to calculate the fan output power P at this speed. MPPT Substituting the initial rotor speed ω0 into equation (5), the initial captured power P of the fan is calculated. Me0 Ultimately through P MPPT +P Me0 -ΔP set The actual output of the fan during frequency regulation is calculated and used as the output, such as Figure 2 As shown.

[0034] At this point, the probabilistic characteristics of wind power primary frequency regulation can be described based on S1-4 and the PDF of wind speed, which is obtained from GMM.

[0035] S2: The probabilistic estimation method for the analytical properties of the lowest point proposed in this invention requires first constructing an analytical expression between the lowest point and influencing factors before probability estimation. The establishment of this analytical expression relies on a frequency response model. The frequency response model upon which this invention relies is as follows: the input term is a disturbance, which, after passing through an inertial response stage, outputs a frequency difference. An additional frequency modulation stage is added from the output to the input, thus forming a closed-loop feedback model. The model is as follows: Figure 3 As shown. The model is simplified and analyzed to construct an analytical expression between influencing factors and the minimum point parameter. The specific steps are as follows:

[0036] S2-1: For the analytical description of the probabilistic characteristics of the system's frequency regulation capability, this invention uses the external characteristics of the speed governor's time domain to describe it, that is, the output magnitude of the speed governor as a function of time when responding to disturbances. Specifically:

[0037] First, the external characteristics of the speed controller are fitted using a high-order polynomial according to equation (8):

[0038] G k (t)=α Gk,0 +α Gk,1 t+α Gk,2 t 2 (8)

[0039] In the formula, G k (t) represents the time-domain output of the governor of unit k within the system, α Gk,0 α Gk,1 α Gk,2 These are the constants, linear coefficients, and quadratic coefficients in the governor output fitting of unit k, respectively.

[0040] Using GMM cluster analysis of the datasets of wind speed, main steam pressure, and valve opening, the cluster centers in the clustering results are extracted as representative data points. The governor external characteristic fitting coefficients are calculated for each representative data point. Based on the probability of each representative data point, the governor external characteristic fitting coefficients of wind power and thermal power are weighted to synthesize the probabilistic output expression of the system's primary frequency regulation stage.

[0041]

[0042] In the formula, α G_sys,i λ is the coefficient of the i-th term of the output curve of the system speed controller, q is the number of representative operating points, and λ is the coefficient of the i-th term. k α is the weight of the representative working condition k. Gk,i The coefficient of the i-th term of the governor output curve under representative operating condition k.

[0043] S2-2: To establish the relationship between influencing factors and minimum point parameters, a simplified loop-solving approach was taken for the ASF model of the system containing new energy sources. Based on the simplified loop-solving approach of the transfer function model, combined with equation (8), the power expression for the frequency response of the system containing new energy sources can be obtained as follows:

[0044]

[0045] In the formula, k represents the kth unit of the total number of units in the system.

[0046] Combining the above formulas (9) and (10), we obtain the analytical model for the lowest frequency point containing new energy sources:

[0047]

[0048] In the formula, α G_sys,1 α is the coefficient of the first term of the output curve of the system speed controller. G_sys,2 t represents the coefficient of the quadratic term of the output curve of the system speed controller. M It is the time to reach the lowest frequency point, f. nadir It is the lowest frequency value, f0 is the initial frequency before the disturbance, and Δf M It is the frequency difference at the lowest point.

[0049] S3: The minimum frequency point of a power system has two parameters: the time to reach the minimum point and the value of the minimum frequency point. The probability estimation of the analytical properties of these two parameters needs to be based on the characteristics of the expressions in equations (11) and (12), respectively. The specific steps are as follows:

[0050] S3-1: The probability estimation of the analytical properties of the time to reach the minimum point needs to be based on equation (11), where H in equation (11) total Given the probability quantity to be determined, according to equation (1), the probability of the inertial time constant of a single fan follows H. wg ~f V (v w 2 Therefore, when multiple wind turbines are connected to the grid, according to the central limit theorem, H total The probability density function can be viewed as the sum of the probability density functions of the squares of multiple independent and identically distributed wind speeds, that is:

[0051]

[0052] In the formula, E Htotal Let σ be the expected value of the system's total inertial time constant. Htotal E is the standard deviation of the system's total inertial time constant. Hwg σ is the expected value of the inertial time constant of the wind turbine. Hwg is the inertial time constant of the wind turbine.

