Frequency lowest point probability estimation analysis method after new energy power system is disturbed

Abstract

The invention provides a frequency lowest point probability estimation analysis method after a new energy power system is disturbed, and belongs to the field of power system frequency stability analysis. The frequency lowest point probability estimation analysis method comprises the following steps: firstly, analyzing influence factors of a frequency lowest point of a disturbed power system, and extracting probability characteristics of each influence factor; then, establishing analytic expressions of the influence factors and the lowest point of the frequency; and finally, performing specific nonlinear function transformation on the analytic expression, and quickly and accurately calculating the probability distribution condition of the lowest point of the frequency after the power system containing the new energy is disturbed. According to the method, the probability characteristics of the power system at the initial frequency, the disturbance quantity and the unit state can be considered, and the probability distribution condition of the lowest point of the frequency of the disturbed power system is calculated through an analytical method, so that a more reliable basis can be provided for stable analysis and control of the frequency of the power system quickly and accurately.

Description

Technical Field

[0001] The invention belongs to the field of power system frequency stability analysis and relates to a method for estimating the probability of the lowest frequency point of a power system containing new energy after being disturbed. Background Art

[0002] After a power system is subjected to a large disturbance, the system frequency will undergo a more intense and complex dynamic process, either recovering to a quasi-steady-state frequency after several oscillations and maintaining stability, or losing control and deviating significantly from the rated value in an oscillating or monotonically increasing / decreasing manner and eventually becoming unstable. In system operation management, it is necessary to analyze future or anticipated operation scenarios to obtain the frequency dynamic process after the system is disturbed, and then quickly and accurately evaluate the frequency safety level, thereby providing a basis and reference for planning and operation.

[0003] The frequency dynamic process can be described by differential equations (rotor motion equations), and its solution methods currently include three categories: time domain simulation method, model analysis method and machine learning method. Among them, the model analysis method can give the analytical relationship between the system 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 achieved relatively rich research results.

[0004] The factors that affect the frequency dynamic process, that is, the boundary conditions for solving the differential equation, mainly include: the active power shortage caused by the disturbance (referred to as power shortage), the initial frequency deviation at the time of the disturbance (referred to as initial frequency difference), and the frequency response capability of the system at the time of the disturbance (referred to as response capability, including inertia and primary frequency regulation capability). In the actual operation of the power system, the above three influencing factors are constantly changing randomly, that is, these influencing factors are random variables. This means that the frequency dynamic process affected by them is a random variable with probability.

[0005] In the past, as the system operation status was relatively stable and the frequency regulation resources were relatively sufficient, the system operation analysis was carried out based on the deterministic frequency dynamic process analysis results. The results had little deviation and could fully meet the analysis accuracy requirements of system safe operation planning and program formulation and control strategy design. Therefore, the deterministic analysis method has been adopted in actual power grid operation.

[0006] If deterministic analysis is adopted, the probabilistic characteristics of the above three boundary conditions are ignored and deterministic values ​​are adopted, namely: 1) The power shortage adopts the maximum value: only the most serious 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 adjustment capabilities of all control elements and it always remains unchanged.

[0007] With the continuous increase in the proportion of new energy capacity, frequency regulation resources are increasingly scarce, the frequency stability situation is becoming increasingly tense, the uncertainty of operating parameters is increasing, the fluctuation range of operating conditions is increasing, the system operation state is becoming more and more extreme, and the adjustment capacity of frequency regulation resources is also gradually increasing with the fluctuation range of operating conditions. This leads to the increasingly significant probability characteristics of the frequency dynamic process after the system is disturbed. At this time, if the existing deterministic analysis method is still used, the obtained frequency dynamic process may not accurately and comprehensively characterize the system frequency security state and evolution trend, resulting in loopholes in the three lines of security defense set up based on its analysis results, thus burying safety hazards.

