Power system transient stability analysis method and device, power equipment, storage medium and program product

Abstract

The invention relates to a power system transient stability analysis method and device, power equipment, a computer readable storage medium and a computer program product. The method comprises the following steps: acquiring at least two random variables in a power system; determining an independent standard normal random variable based on the random variable, and obtaining a response function corresponding to the independent standard normal random variable; performing dimension reduction processing on the response function to obtain a one-dimensional function and a two-dimensional function corresponding to the response function; determining a one-dimensional probability feature corresponding to the independent standard normal random variable based on the one-dimensional function, and determining a two-dimensional probability feature corresponding to the independent standard normal random variable based on the two-dimensional function; determining a target probability feature of the response function according to the one-dimensional probability feature and the two-dimensional probability feature; and determining the transient stability of the power system according to the target probability characteristics. By adopting the method, the calculation amount can be reduced, and the transient stability analysis efficiency of the power system is improved.

Description

Technical Field

[0001] The present application relates to the field of electric power technology, and in particular to a method, device, electric power equipment, computer-readable storage medium and computer program product for analyzing transient stability of an electric power system. Background Art

[0002] The transient stability of the power system refers to the ability of the power system to recover to a stable operating state when it is subjected to a large disturbance (such as a short circuit fault). As a large number of renewable energy sources are connected to the power grid, the complexity of the power grid structure increases, and the dynamic behavior of the power system is affected by random factors, such as the randomness of renewable energy output, load power randomness, and parameter randomness. Under the influence of these random factors, the transient stability of the power system is a random event. In this case, the amount of calculation required for the transient stability analysis of the power system is large, and the corresponding efficiency is low. Summary of the invention

[0003] Based on this, it is necessary to provide a method, device, power equipment, computer-readable storage medium and computer program product for analyzing transient stability of a power system in order to improve the efficiency of transient stability analysis of the power system.

[0004] In a first aspect, the present application provides a method for analyzing transient stability of a power system, comprising:

[0005] obtaining at least two random variables in the power system;

[0006] Determine the corresponding independent standard normal random variable based on the random variable, and obtain the response function corresponding to the independent standard normal random variable;

[0007] Perform dimension reduction processing on the response function to obtain a one-dimensional function and a two-dimensional function corresponding to the response function;

[0008] Determine the one-dimensional probability characteristics corresponding to independent standard normal random variables based on the one-dimensional function, and determine the two-dimensional probability characteristics corresponding to independent standard normal random variables based on the two-dimensional function;

[0009] According to the one-dimensional probability characteristics and the two-dimensional probability characteristics, the target probability characteristics of the response function are determined;

[0010] Determine the transient stability of the power system based on the target probability characteristics.

[0011] In one embodiment, determining a one-dimensional probability feature corresponding to an independent standard normal random variable based on a one-dimensional function, and determining a two-dimensional probability feature corresponding to an independent standard normal random variable based on a two-dimensional function, includes:

[0012] Determine one-dimensional probability characteristics based on one-dimensional functions and one-dimensional Gauss-Hermite integration;

[0013] Determine two-dimensional probability characteristics based on two-dimensional functions and two-dimensional Gauss-Hermite integration; wherein,

[0014] The samples corresponding to the two-dimensional Gauss-Hermite integration are determined based on the one-dimensional samples corresponding to the one-dimensional Gauss-Hermite integration; the integration weights corresponding to the two-dimensional Gauss-Hermite integration are the product of the one-dimensional integration weights corresponding to the one-dimensional Gauss-Hermite integration.

[0015] In one embodiment, determining one-dimensional probability characteristics based on one-dimensional functions and one-dimensional Gauss-Hermite integration includes: determining one-dimensional samples and one-dimensional integration weights based on independent standard normal random variables; wherein, the one-dimensional samples include at least three sampling points, and the sum of the one-dimensional integration weights corresponding to each sampling point is equal to 1;

[0016] Determine the one-dimensional probability characteristics corresponding to the one-dimensional function based on the one-dimensional samples and one-dimensional integration weights and based on the one-dimensional Gauss-Hermite integration.