[0053] Equation (11) can be written as tM =g(H total According to the principles of probability, when H is known... total When the probability density function is t M The probability density function can be expressed as:

[0054]

[0055] In the formula, f Ht For H total The probability density function, f tM For t M The probability density function.

[0056] S3-2: Then perform a probabilistic estimation of the frequency value at the lowest point using analytical properties;

[0057] First, calculate Δf. M According to equation (12), the function transformation process of the PDF can first construct a mapping relationship to form a new random variable:

[0058]

[0059] Based on the mapping relationship, obtain the Jacobian matrix, and then obtain the new function composed of the new variables S1, S2, and S3 according to the probability density functions of the variables x, y, and z:

[0060]

[0061] S1 represents the original function h(x,y,z), therefore, by taking the marginal density of S1 in equation (18), Δf can be obtained. M The probability density function.

[0062] Finally, by applying convolution, we can obtain f. nadir The probability density function,

[0063]

[0064] In the formula, f fnadir f nadir The probability density function, f f0 Let f be the probability density function of the initial frequency f0. ΔfM The lowest point frequency Δf M The probability density function.

[0065] The beneficial effects of this invention are as follows:

[0066] This invention can take into account the probabilistic characteristics of the power system in terms of initial frequency, number of disturbances, and unit status. It calculates the probability distribution of the lowest frequency point of the power system after disturbance using analytical methods, thereby providing a more reliable basis for power system frequency stability analysis and control in a fast and accurate manner. Attached Figure Description

[0067] Figure 1 This is an IEEE G1 speed controller model.

[0068] Figure 2 This is a model of a wind turbine governor.

[0069] Figure 3 For the system frequency modulation model

[0070] Figure 4 To improve the IEEE 10-machine 39-node system.

[0071] Figure 5 Comparison of PDF and CDF for the time point of lowest frequency.

[0072] Figure 6 Comparison of PDF and CDF for the lowest point frequency difference.

[0073] Figure 7 Comparison of PDF and CDF values ​​for the lowest frequency point. Detailed Implementation

[0074] The present invention will be further described below with reference to specific implementation examples.

[0075] To make the technical solution and advantages of the present invention clearer, the following are introduced: Figure 4 The improved IEEE 10-machine 39-node system shown is improved by replacing four thermal power units with four wind farms. The governor models for the thermal and wind power units are shown in S1-3 and S1-4, with parameters as shown in Table 1. The technical solution of this invention will be clearly and completely described below with reference to specific embodiments and accompanying drawings.

[0076] Table 1 Parameters of the Improved IEEE 10 Machines 39 Node System

[0077]

[0078] Other parameters of the thermal power model: T2 = 0, K2 = K4 = K6 = K8 = 0

[0079] An analytical method for probabilistic estimation of the frequency minimum point in a power system containing renewable energy sources after disturbance includes the following steps:

[0080] S1: This invention uses the initial frequency at the time of disturbance, the number of disturbances, and the system frequency response capability as influencing factors on the lowest frequency point of the power system after disturbance. The initial frequency and the number of disturbances are described using a probability model (PDF) calculated by the Gaussian Mixture Model (GMM). For the system frequency response capability, a model is first constructed, and then the wind speed and thermal power unit status are calculated using the GMM. The probabilistic characteristics are described by combining the model and the PDF. The specific steps are as follows:

[0081] S1-1: The uncertainties in the initial frequency and the number of disturbances are caused by numerous factors, and their formation process is complex and difficult to analyze. Based on probability and statistics theory, this invention describes the probabilistic characteristics of these two factors using PDF extraction from GMM.

[0082] S1-2: Regarding the uncertainty of the system's frequency response capability, this invention only considers two energy sources: wind power and thermal power. First, it constructs models for the inertial response link and the primary frequency regulation link for each of them.