[0008] Judging from the current research results, the research on the probability analysis of the frequency dynamic process after the system is disturbed is still in the exploratory stage. In the few studies conducted from a probabilistic perspective, there is insufficient consideration of system uncertainty factors, such as only taking the uncertainty of wind power output fluctuations as the source of disturbance and describing it with Weibull distribution; or there is low computational efficiency, such as using time domain simulation method to obtain the lowest / highest frequency point after the system is disturbed. Therefore, it is necessary to carry out research on the analytical method of probabilistic estimation of the lowest frequency point after the power system containing new energy is disturbed.

[0009] The present invention proposes an analytical method for estimating the probability of the lowest frequency point after a power system containing renewable energy is disturbed. The method provides a framework, firstly analyzes the influencing factors in the frequency dynamic process, and extracts the probability characteristics of each factor, then establishes an analytical expression of the influencing factors and the lowest frequency point, and finally uses a specific nonlinear function transformation to calculate the probability density function of each parameter of the lowest point. The proposed method can quickly and accurately calculate the probability distribution of the lowest frequency point after a power system containing renewable energy is disturbed. Summary of the invention

[0010] The frequency fluctuation of the new power system is becoming more and more complicated. At present, the stability model of the power system after power electronics can still be abstracted as the rotor motion equation. The essence of the analysis of the frequency dynamic process after the disturbance is still the solution of the differential equation group, but it is difficult to obtain an explicit solution through an analytical method. Therefore, in order to solve the lowest frequency point, the present invention transforms the time domain problem into a non-time domain problem, and constructs a method for analytical estimation of the probability of the lowest frequency point: the first step is to classify and describe the influencing factors of the lowest frequency point of the power system after the disturbance (hereinafter referred to as the lowest point), and the Gaussian mixture model (GMM, Gaussian mixture model) is used to calculate the probability density function (PDF, probability density function) of the factors that can be directly obtained through data. function) to describe the factors. For the factors that need to be described by the model, the model is first built, and then the PDF of the parameters that can reflect the uncertainty is calculated by GMM, and the PDF and the model are combined to describe the factors; the second step is to construct the analytical expression between the influencing factors and the lowest point parameters by simplifying the model and fitting the output curve with polynomials; finally, the analytical expression is transformed by a specific nonlinear function, and the expression relationship between the PDF of the influencing factors and the PDF of the lowest point is established, and the PDF of the lowest point is calculated by the PDF of the influencing factors. The proposed method can quickly and accurately calculate the probability distribution of the lowest point of the frequency after the power system containing new energy is disturbed.

[0011] In order to achieve the above object, the technical solution adopted by the present invention is:

[0012] A method for estimating the probability of the lowest frequency point after a power system containing new energy sources is disturbed, comprising the following steps:

[0013] S1: The present invention uses the initial frequency at the time of disturbance, the number of disturbances, and the system frequency response capability as the influencing factors of the lowest frequency point of the power system after the disturbance, uses GMM to calculate PDF for the initial frequency and the number of disturbances to describe the probability characteristics, first builds a model for the system frequency response capability, and then uses GMM to calculate PDF for the wind speed and the state of the thermal power unit, and combines the model with PDF to describe the probability characteristics. The specific steps are as follows:

[0014] S1-1: There are many reasons for the uncertainty of the initial frequency and the number of disturbances, and the formation process is also relatively complex and difficult to analyze. According to the probability statistics theory, the description of the probability characteristics of the two in the present invention is based on the GMM extraction PDF.

[0015] S1-2: With regard to the uncertainty of the system frequency response capability, the present invention only considers two energy sources, wind power and thermal power. First, the inertial response link and primary frequency regulation link models are constructed for the two respectively.

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

[0017]

[0018] In the formula, H wg is the wind power inertia time constant, λ is the blade tip speed ratio, v w is the wind speed, K G is the gearbox ratio, R is the wind wheel radius, J wr is the moment of inertia of the wind turbine generator, J t is the moment of inertia of the wind wheel, S wg is the capacity of wind turbine.

[0019] By weighting and aggregating the inertia time constants of wind power and thermal power, the system inertia time constant can be obtained, as shown in formula (2):

[0020]

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

[0022] At this point, the probability characteristics of the system inertia can be described based on equation (2) and the PDF of wind speed, which is obtained by GMM.