[0017] In one embodiment, the one-dimensional samples include sampling points with a value of 0, the total number of sampling points included in the one-dimensional samples is odd, and the sum of the values corresponding to each sampling point is 0.

[0018] In one embodiment, determining the transient stability of a power system according to the target probability characteristics includes:

[0019] When the target probability characteristic is within the preset probability characteristic range, determine that the power system is in transient stability;

[0020] When the target probability characteristic is greater than or less than the preset probability characteristic range, determine that the power system is in transient instability.

[0021] In one embodiment, the target probability characteristics include the mean and standard deviation; determining the transient stability of a power system according to the target probability characteristics includes: determining the fluctuation of the power system under the influence of random factors corresponding to the random variables based on the mean and standard deviation; the random factors include at least one of the following: renewable energy generation data, load power, parameters of power equipment, and environmental information of the power system; determine the transient stability of the power system according to the fluctuation.

[0022] In a second aspect, the present application also provides a device for analyzing the transient stability of a power system, including:

[0023] An acquisition module, configured to acquire at least two random variables in the power system;

[0024] A dimension reduction module, configured to determine corresponding independent standard normal random variables based on random variables, and obtain response functions corresponding to the independent standard normal random variables; perform dimension reduction processing on the response functions to obtain one-dimensional functions and two-dimensional functions corresponding to the response functions.

[0025] A determination module, configured to determine one-dimensional probability characteristics corresponding to the independent standard normal random variables based on the one-dimensional functions, and determine two-dimensional probability characteristics corresponding to the independent standard normal random variables based on the two-dimensional functions; determine target probability characteristics of the response functions according to the one-dimensional probability characteristics and the two-dimensional probability characteristics; determine the transient stability of the power system according to the target probability characteristics.

[0026] In a third aspect, the present application further provides a power device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, the steps of the above power system transient stability analysis method are implemented.

[0027] In a fourth aspect, the present application further provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above power system transient stability analysis method are implemented.

[0028] In a fifth aspect, the present application further provides a computer program product, including a computer program, and when the computer program is executed by a processor, the steps of the above power system transient stability analysis method are implemented.

[0029] For the above power system transient stability analysis method, device, power device, computer-readable storage medium, and computer program product, corresponding independent standard normal random variables are determined based on random variables, which can more accurately handle the correlation between input random variables; response functions corresponding to the independent standard normal random variables are obtained, and then by reducing the dimension of the response functions, one-dimensional functions and two-dimensional functions corresponding to the response functions are obtained. The target probability characteristics of the response functions are determined through the corresponding one-dimensional probability characteristics and two-dimensional probability characteristics, so as to determine the transient stability of the power system. This can avoid the curse of dimensionality caused by directly determining the target probability characteristics of the response functions, reduce the calculation amount, and thus help improve the efficiency of power system transient stability analysis. In addition, since this method does not require any modification to the mathematical structure or calculation process of the original model, the system behavior is evaluated and analyzed by sampling and analyzing data outside the model, so it is non-invasive, does not affect the normal operation of the power system, does not involve hardware modification or addition, reduces costs, and is more efficient in analyzing the transient stability of the power system. Description of the Drawings

[0030] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the drawings required for use in the embodiments of the present application or related technical descriptions will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0031] Figure 1 is a flow chart of a method for analyzing transient stability of a power system in one embodiment;

[0032] Figure 2 is another flow chart of a method for analyzing transient stability of a power system in one embodiment;

[0033] Figure 3 A sample schematic diagram of a secondary dimensionality reduction method in an embodiment;

[0034] Figure 4 is another flow chart of a method for analyzing transient stability of a power system in one embodiment;

[0035] Figure 5.1 is a graph showing the average error of the synchronous generator speed calculated based on the LHS and BDRM5 methods in one embodiment;

[0036] Figure 5.2 A variance diagram of the synchronous generator speed calculated based on the MCS, LHS and BDRM5 methods in one embodiment;

[0037] Figure 5.3 It is a third-order moment diagram of the rotation speed of the balancing machine under the three methods of MCS, LHS and BDRM5 in one embodiment;