[0083] In terms of inertial response modeling, the inertial time constant is used to describe inertia. In this invention, the inertial time constant of thermal power is taken as a fixed value, and the inertial time constant of wind power is calculated by equation (1).

[0084]

[0085] In the formula, H wg Let λ be the wind turbine inertial time constant, λ be the tip speed ratio, and v be the blade tip rotation speed ratio. w For wind speed, K G R is the gearbox ratio, R is the rotor radius, and J is the rotor radius. wr J is the moment of inertia of the wind turbine generator. t Let S be the moment of inertia of the wind turbine. wg This refers to the capacity of the wind turbine generator set.

[0086] By weighted aggregation of the inertial time constants of wind power and thermal power, the system inertial time constant can be obtained, as shown in equation (2).

[0087]

[0088] In the formula, H total H is the total inertial time constant of the system. wg_i H gt_j Let S be the inertial time constant of the i-th wind turbine and the j-th thermal power unit. wg_i S gt_j Let n be the capacity of the i-th wind turbine and the j-th thermal power unit, and m be the number of wind turbines and thermal power units.

[0089] Therefore, the probabilistic characteristics of the system inertia can be described based on equation (2) and the PDF of wind speed, which is obtained from GMM.

[0090] S1-3: Regarding the modeling of the primary frequency regulation stage, for the primary frequency regulation stage of thermal power plants, the IEEE G1 governor model can be used, such as... Figure 1 As shown, the governor gain coefficient K in the governor model can reflect the frequency regulation capability of the unit. The uncertainty of the frequency response capability of the thermal power unit comes from the heat storage state of the unit. Therefore, the analytical expression shown in equation (3) is established.

[0091]

[0092] In the formula, K fr C is a fixed parameter within the unit. E Where P0 is the heat storage coefficient, V0 is the main steam pressure, and R is the valve opening. t This is the unit's droop coefficient.

[0093] At this point, the probabilistic characteristics of primary frequency regulation of thermal power plants can be described based on the PDF of main steam pressure and valve opening and the IEEE G1 governor model. The PDF of main steam pressure and valve opening is obtained from GMM.

[0094] S1-4: For the primary frequency regulation stage of wind power, the speed governor model in Figure (3) can be used to describe it, and the parameters are calculated as shown in equations (4)-(7).

[0095] J wg =J wr ·K G 2 +J t (4)

[0096]

[0097] P MPPT =k opt ω 3 (6)

[0098] λ=K G Rω / v (7)

[0099] In the formula, J wg Let ω be the fan inertia, ρ be the rotor speed, and C be the air density. p Where is the wind energy utilization coefficient, v is the wind speed, λ is the tip speed ratio, and K is the tip speed ratio. G P is the gearbox ratio. MPPT To control the output power of the fan in MPPT mode, k opt This represents the control coefficient for the wind turbine.

[0100] Furthermore, in S1-4, the speed governor model is specifically as follows: the input is the system frequency difference Δf, firstly based on the virtual droop coefficient K... drGenerate the wind turbine power increment signal ΔP set Based on the power signal, via 1 / J wg The change in fan rotor speed is calculated using ω0s. The change in rotor speed is then subtracted from the initial speed ω0 to obtain the frequency-adjusted rotor speed ω. This ω is then substituted into equation (6) to calculate the fan output power P at this speed. MPPT Substituting the initial rotor speed ω0 into equation (5), the initial captured power P of the fan is calculated. Me0 Ultimately through P MPPT +P Me0 -ΔP set The actual output of the fan during frequency regulation is calculated and used as the output, such as Figure 2 As shown.

[0101] At this point, the probabilistic characteristics of wind power primary frequency regulation can be described based on S1-4 and the PDF of wind speed, which is obtained from GMM.