[0023] S1-3: In terms of modeling of primary frequency regulation, for thermal power primary frequency regulation, the IEEE G1 speed regulator 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, and 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 formula (3) is established.

[0024]

[0025] In the formula, K fr is a fixed parameter in the unit, C E is the heat storage coefficient, P0 is the main steam pressure, V0 is the valve opening, R t is the unit adjustment coefficient.

[0026] At this point, the probability characteristics of primary frequency regulation of thermal power 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 by GMM.

[0027] S1-4: For the primary frequency regulation link of wind power, the speed regulator model in Figure (3) can be used to describe it, where 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 is the fan inertia, ω is the rotor speed, ρ is the air density, C p is the wind energy utilization coefficient, v is the wind speed, λ is the tip speed ratio, K G is the gearbox ratio, P MPPT is the output power of the fan controlled in MPPT mode, k opt is the fan control coefficient.

[0033] Furthermore, in S1-4, the speed regulator model is specifically as follows: the input is the system frequency difference Δf, firstly according to the virtual droop coefficient K dr , generate the fan power increment signal ΔP set , according to the power signal, through 1 / J wg ω0s is used to calculate the change in the fan rotor speed. The rotor speed change is subtracted from the initial speed ω0 to obtain the rotor speed after frequency modulation ω. Substituting it into formula (6) is used to calculate the fan output power P at this speed. MPPT , put the initial rotor speed ω0 into formula (5) to calculate the initial captured power P of the fan Me0 , and finally MPPT +P Me0 -ΔP set The actual output of the fan frequency regulation is calculated as output, such as Figure 2 shown.

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

[0035] S2: The probability estimation method of the lowest point analytical property proposed in the present invention needs to construct an analytical expression between the lowest point and the influencing factor before the probability estimation. The establishment of the analytical expression relies on the frequency response model. The frequency response model relied on by the present invention is: the input term is the disturbance, the frequency difference is output through the inertial response link, and a frequency modulation link is added from the output to the input, so that the model forms a closed-loop feedback. The model is as follows Figure 3 The model is simplified and analyzed to construct an analytical expression between the influencing factors and the lowest point parameters. The specific steps are as follows:

[0036] S2-1: For the analytical description of the probability characteristics of the system frequency regulation capability, the present invention describes it using the external characteristics of the speed regulator in the time domain, that is, the function of the output size and time of the speed regulator when responding to disturbances, specifically:

[0037] First, a high-order polynomial fitting is performed on the external characteristics of the speed regulator according to formula (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) is the time domain representation of the governor output of unit k in the system, α Gk,0 , α Gk,1 , α Gk,2 They are respectively the constant, first-order coefficient and second-order coefficient in the governor output fitting of unit k.

[0040] GMM clustering is used to analyze the data sets of wind speed, main steam pressure and valve opening, and the cluster centers in the clustering results are extracted as representative data points. The governor external characteristic fitting coefficients under each representative data point are calculated respectively. The governor external characteristic fitting coefficients of wind power and thermal power are weighted according to the probability of each representative data point, and the output expression with probabilistic characteristics of the total primary frequency regulation link of the synthesis system is:

[0041]

[0042] In the formula, α G_sys,i is the i-th order coefficient of the system speed regulator output curve, q is the number of representative operating points, λ k is the weight of the representative working condition k, α Gk,i is the i-th order coefficient of the speed regulator output curve of the representative working condition k.

[0043] S2-2: In order to build the relationship between the influencing factors and the lowest point parameters, the simplified solution of the ASF mode of the system containing new energy was carried out. Based on the simplified solution of the transfer function model and combined with equation (8), the frequency response power expression of the system containing new energy can be obtained as follows:

[0044]

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

[0046] Combining the above formulas (9) and (10), the frequency minimum point analytical model containing new energy is obtained:

[0047]

[0048] In the formula, α G_sys,1 is the first-order coefficient of the output curve of the system speed regulator link, α G_sys,2 is the quadratic coefficient of the system speed regulator output curve, t M is the time to reach the lowest frequency point, f nadir is the lowest frequency point value, f0 is the initial frequency before disturbance, Δf M It is the frequency difference reaching the lowest point.