[0038] Figure 5.4 It is a fourth-order moment diagram of the power angle of the synchronous generator under the three methods of MCS, LHS and BDRM5 in one embodiment;

[0039] Figure 5.5 is an error diagram of the variance of the balancing machine speed under different P values ​​of BDRM in one embodiment;

[0040] Figure 5.6 : is a variance error diagram of bus voltage amplitude calculated based on LHS and BDRM5 methods in one embodiment;

[0041] Figure 6 A topological structure diagram of an IEEE39 node system in one embodiment;

[0042] Figure 7 is a structural block diagram of a power system transient stability analysis device in one embodiment;

[0043] Figure 8 FIG. 4 is a diagram showing the internal structure of an electric power device in one embodiment. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. The "multiple" referred to herein may include two and / or more than two, unless otherwise specified, and the same applies to "multiple".

[0045] Before describing the technical solution of the present application, the following is an explanation of the relevant technical terms:

[0046] The Curse of Dimensionality refers to the phenomenon that in computational problems involving vectors, as the dimension increases, the amount of computation increases exponentially, which leads to a corresponding increase in the amount of computation.

[0047] Time-domain simulation is a numerical calculation method used to solve differential equations or differential-algebraic equations that describe the dynamic behavior of physical systems in order to predict the behavior of these systems over time.

[0048] Nataf transformation is a numerical method for solving the discretization problem of partial differential equations. Its principle is to transform the discretized grid so that the originally complex partial differential equation becomes simpler in the new coordinate system, thereby simplifying the numerical solution process.

[0049] Non-intrusive methods refer to algorithms that do not require modification or reconstruction of the original model or system. Specifically, non-intrusive methods process input or output data outside the model without changing the internal structure or equations of the model.

[0050] The technical solution of this application is described below:

[0051] As a large number of renewable energy sources are connected to the power grid, the grid structure becomes more and more complex, and the dynamic behavior of the power system is affected by more and more random factors, such as the randomness of renewable energy output, load power randomness, and parameter randomness. These randomnesses pose serious challenges to the prediction and analysis of the dynamic behavior of the power system. For example, when the output value of the wind farm is small, the simulation results show that the power system is stable. However, due to the randomness of wind speed, the actual output of the wind farm is different from the simulation setting value, and the dynamic behavior of the system changes with the actual output of the wind farm. The transient stability of the power system is a random event.

[0052] The transient stability of a power system can be analyzed based on time-domain simulation. However, modern power systems are affected by many random factors, including wind power randomness, photovoltaic randomness, and system parameter randomness. Under the influence of these random factors, for the same fault, the system state is often random. Therefore, deterministic time-domain simulation cannot correctly analyze the transient stability of a power system. Quantifying the influence of these random factors can not only analyze the transient stability of a power system but also identify weak generators. For synchronous generators greatly affected by random factors, the possibility of losing synchronization is greater. Therefore, it is increasingly important to analyze the influence of randomness on the transient stability of a power system. Through random time-domain simulation, the influence of randomness on the transient stability of a power system can be analyzed more intuitively.

[0053] At present, the probabilistic analysis methods for randomness analysis in power system time-domain simulation are mainly divided into two categories: simulation methods and approximation methods. As a simulation method, the Monte Carlo Simulation (MCS) is the most direct and effective probabilistic analysis method. When the sample size of MCS is large enough, the results are usually considered accurate. However, the computational efficiency of MCS is very low, and it is usually used as a reference to verify the accuracy of other methods. To develop more effective sampling techniques, researchers use low-discrepancy samples to replace the pseudo-random samples of MCS, thereby accelerating the convergence speed and shortening the calculation time. Among them, Latin Hypercube Sampling (LHS) is a widely used sampling method. Compared with MCS, the Latin hypercube sampling method improves the convergence speed through stratified sampling of the sample space, thus improving the computational efficiency. However, to achieve the desired accuracy, the number of samples required by LHS is usually still large. Therefore, the computational efficiency of LHS in complex power systems needs to be further improved.