[0102] S2: The probabilistic estimation method for the analytical properties of the lowest point proposed in this invention requires first constructing an analytical expression between the lowest point and influencing factors before probability estimation. The establishment of this analytical expression relies on a frequency response model. The frequency response model upon which this invention relies is as follows: the input term is a disturbance, which, after passing through an inertial response stage, outputs a frequency difference. An additional frequency modulation stage is added from the output to the input, thus forming a closed-loop feedback model. The model is as follows: Figure 3 As shown. The model is simplified and analyzed to construct an analytical expression between influencing factors and the minimum point parameter. The specific steps are as follows:

[0103] S2-1: For the analytical description of the probabilistic characteristics of the system's frequency regulation capability, this invention uses the external characteristics of the speed governor's time domain to describe it, that is, the output magnitude of the speed governor as a function of time when responding to disturbances. Specifically:

[0104] First, the external characteristics of the speed controller are fitted using a high-order polynomial according to equation (8):

[0105] G k (t)=α Gk,0 +α Gk,1 t+α Gk,2 t 2 (8)

[0106] In the formula, G k (t) represents the time-domain output of the governor of unit k within the system, α Gk,0 α Gk,1 α Gk,2 These are the constants, linear coefficients, and quadratic coefficients in the governor output fitting of unit k, respectively.

[0107] Using GMM cluster analysis of the datasets of wind speed, main steam pressure, and valve opening, the cluster centers in the clustering results are extracted as representative data points. The governor external characteristic fitting coefficients are calculated for each representative data point. Based on the probability of each representative data point, the governor external characteristic fitting coefficients of wind power and thermal power are weighted to synthesize the probabilistic output expression of the system's primary frequency regulation stage.

[0108]

[0109] In the formula, α G_sys,i λ is the coefficient of the i-th term of the output curve of the system speed controller, q is the number of representative operating points, and λ is the coefficient of the i-th term. k α is the weight of the representative working condition k. Gk,i The coefficient of the i-th term of the governor output curve under representative operating condition k.

[0110] S2-2: To establish the relationship between influencing factors and minimum point parameters, a simplified loop-solving approach was taken for the ASF model of the system containing new energy sources. Based on the simplified loop-solving approach of the transfer function model, combined with equation (8), the power expression for the frequency response of the system containing new energy sources can be obtained as follows:

[0111]

[0112] In the formula, k represents the kth unit of the total number of units in the system.

[0113] Combining the above formulas (9) and (10), we obtain the analytical model for the lowest frequency point containing new energy sources:

[0114]

[0115] In the formula, α G_sys,1 α is the coefficient of the first term of the output curve of the system speed controller. G_sys,2 t represents the coefficient of the quadratic term of the output curve of the system speed controller. M It is the time to reach the lowest frequency point, f. nadir It is the lowest frequency value, f0 is the initial frequency before the disturbance, and Δf M It is the frequency difference at the lowest point.

[0116] S3: The minimum frequency point of a power system has two parameters: the time to reach the minimum point and the value of the minimum frequency point. The probability estimation of the analytical properties of these two parameters needs to be based on the characteristics of the expressions in equations (11) and (12), respectively. The specific steps are as follows:

[0117] S3-1: The probability estimation of the analytical properties of the time to reach the minimum point needs to be based on equation (11), where H in equation (11) total Given the probability quantity to be determined, according to equation (1), the probability of the inertial time constant of a single fan follows H. wg~f V (v w 2 Therefore, when multiple wind turbines are connected to the grid, according to the central limit theorem, H total The probability density function can be viewed as the sum of the probability density functions of the squares of multiple independent and identically distributed wind speeds, that is:

[0118]

[0119] In the formula, E Htotal Let σ be the expected value of the system's total inertial time constant. Htotal E is the standard deviation of the system's total inertial time constant. Hwg σ is the expected value of the inertial time constant of the wind turbine. Hwg is the inertial time constant of the wind turbine.

[0120] Equation (11) can be written as t M =g(H total According to the principles of probability, when H is known... total When the probability density function is t M The probability density function can be expressed as:

[0121]

[0122] In the formula, f Ht For H total The probability density function, f tM For t M The probability density function.