[0049] S3: The frequency minimum point of the power system has two parameters: the time to reach the minimum point and the frequency minimum point value. The probability estimation of the analytical properties of the two needs to be based on the expression characteristics of 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 lowest point needs to be based on formula (11), where H total is the probability quantity to be determined. According to formula (1), the probability of the inertia time constant of a single fan obeys H wg ~f V (v w 2 ), so when multiple wind turbines are connected to the grid, according to the central limit theorem, H total The probability density function of can be regarded as the sum of the probability density functions of multiple independent and identically distributed wind speed squares, that is:

[0051]

[0052] In the formula, E Htotal is the expectation of the total inertia time constant of the system, σ Htotal is the standard deviation of the total inertia time constant of the system, E Hwg is the expected inertia time constant of the wind turbine, σ Hwg is the inertia time constant of the wind turbine.

[0053] Formula (11) can be expressed as tM =g(H total ), according to the principle of probability, when H is known total When the probability density function is M The probability density function of can be expressed as:

[0054]

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

[0056] S3-2: Then the probability of the analytical properties of the lowest point frequency value is estimated;

[0057] First calculate Δf M The PDF of , according to formula (12), its function transformation process can first construct a mapping relationship to form a new random variable:

[0058]

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

[0060]

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

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

[0063]

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

[0065] The beneficial effects of the present invention are:

[0066] The present invention can take into account the probability characteristics of the initial frequency, disturbance quantity and unit status of the power system, and calculate the probability distribution of the lowest frequency point of the power system after the disturbance through an analytical method, thereby providing a more reliable basis for the frequency stability analysis and control of the power system both quickly and accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is the IEEE G1 governor model.

[0068] Figure 2 This is the wind turbine speed governor model.

[0069] Figure 3 Frequency tuning model for the system

[0070] Figure 4 To improve the IEEE10 machine 39 node system.

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

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

[0073] Figure 7 Comparison of PDF and CDF of the lowest frequency point value. DETAILED DESCRIPTION

[0074] The present invention is further described below in conjunction with specific implementation cases.

[0075] In order to make the technical solutions and advantages of the present invention clearer, the following is introduced: Figure 4 The improved IEEE 10-machine 39-node system shown in the figure has the following improvements: on the basis of the original system, four thermal power units are replaced by four wind farms, and the thermal power and wind power unit speed regulator models are shown in S1-3 and S1-4, where the parameters are shown in Table 1. The technical solution of the present invention is described clearly and completely below in conjunction with specific embodiments and drawings.

[0076] Table 1 Improved IEEE 10-machine 39-node system parameters

[0077]

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

[0079] A method for estimating the probability of the lowest frequency point after a power system containing new energy sources is disturbed, comprising the following steps:

[0080] S1: The present invention uses the initial frequency at the time of disturbance, the number of disturbances, and the system frequency response capability as the influencing factors of the lowest frequency point of the power system after the disturbance, uses GMM to calculate PDF for the initial frequency and the number of disturbances to describe the probability characteristics, first builds a model for the system frequency response capability, and then uses GMM to calculate PDF for the wind speed and the state of the thermal power unit, and combines the model with PDF to describe the probability characteristics. The specific steps are as follows:

[0081] S1-1: There are many reasons for the uncertainty of the initial frequency and the number of disturbances, and the formation process is also relatively complex and difficult to analyze. According to the probability statistics theory, the description of the probability characteristics of the two in the present invention is based on the GMM extraction PDF.

[0082] S1-2: With regard to the uncertainty of the system frequency response capability, the present invention only considers two energy sources, wind power and thermal power. First, the inertial response link and primary frequency regulation link models are constructed for the two respectively.

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

[0084]

[0085] In the formula, H wg is the wind power inertia time constant, λ is the blade tip speed ratio, v w is the wind speed, K G is the gearbox ratio, R is the wind wheel radius, J wr is the moment of inertia of the wind turbine generator, J t is the moment of inertia of the wind wheel, S wg is the capacity of wind turbine.