[0054] The methods suitable for random time-domain simulation of complex power systems need to meet the following characteristics: (1) The method can handle the correlation of input random variables; (2) The method is non-invasive to adapt to complex power system models and then adopt efficient time-domain simulation algorithms; (3) The number of samples is small and precise, and the strategy for obtaining samples should be as stable as possible. However, most of the existing methods cannot meet these three characteristics simultaneously. For example, the computational efficiency of simulation methods such as MCS and LHS is not high enough, the approximation methods based on polynomial chaos methods will suffer from the curse of dimensionality, and some improved polynomial chaos methods, such as polynomial chaos methods based on sparse grids, although can reduce the influence of the curse of dimensionality, but the research on dealing with the correlation of input random variables of such methods is not yet mature.

[0055] Based on the above analysis, the present application provides a method for analyzing transient stability of a power system. This method reduces the amount of calculation by ignoring low-probability samples and retaining high-probability samples through dimensionality reduction processing when there are multiple input random variables; converts the random variables into independent standard normal random variables, determines the corresponding samples and integral weights in the normal space; then calculates the corresponding mean and standard deviation, and judges the transient stability of the power system by the mean and standard deviation, which helps to improve the calculation efficiency and the accuracy of transient stability analysis of the power system. The following is an illustration by way of example:

[0056] The method for analyzing transient stability of a power system provided in an embodiment of the present application can be applied to a power system. For example, it can be a server applied to a power system. The server can be an independent physical server, a server cluster or a distributed system composed of multiple physical servers, or a cloud server that provides cloud computing services. In some embodiments, the server stores or can obtain data of each power device. It is understandable that the method is also applied to a system including a terminal (specific power device) and a server, and is implemented through the interaction between the terminal and the server.

[0057] In one embodiment, a method for analyzing transient stability of a power system is provided, the method comprising steps S101 to S106:

[0058] Step S101, obtaining at least two random variables in the power system.

[0059] Among them, random variables can be variables caused by one or more random factors in the power system. For example, the power generation side in the power system can be based on wind power generation, and the size of the wind force is uncertain and random, and accordingly, random variables will be generated.

[0060] Step S102, determining a corresponding independent standard normal random variable based on the random variable, and obtaining a response function corresponding to the independent standard normal random variable.

[0061] In some embodiments, Nataf transformation may be used to process random variables and convert them into independent standard normal random variables.

[0062] In some embodiments, the response function values ​​corresponding to one or more random variables may be obtained by simulation, so that the target probability characteristics of the response function may be determined by multiple response function values.

[0063] In some embodiments, when there is only one random variable, a specific calculation formula can be used to determine the corresponding target probability feature. However, in practical applications, the number of input random variables is usually greater than 1. In this case, if a specific calculation formula is still used to determine the corresponding target probability feature, this means that - assuming that each random variable uses P integral points, and the sample is composed of P integral points, then a total of P random variables are required. d samples, which leads to an exponential growth trend in the corresponding amount of calculation and a serious dimensionality disaster problem. To this end, the response function can be reduced in dimension:

[0064] Step S103, performing dimensionality reduction processing on the response function to obtain a one-dimensional function and a two-dimensional function corresponding to the response function.

[0065] In some embodiments, a possible method for reducing the dimension of a response function is provided: based on the generalized dimensionality reduction method, a quadratic dimensionality reduction method (Bivariate Dimension Reduction Method, BDRM) is provided. This method approximates the response function as a linear combination of a one-dimensional function and a two-dimensional function, and uses a one-dimensional Gauss-Hermite integral and a two-dimensional Gauss-Hermite integral to respectively calculate the one-dimensional probability characteristics of the one-dimensional function and the two-dimensional probability characteristics of the two-dimensional function, and finally calculates the target probability characteristics of the response function based on the probability characteristics of the one-dimensional function and the two-dimensional function.

[0066] Step S104, determining the one-dimensional probability characteristics corresponding to the independent standard normal random variables based on the one-dimensional function, and determining the two-dimensional probability characteristics corresponding to the independent standard normal random variables based on the two-dimensional function.

[0067] Step S105, determining the target probability feature of the response function according to the one-dimensional probability feature and the two-dimensional probability feature.