[0123] In this example, the results obtained by the probability estimation method proposed in this invention are compared with the results obtained by the same-model simulation method. The same-model simulation method is implemented as follows: the initial frequency, disturbance quantity, and unit status dataset are randomly sampled to determine their values, and 10,000 time-domain simulations of the frequency dynamic process after system disturbance are repeatedly performed, with a simulation duration of 30 seconds. Based on the frequency dynamic curve of each simulation, 10,000 minimum point data points are obtained, and the probability of each parameter is analyzed. The probability density curves and probability distribution curves of the time to reach the minimum point calculated by the two methods are shown below. Figure 5 Table 2 compares the computational efficiency and accuracy of the two methods.

[0124] S3-2: Then perform a probabilistic estimation of the frequency value at the lowest point using analytical properties;

[0125] First, calculate Δf. M According to equation (12), the function transformation process of the PDF can first construct a mapping relationship to form a new random variable:

[0126]

[0127] Based on the mapping relationship, obtain the Jacobian matrix, and then obtain the new function composed of the new variables S1, S2, and S3 according to the probability density functions of the variables x, y, and z:

[0128]

[0129] S1 represents the original function h(x,y,z), therefore, by taking the marginal density of S1 in equation (18), Δf can be obtained. M The probability density function.

[0130] Finally, by applying convolution, we can obtain f. nadir The probability density function,

[0131]

[0132] In the formula, f fnadir f nadir The probability density function, f f0 Let f be the probability density function of the initial frequency f0. ΔfM The lowest point frequency Δf M The probability density function.

[0133] In this example, the results obtained by the probability estimation method proposed in this invention are compared with the results obtained by the same model simulation method. The probability density curves and probability distribution curves of the minimum point frequency difference and the minimum frequency value calculated by the two methods are shown below. Figure 6 , Figure 7 Table 2 compares the computational efficiency and accuracy of the two methods.

[0134] Table 2. Accuracy and computational efficiency of probability estimation

[0135]

[0136] In terms of computational efficiency, the analytical method improves computational efficiency by 99.52% compared to the Monte Carlo method. Regarding computational accuracy, under the KL divergence evaluation standard, the errors of all parameters at the lowest frequency point are within 0.0743, and more importantly, the errors of the lowest frequency difference and the lowest frequency value are only 0.0349 and 0.0388, respectively. Therefore, the method proposed in this invention not only considers the complexity of frequency dynamics in new power systems and describes the state of the lowest frequency point under disturbances from a probabilistic perspective, but also significantly improves the solution speed while ensuring solution accuracy, thus meeting the requirements of real-time analysis and control.

[0137] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. An analytical method for probabilistic estimation of the frequency minimum point after a disturbance in a power system containing new energy sources, characterized in that, The analytical method for probabilistic estimation of the frequency minimum point first analyzes the influencing factors of the frequency minimum point of the power system after disturbance and extracts the probabilistic characteristics of each influencing factor; then, it establishes an analytical expression of the influencing factors and the frequency minimum point; finally, it performs a specific nonlinear function transformation on the analytical expression to calculate the probability density function of each parameter at the minimum point; the steps are as follows: S1: Taking the initial frequency, number of disturbances, and system frequency response capability at the time of disturbance as the influencing factors on the lowest frequency point of the power system after disturbance, the probability characteristics of the initial frequency and number of disturbances are described by calculating the probability vector (PDF) using the Gaussian Model (GMM). For the system frequency response capability, a model is first constructed, and then the wind speed and thermal power unit status are calculated using the GMM. The probability characteristics are described by combining the model and the PDF. S2: Before probability estimation, it is necessary to first construct an analytical expression between the minimum point and the influencing factors. The establishment of the analytical expression is based on the frequency response model. The frequency response model is as follows: the input term is a disturbance, which outputs the frequency difference after passing through the inertial response stage. An additional frequency modulation stage is added from the output to the input to make the frequency response model form a closed-loop feedback. The frequency response model is simplified and analyzed to construct an analytical expression between the influencing factors and the minimum point parameters. S3: The frequency minimum point of a power system has two parameters: the time to reach the minimum point and the value of the frequency minimum point. The probability estimation of the analytical properties of these two parameters is performed, including the probability distribution of the frequency minimum point after the disturbance of the new energy power system.