[0086] By weighting and aggregating the inertia time constants of wind power and thermal power, the system inertia time constant can be obtained, as shown in formula (2):

[0087]

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

[0089] At this point, the probability characteristics of the system inertia can be described based on equation (2) and the PDF of wind speed, which is obtained by GMM.

[0090] S1-3: In terms of modeling of primary frequency regulation, for thermal power primary frequency regulation, the IEEE G1 speed regulator 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, and 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 formula (3) is established.

[0091]

[0092] In the formula, K fr is a fixed parameter in the unit, C E is the heat storage coefficient, P0 is the main steam pressure, V0 is the valve opening, R t is the unit adjustment coefficient.

[0093] At this point, the probability characteristics of primary frequency regulation of thermal power 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 by GMM.

[0094] S1-4: For the primary frequency regulation link of wind power, the speed regulator model in Figure (3) can be used to describe it, where 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 is the fan inertia, ω is the rotor speed, ρ is the air density, C p is the wind energy utilization coefficient, v is the wind speed, λ is the tip speed ratio, K G is the gearbox ratio, P MPPT is the output power of the fan controlled in MPPT mode, k opt is the fan control coefficient.

[0100] Furthermore, in S1-4, the speed regulator model is specifically as follows: the input is the system frequency difference Δf, firstly according to the virtual droop coefficient K dr, generate the fan power increment signal ΔP set , according to the power signal, through 1 / J wg ω0s is used to calculate the change in the fan rotor speed. The rotor speed change is subtracted from the initial speed ω0 to obtain the rotor speed after frequency modulation ω. Substituting it into formula (6) is used to calculate the fan output power P at this speed. MPPT , put the initial rotor speed ω0 into formula (5) to calculate the initial captured power P of the fan Me0 , and finally MPPT +P Me0 -ΔP set The actual output of the fan frequency regulation is calculated as output, such as Figure 2 shown.

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

[0102] S2: The probability estimation method of the lowest point analytical property proposed in the present invention needs to construct an analytical expression between the lowest point and the influencing factor before the probability estimation. The establishment of the analytical expression relies on the frequency response model. The frequency response model relied on by the present invention is: the input term is the disturbance, the frequency difference is output through the inertial response link, and a frequency modulation link is added from the output to the input, so that the model forms a closed-loop feedback. The model is as follows Figure 3 The model is simplified and analyzed to construct an analytical expression between the influencing factors and the lowest point parameters. The specific steps are as follows:

[0103] S2-1: For the analytical description of the probability characteristics of the system frequency regulation capability, the present invention describes it using the external characteristics of the speed regulator in the time domain, that is, the function of the output size and time of the speed regulator when responding to disturbances, specifically:

[0104] First, a high-order polynomial fitting is performed on the external characteristics of the speed regulator according to formula (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) is the time domain representation of the governor output of unit k in the system, α Gk,0 , α Gk,1 , α Gk,2 They are respectively the constant, first-order coefficient and second-order coefficient in the governor output fitting of unit k.

[0107] GMM clustering is used to analyze the data sets of wind speed, main steam pressure and valve opening, and the cluster centers in the clustering results are extracted as representative data points. The governor external characteristic fitting coefficients under each representative data point are calculated respectively. The governor external characteristic fitting coefficients of wind power and thermal power are weighted according to the probability of each representative data point, and the output expression with probabilistic characteristics of the total primary frequency regulation link of the synthesis system is:

[0108]

[0109] In the formula, α G_sys,i is the i-th order coefficient of the system speed regulator output curve, q is the number of representative operating points, λ k is the weight of the representative working condition k, α Gk,i is the i-th order coefficient of the speed regulator output curve of the representative working condition k.