[0068] The target probability feature may be a probability feature in the response function that reflects whether the power system has transient stability. For example, if the mean of the target function exceeds a preset stable range, it can be determined that the power system does not have transient stability.

[0069] Step S106, determining the transient stability of the power system according to the target probability characteristics.

[0070] The above-mentioned power system suspension stability analysis method determines the corresponding independent standard normal random variables based on random variables, which can more accurately handle the correlation between input random variables; by reducing the dimension of the response function, the one-dimensional function and the two-dimensional function corresponding to the response function are obtained, and the target probability characteristics of the response function are determined by the corresponding one-dimensional probability characteristics and two-dimensional probability characteristics, thereby determining the transient stability of the power system, which can avoid the dimensionality disaster caused by directly determining the target probability characteristics of the response function, reduce the amount of calculation, and thus help improve the efficiency of the transient stability analysis of the power system. In addition, since this method does not require any modification to the mathematical structure or calculation process of the original model, by sampling and analyzing the data outside the model, the evaluation and analysis of the system behavior is achieved, so it is non-invasive, will not affect the normal operation of the power system, does not involve hardware changes or additions, reduces costs, and is more efficient in analyzing the suspension stability of the power system.

[0071] In one embodiment, the "determining one-dimensional probability features corresponding to independent standard normal random variables based on one-dimensional functions, and determining two-dimensional probability features corresponding to independent standard normal random variables based on two-dimensional functions" in the aforementioned embodiment may include: determining one-dimensional probability features based on one-dimensional functions and one-dimensional Gauss-Hermite integrals; determining two-dimensional probability features based on two-dimensional functions and two-dimensional Gauss-Hermite integrals; wherein samples corresponding to the two-dimensional Gauss-Hermite integrals are determined based on one-dimensional samples corresponding to the one-dimensional Gauss-Hermite integrals; and the integral weight corresponding to the two-dimensional Gauss-Hermite integrals is the product of the one-dimensional integral weights corresponding to the one-dimensional Gauss-Hermite integrals.

[0072] In some embodiments, samples corresponding to the two-dimensional Gauss-Hermitian integral may be determined based on one-dimensional samples, and integral weights corresponding to the two-dimensional Gauss-Hermitian integral may be determined based on one-dimensional integral weights. The following is explained by way of example, in which the sampling points and integral weights listed are only for illustration, do not represent the actual situation, and may be an incomplete list:

[0073] One-dimensional samples include multiple sampling points: 0, 0.1, -0.1, etc., and the corresponding one-dimensional integral weights are 0.6, 0.2, 0.2, etc. Then the samples corresponding to the two-dimensional Gauss-Hermite integral can include (0, 0.1), (0, -0.1), etc., and the integral weights corresponding to the two-dimensional Gauss-Hermite integral are 0.6×0.2=0.18, 0.6×0.2=0.18, etc.

[0074] In this embodiment, a one-dimensional probability feature and a two-dimensional probability feature are determined respectively by a one-dimensional Gauss-Hermite integral and a two-dimensional Gauss-Hermite integral; at the same time, the samples corresponding to the two-dimensional Gauss-Hermite integral are determined based on the one-dimensional samples; the integral weight corresponding to the two-dimensional Gauss-Hermite integral is the product of the corresponding one-dimensional integral weights, which ensures that the one-dimensional probability feature and the two-dimensional probability feature are both for the same random variable, so that the two are consistent, thereby achieving dimensionality reduction while ensuring data consistency, obtaining accurate one-dimensional probability features and two-dimensional probability features, and providing an accurate basis for determining subsequent target probability features.

[0075] In one embodiment, the “determining a one-dimensional probability feature corresponding to a one-dimensional function based on a one-dimensional Gauss-Hermite integral” in the above embodiment may include steps S201 to S202:

[0076] Step S201, determining a one-dimensional sample and a one-dimensional integral weight based on an independent standard normal random variable; wherein the one-dimensional sample includes at least three sampling points, and the sum of the one-dimensional integral weights corresponding to the sampling points is equal to 1.