2. The analytical method for probabilistic estimation of the frequency minimum point after disturbance in a power system containing new energy sources, as described in claim 1, is characterized in that... The specific steps of S1 are as follows: S1-1: For the uncertainty of the initial frequency and the number of disturbances, the probabilistic characteristics of the two are described based on the PDF extracted by GMM; S1-2: For the uncertainty of the system frequency response capability, only wind power and thermal power are considered. First, the inertial response link and primary frequency regulation link models are constructed for each of them respectively. In terms of inertial response modeling, the inertial time constant of thermal power is taken as a fixed value, while the inertial time constant of wind power is calculated using equation (1). In the formula, H wg Let λ be the wind turbine inertial time constant, λ be the tip speed ratio, and v be the blade tip rotation speed ratio. w For wind speed, K G R is the gearbox ratio, R is the rotor radius, and J is the rotor radius. wr J is the moment of inertia of the wind turbine generator. t Let S be the moment of inertia of the wind turbine. wg For wind turbine capacity; The inertial time constants of wind power and thermal power are weighted and aggregated to obtain the system inertial time constant, as shown in equation (2). In the formula, H total H is the total inertial time constant of the system. wg_i H gt_j Let S be the inertial time constant of the i-th wind turbine and the j-th thermal power unit. wg_i S gt_j Let n be the capacity of the i-th wind turbine and the j-th thermal power unit, and m be the number of wind turbines and thermal power units, respectively. Based on equation (2) and the PDF of wind speed, the probabilistic characteristics of the system inertia are described. The PDF of wind speed is obtained from GMM. S1-3: Regarding the modeling of the primary frequency regulation link, for the primary frequency regulation link of thermal power, the governor model of IEEE G1 is adopted. The governor gain coefficient K in the governor model can reflect the frequency regulation capability of the unit. The uncertainty of the frequency response capability of thermal power unit comes from the heat storage state of the unit. Therefore, the analytical expression shown in equation (3) is established. In the formula, K fr C is a fixed parameter within the unit. E Where P0 is the heat storage coefficient, V0 is the main steam pressure, and R is the valve opening. t This refers to the unit's droop coefficient; Based on the PDF of main steam pressure and valve opening and the IEEE G1 governor model, the probabilistic characteristics of primary frequency regulation of thermal power are described. The PDF of main steam pressure and valve opening is obtained from GMM. S1-4: For the primary frequency regulation stage of wind power, a speed governor model is used for description, and the parameters are calculated as shown in equations (4)-(7). J wg *J wr ·K G 2 +J t (4) P MPPT =k opt oh 3 (6) λ=K G Rω / v (7) In the formula, J wg Let ω be the fan inertia, ρ be the rotor speed, and C be the air density. p Where is the wind energy utilization coefficient, v is the wind speed, λ is the tip speed ratio, and K is the tip speed ratio. G P is the gearbox ratio. MPPT To control the output power of the fan in MPPT mode, k opt This represents the wind turbine control coefficient; thus, based on S1-4 and the wind speed PDF, the probabilistic characteristics of wind power primary frequency regulation are described. The wind speed PDF is obtained from GMM.

3. The analytical method for probabilistic estimation of the frequency minimum point after disturbance in a power system containing new energy sources, as described in claim 2, is characterized in that... In S1-4, the speed governor model is specifically as follows: the input is the system frequency difference Δf, and firstly, based on the virtual droop coefficient K... dr Generate the wind turbine power increment signal ΔP set Based on the power signal, via 1 / J wg The change in fan rotor speed is calculated using ω0s. The change in rotor speed is then subtracted from the initial speed ω0 to obtain the frequency-adjusted rotor speed ω. This ω is then substituted into equation (6) to calculate the fan output power P at this speed. MPPT Substituting the initial rotor speed ω0 into equation (5), the initial captured power P of the fan is calculated. Me0 Ultimately through P MPPT +P Me0 -ΔP set The actual output power of the fan is calculated and used as the output.