[0110] S2-2: In order to build the relationship between the influencing factors and the lowest point parameters, the simplified solution of the ASF mode of the system containing new energy was carried out. Based on the simplified solution of the transfer function model and combined with equation (8), the frequency response power expression of the system containing new energy can be obtained as follows:

[0111]

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

[0113] Combining the above formulas (9) and (10), the frequency minimum point analytical model containing new energy is obtained:

[0114]

[0115] In the formula, α G_sys,1 is the first-order coefficient of the output curve of the system speed regulator link, α G_sys,2 is the quadratic coefficient of the system speed regulator output curve, t M is the time to reach the lowest frequency point, f nadir is the lowest frequency point value, f0 is the initial frequency before disturbance, Δf M It is the frequency difference reaching the lowest point.

[0116] S3: The frequency minimum point of the power system has two parameters: the time to reach the minimum point and the frequency minimum point value. The probability estimation of the analytical properties of the two needs to be based on the expression characteristics of 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 lowest point needs to be based on formula (11), where H total is the probability quantity to be determined. According to formula (1), the probability of the inertia time constant of a single fan obeys H wg~f V (v w 2 ), so when multiple wind turbines are connected to the grid, according to the central limit theorem, H total The probability density function of can be regarded as the sum of the probability density functions of multiple independent and identically distributed wind speed squares, that is:

[0118]

[0119] In the formula, E Htotal is the expectation of the total inertia time constant of the system, σ Htotal is the standard deviation of the total inertia time constant of the system, E Hwg is the expected inertia time constant of the wind turbine, σ Hwg is the inertia time constant of the wind turbine.

[0120] Formula (11) can be expressed as t M =g(H total ), according to the principle of probability, when H is known total When the probability density function is M The probability density function of can be expressed as:

[0121]

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

[0123] In this example, the results obtained by the probability estimation method proposed by the present invention are compared with the results obtained by the same model simulation method. The implementation plan of the same model simulation method is: randomly sample the data sets of initial frequency, disturbance number, and unit status to determine their values, repeat 10,000 times of time domain simulation of the frequency dynamic process after the system is disturbed, the simulation time is 30 seconds, and 10,000 lowest point data are obtained according to the frequency dynamic curve of each simulation, and the probability of each parameter is sorted and analyzed. The probability density curve and probability distribution curve of the time to reach the lowest point calculated by the two methods are shown in Figure 2. Figure 5 The comparison of the calculation efficiency and accuracy of the two methods is shown in Table 2.

[0124] S3-2: Then the probability of the analytical properties of the lowest point frequency value is estimated;

[0125] First calculate Δf M The PDF of , according to formula (12), its function transformation process can first construct a mapping relationship to form a new random variable:

[0126]

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

[0128]

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

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

[0131]

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

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

[0134] Table 2 Probability estimation accuracy and computational efficiency

[0135]

[0136] In terms of computational efficiency, compared with the Monte Carlo method, the computational efficiency of the analytical method is improved by 99.52%; in terms of computational accuracy, under the KL divergence evaluation standard, the errors of each parameter at the lowest frequency point are all within 0.0743, and the more important lowest frequency difference and lowest frequency value, the errors are only 0.0349 and 0.0388 respectively. It can be seen that the method proposed in the present invention can not only take into account the complexity of the frequency dynamic process under the new power system, and describe the state of the lowest frequency point under disturbance from a probabilistic perspective, but also significantly improve the solution speed on the basis of ensuring the solution accuracy, thereby meeting the requirements of real-time analysis and control.

[0137] The above-described embodiments merely express the implementation methods of the present invention, but they should not be understood as limiting the scope of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for estimating the probability of the lowest frequency point after a disturbance in a power system containing new energy, characterized in that: The frequency minimum point probability estimation analytical method first analyzes the influencing factors of the frequency minimum point of the power system after the disturbance and extracts the probability characteristics of each influencing factor; then, an analytical expression of the influencing factors and the frequency minimum point is established; finally, the analytical expression is transformed into a specific nonlinear function to calculate the probability density function of each parameter of the minimum point; the steps are as follows: S1: The initial frequency at the time of disturbance, the number of disturbances, and the system frequency response capability are used as the influencing factors for the lowest frequency point of the power system after the disturbance. The initial frequency and the number of disturbances are calculated using GMM to describe the probability characteristics of PDF. A model is first built for the system frequency response capability, and then the wind speed and the state of the thermal power unit are calculated using GMM to calculate PDF. The probability characteristics are described by combining the model and PDF: S2: Before probability estimation, it is necessary to first construct an analytical expression between the lowest point and the influencing factors. The establishment of the analytical expression relies on the frequency response model. The frequency response model is: the input item is the disturbance, the frequency difference is output after the inertial response link, and a frequency modulation link is added from output to 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 lowest point parameters; S3: The lowest frequency point of the power system has two parameters: the time to reach the lowest point and the value of the lowest frequency point. The probability estimation of the analytical properties of the two is carried out, including the probability distribution of the lowest frequency point after the new energy power system is disturbed.