[0077] In some embodiments, the sampling points and the corresponding one-dimensional integral weights may be determined by a specific calculation formula.

[0078] In some embodiments, a table of sampling points and one-dimensional integral weights can be pre-constructed, so that the one-dimensional samples and one-dimensional integral weights can be directly determined by looking up the table, which can improve the corresponding efficiency. For example, in the table, when the number of sampling points is determined, the corresponding one-dimensional integral weight is a constant.

[0079] Step S202 : determining a one-dimensional probability feature corresponding to the one-dimensional function according to the one-dimensional sample and the one-dimensional integral weight, and based on the one-dimensional Gauss-Hermite integral.

[0080] In this embodiment, one-dimensional samples and one-dimensional integral weights are determined based on independent standard normal random variables, thereby achieving one-dimensional probability features determined by one-dimensional samples and one-dimensional integral weights. This makes the one-dimensional probability features correspond to independent standard normal random variables and to random variables, thereby providing a more accurate basis for determining subsequent target probability features.

[0081] In one embodiment, the one-dimensional sample in the aforementioned embodiment may include sampling points with a value of 0, the total number of sampling points included in the one-dimensional sample in the aforementioned embodiment may be an odd number, and the sum of the values ​​corresponding to the sampling points may be 0.

[0082] For example, in an actual calculation process, an odd number of integration points is usually used. This is because the sampling points with an odd number of integration points contain a mean of 0, which is conducive to the application of subsequent dimensionality reduction methods.

[0083] In one of the embodiments, the “determining the transient stability of the power system according to the target probability characteristic” in the aforementioned embodiment may include: when the target probability characteristic is within a preset probability characteristic range, determining that the power system is transiently stable; when the target probability characteristic is greater than or less than the preset probability characteristic range, determining that the power system is transiently unstable.

[0084] In some embodiments, multiple corresponding target probability features may be determined based on multiple adjacent time points, and the transient stability of the power system may be comprehensively determined by comparing the sizes of the multiple target probability features with a preset probability feature range.

[0085] In this embodiment, by determining the size of the target probability feature compared to a preset probability feature range, rapid determination of the transient stability of the power system is achieved.

[0086] In one of the embodiments, the target probability characteristics in the aforementioned embodiment may include a mean and a standard deviation; "determining the transient stability of the power system based on the target probability characteristics" in the aforementioned embodiment may include: determining the fluctuation of the power system under the influence of random factors corresponding to the random variables based on the mean and the standard deviation; the random factors include at least one of the following: renewable energy generation data, load power, parameters of power equipment and environmental information of the power system; determining the transient stability of the power system based on the fluctuation.

[0087] The renewable energy power generation data may be data characterizing the renewable energy power generation situation, such as wind power generation, solar power generation, etc.

[0088] The load power may be the power related to power consumption corresponding to the power consumption side in the power system, for example, power for lighting, charging of electric vehicles, etc.

[0089] The parameters of the power equipment may be the parameters of various types of power equipment in the power system. For example, the parameters of the power equipment may change in real time, for example, temperature changes may lead to corresponding parameter changes.

[0090] Among them, the environmental information of the power system, for example, temperature, humidity, etc., and also the weather conditions.

[0091] In some embodiments, the mean value can be used as a benchmark for determining the stability of the power system. If the mean value is within a preset stability range, then the power system can be considered to be stable on average. Conversely, if the mean value exceeds the stability range, then the power system may face the risk of instability.

[0092] In some embodiments, the mean and standard deviation (or variance) together can more comprehensively describe the distribution of the output random variable. The standard deviation reflects the degree of dispersion of the output random variable, while the mean reflects the central position. The mean and standard deviation can be used to determine the fluctuation of the power system state and the stability of the power system under the influence of random factors.

[0093] In this embodiment, based on the mean and the standard deviation, the fluctuation of the power system under the influence of the random factors corresponding to the random variables is determined, and according to the fluctuation, the transient stability of the power system can be determined more accurately.