4. The analytical method for probabilistic estimation of the frequency minimum point after disturbance in a power system containing new energy sources, as described in claim 2, is characterized in that... The specific steps of S2 are as follows: S2-1: For the analytical description of the probabilistic characteristics of the system's frequency regulation capability, the external characteristics of the speed governor in the time domain are used to describe it, that is, the output of the speed governor as a function of time when responding to disturbances. Specifically: First, the external characteristics of the speed controller are fitted using a high-order polynomial according to equation (8): G k (t)=a Gk,0 +a Gk,1 t+a Gk,2 t 2 (8) In the formula, G k (t) represents the time-domain output of the governor of unit k within the system, α Gk,0 α Gk,1 α Gk,2 These are the constants, linear coefficients, and quadratic coefficients in the governor output fitting of unit k, respectively. Using GMM cluster analysis of the datasets of wind speed, main steam pressure, and valve opening, the cluster centers in the clustering results are extracted as representative data points. The governor external characteristic fitting coefficients are calculated for each representative data point. Based on the probability of each representative data point, the governor external characteristic fitting coefficients of wind power and thermal power are weighted to synthesize the probabilistic output expression of the system's primary frequency regulation stage. In the formula, α G_sys,i λ is the coefficient of the i-th term of the output curve of the system speed controller, q is the number of representative operating points, and λ is the coefficient of the i-th term. k α is the weight of the representative working condition k. Gk,i The coefficient of the i-th term of the governor output curve under representative working condition k; S2-2: To construct the relationship between influencing factors and the minimum point parameter, based on the simplified solution of the transfer function model and combined with equation (8), the power expression of the system frequency response containing new energy sources is obtained as follows: In the formula, k represents the kth unit of the total number of units in the system; Combining the above formulas (9) and (10), we obtain the analytical model for the lowest frequency point containing new energy sources: In the formula, α G_sys,1 α is the coefficient of the first term of the output curve of the system speed controller. G_sys,2 t represents the coefficient of the quadratic term of the output curve of the system speed controller. M It is the time to reach the lowest frequency point, f. nadir It is the lowest frequency value, f0 is the initial frequency before the disturbance, and Δf M It is the frequency difference at the lowest point.

5. The analytical method for probabilistic estimation of the frequency minimum point after disturbance in a power system containing new energy sources, as described in claim 4, is characterized in that... In S3, the minimum frequency of the power system has two parameters: the time to reach the minimum point and the value of the minimum frequency. The probability estimation of the analytical properties of these two parameters needs to be based on the characteristics of the expressions in equations (11) and (12), respectively. The specific steps are as follows: S3-1: The probability estimation of the time to reach the minimum point needs to be based on equation (11), where H in equation (11)... total As the probability quantity to be determined, according to equation (1), the probability of the inertial time constant of a single fan follows the pattern H. wg ~f V (v w 2 Therefore, when multiple wind turbines are connected to the grid, according to the central limit theorem, H total The probability density function can be viewed as the sum of the probability density functions of the squares of multiple independent and identically distributed wind speeds, that is: In the formula, E Htotal σ is the expected value of the system's total inertial time constant. Htotal E is the standard deviation of the system's total inertial time constant. Hwg σ is the expected value of the inertial time constant of the wind turbine. Hwg The inertial time constant of the wind turbine unit; Equation (11) is denoted as t M =g(H total According to the principles of probability, when H is known... total When the probability density function is t M The probability density function is expressed as: In the formula, f Ht For H total The probability density function, f tM For t M The probability density function; S3-2: Probabilistic estimation of the frequency value at the minimum point using analytical properties; Calculate Δf M According to equation (12), the PDF's function transformation process first constructs a mapping relationship to form a new random variable: Based on the mapping relationship, obtain the Jacobian matrix, and then obtain the new function composed of the new variables S1, S2, and S3 according to the probability density functions of the variables x, y, and z: S1 represents the original function h(x,y,z), therefore, by taking the marginal density of S1 in equation (18), Δf can be obtained. M The probability density function; Finally, convolution is used to obtain f. nadir The probability density function: In the formula, f fnadir f nadir The probability density function, f f0 Let f be the probability density function of the initial frequency f0. ΔfM The lowest point frequency Δf M The probability density function.

Images