2. According to claim 1, a method for estimating the probability of the lowest frequency point of a power system containing new energy after a disturbance, characterized in that: The specific steps of S1 are as follows: S1-1: For the uncertainty of initial frequency and disturbance quantity, the description of their probability characteristics is based on the GMM extraction PDF; S1-2: For the uncertainty of the system frequency response capability, only two energy sources, wind power and thermal power, are considered. First, the inertial response link and primary frequency regulation link models are constructed for the two respectively; In terms of inertial response modeling, the inertia time constant of thermal power is taken as a fixed value, and the inertia time constant of wind power is calculated by formula (1): In the formula, H wg is the wind power inertia time constant, λ is the blade tip speed ratio, v w is the wind speed, K G is the gearbox ratio, R is the wind wheel radius, J wr is the moment of inertia of the wind turbine generator, J t is the moment of inertia of the wind wheel, S wg is the capacity of wind turbine; The inertia time constants of wind power and thermal power are weighted and aggregated to obtain the system inertia time constant, as shown in formula (2): In the formula, H total is the total inertia time constant of the system, H wg_i , H gt_j is the inertia time constant of the i-th wind turbine and the j-th thermal power unit, S wg_i , S gt_j is the capacity of the i-th wind turbine and the j-th thermal power unit, n and m are the number of wind turbines and thermal power units; So far, the probability characteristics of system inertia are described according to equation (2) and the PDF of wind speed, and the PDF of wind speed is obtained by GMM; S1-3: In terms of modeling of the primary frequency regulation link, for the primary frequency regulation link of thermal power, the IEEE G1 speed regulator model is adopted. The speed regulator gain coefficient K in the speed regulator 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 formula (3) is established. In the formula, K fr is a fixed parameter in the unit, C E is the heat storage coefficient, P0 is the main steam pressure, V0 is the valve opening, R t is the unit adjustment coefficient; So far, the probability characteristics of primary frequency regulation of thermal power are 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 by GMM; S1-4: For the primary frequency regulation link of wind power, the speed regulator model is used for description, and the calculation of parameters is as shown in equations (4)-(7). I 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 is the fan inertia, ω is the rotor speed, ρ is the air density, C p is the wind energy utilization coefficient, v is the wind speed, λ is the tip speed ratio, K G is the gearbox ratio, P MPPT is the output power of the fan controlled in MPPT mode, k opt is the wind turbine control coefficient; so far, the probability characteristics of wind power primary frequency regulation are described based on S1-4 and the PDF of wind speed, and the PDF of wind speed is obtained by GMM.

3. According to claim 2, a method for estimating the probability of the lowest frequency point of a power system containing new energy after a disturbance, characterized in that: In S1-4, the speed regulator model is specifically as follows: the input is the system frequency difference Δf, firstly according to the virtual droop coefficient K dr , generate the fan power increment signal ΔP set , according to the power signal, through 1 / J wg ω0s is used to calculate the change in the fan rotor speed. The rotor speed change is subtracted from the initial speed ω0 to obtain the rotor speed after frequency modulation ω. Substituting it into formula (6) is used to calculate the fan output power P at this speed. MPPT , put the initial rotor speed ω0 into formula (5) to calculate the initial captured power P of the fan Me0 , and finally MPPT +P Me0 -ΔP set The actual output of the fan frequency regulation is calculated as output.

4. According to claim 2, a method for estimating the probability of the lowest frequency point of a power system containing new energy after a disturbance, characterized in that: The specific steps of S2 are as follows: S2-1: For the analytical description of the probability characteristics of the system frequency regulation capability, the external characteristics of the speed regulator in the time domain are used to describe it, that is, the function of the output size and time of the speed regulator when responding to disturbances. Specifically: First, a high-order polynomial fitting is performed on the external characteristics of the speed regulator according to formula (8): G k (t)=a Gk,0 +a Gk,1 t+a Gk,2 t 2 (8) In the formula, G k (t) is the time domain representation of the governor output of unit k in the system, α Gk,0 , α Gk,1 , α Gk,2 They are the constant, first-order coefficient and second-order coefficient in the governor output fitting of unit k respectively; GMM clustering is used to analyze the data sets of wind speed, main steam pressure and valve opening, and the cluster centers in the clustering results are extracted as representative data points. The governor external characteristic fitting coefficients under each representative data point are calculated respectively. The governor external characteristic fitting coefficients of wind power and thermal power are weighted according to the probability of each representative data point, and the output expression with probabilistic characteristics of the total primary frequency regulation link of the synthesis system is: In the formula, α G_sys,i is the i-th order coefficient of the system speed regulator output curve, q is the number of representative operating points, λ k is the weight of the representative working condition k, α Gk,i is the coefficient of the i-th order of the speed governor output curve of the representative working condition k; S2-2: For the relationship between the influencing factors and the lowest point parameters, based on the simplified solution of the transfer function model and combined with equation (8), the frequency response power expression of the system containing new energy is obtained as follows: In the formula, k is the kth unit of the total number of units in the system; Combining the above formulas (9) and (10), the frequency minimum point analytical model containing new energy is obtained: In the formula, α G_sys,1 is the first-order coefficient of the output curve of the system speed regulator link, α G_sys,2 is the quadratic coefficient of the system speed regulator output curve, t M is the time to reach the lowest frequency point, f nadir is the lowest frequency point value, f0 is the initial frequency before disturbance, Δf M It is the frequency difference reaching the lowest point.

5. According to claim 4, a method for estimating the probability of the lowest frequency point of a power system containing new energy after a disturbance is described, characterized in that: In the above S3, the lowest frequency point of the power system has two parameters: the time to reach the lowest frequency point and the value of the lowest frequency point. The probability estimation of the analytical properties of the two parameters needs to be based on the expression characteristics of formula (11) and (12) respectively. The specific steps are as follows: S3-1: The probability estimation of the time to reach the lowest frequency point needs to be based on formula (11). In formula (11), H total is the probability quantity to be determined. According to formula (1), the probability of the inertia time constant of a single fan obeys H wg ~f V (v w 2 ), so when multiple wind turbines are connected to the grid, according to the central limit theorem, H total The probability density function of can be regarded as the sum of the probability density functions of multiple independent and identically distributed wind speed squares, that is: In the formula, E Htotal is the expectation of the total inertia time constant of the system, σ Htotal is the standard deviation of the total inertia time constant of the system, E Hwg is the expected inertia time constant of the wind turbine, σ Hwg is the inertia time constant of the wind turbine; Formula (11) is denoted as t M =g(H total ), according to the principle of probability, when H is known total When the probability density function is M The probability density function of is expressed as: In the formula, f Ht H total The probability density function, f tM t M The probability density function of S3-2: Probabilistic estimation of analytical properties of the lowest point frequency value; Calculate Δf M The PDF of , according to formula (12), its function transformation process first constructs a mapping relationship to form a new random variable: Based on the mapping relationship, the Jacobian matrix is ​​obtained, and the new function composed of new variables S1, S2, and S3 is obtained according to the probability density function of the variables x, y, and z: S1 represents the original function h(x, y, z), so the marginal density of S1 in equation (18) can be obtained to obtain Δf M The probability density function of Finally, convolution is applied to obtain f nadir The probability density function of is: In the formula, f fnadir f nadir The probability density function, f f0 is the probability density function of the initial frequency f0, f ΔfM is the lowest frequency Δf M The probability density function of .

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