[0094] In one embodiment, a method for transient stability analysis of a power system is provided, which may have the three characteristics that the method suitable for random time-domain simulation of complex power systems mentioned above needs to meet. The overall framework of the method is "implicit Euler method + Gaussian integral + generalized dimensionality reduction method", which uses the implicit Euler method as the time-domain simulation kernel, converts the related input random variables into independent standard normal variables through Nataf transformation, and then uses Gauss-Hermite integral to calculate the probability characteristics of the output random variables, and proposes two methods to improve the computational efficiency based on the generalized dimensionality reduction method to reduce the impact of the dimensionality curse.

[0095] The main contents are summarized as follows: (1) In order to more accurately handle the correlation between input random variables, this application uses Nataf transform to convert the original input random variables into independent standard normal random variables. (2) In order to improve computational efficiency, this application proposes a randomness analysis method for power system time domain simulation based on Nataf transform and Gauss-Hermite integral. Similar to the simulation method, the method adopted in this application is sample-based, so it is a non-invasive method that can be applied to complex power systems. (3) In order to reduce the impact of the curse of dimensionality, this application proposes a method to reduce the impact of the curse of dimensionality based on the generalized dimensionality reduction method. This method approximates the high-dimensional objective function as a linear combination of a one-dimensional function and a two-dimensional function, and uses the one-dimensional Gauss-Hermite integral and the two-dimensional Gauss-Hermite integral to respectively calculate the probability characteristics of the one-dimensional function and the probability characteristics of the two-dimensional function, and finally calculates the probability characteristics of the high-dimensional objective function based on the probability characteristics of the one-dimensional function and the two-dimensional function.

[0096] The above-mentioned power system transient stability analysis method is described in detail below, and the corresponding order of description is: first, the process of converting the input random variable (i.e., the random variable in the previous article) into an independent standard normal random variable using the Nataf transform is introduced, and the process of using independent standard normal random variables to represent the input random variable is introduced; then, the method of determining the sample (sampling point) and integral weight in the normal space is explained, and then the process of calculating the mean and standard deviation of the output random variable and other probability characteristics based on the Gauss-Hermite integral is introduced; finally, the method of reducing the influence of the dimensionality curse based on the generalized dimensionality reduction method, i.e., the quadratic dimensionality reduction method, is explained.

[0097] (I) Correlation processing of input random variables based on Nataf transformation

[0098] Assume Q=[q 1 ,q 2 ,...,q d ] T is a d-dimensional random variable, Φ i (q i ) is the random variable q i The cumulative probability distribution function of the d-dimensional random variable is recorded as C Q .

[0099]

[0100] Through the marginal transformation corresponding to formula (3.2), Q can be converted into a set of standard normal random variables, denoted as W = [w 1 ,w 2 ,...,w d ] T .

[0101] w k =Θ -1 (Φ k (q k )),k=1,2,...,d(3.2)

[0102] Where Θ is the cumulative probability distribution function corresponding to the standard normal distribution, Θ -1 is its inverse function. The correlation coefficient matrix of W is represented by C W As shown in formula (3.3).

[0103]

[0104] For the above transformation, C Q and C W The corresponding elements of satisfy the relationship shown in formula (3.4).

[0105]

[0106] In the above equation, μ i and μ j The random variables q i and q j The corresponding mean, δ i and δ j They are q i and q j The corresponding standard deviation. W is a set of correlation coefficient matrices C W The standard normal distribution random variable W can be transformed into a set of independent standard normal distribution random variables Z through Cholesky decomposition.

[0107] First, for C W Perform Cholesky decomposition as shown in formula (3.5).

[0108] LL T =C W (3.5)

[0109] C W After Cholesky decomposition, the independent standard normal distribution random variables Z = [z 1 ,z 2 ,...,z d ] T It can be expressed as formula (3.6).

[0110] Z=L -1 W(3.6)

[0111] Equations (3.1)-(3.6) constitute the Nataf transformation process, and the inverse Nataf transformation is the process of solving Q when Z is known, which can be expressed by equation (3.7).

[0112]

[0113] In formula (3.7), Φ i -1 is Φ i The inverse function of . Existing literature proposes an empirical formula for solving equation (3.4), which is shown in equation (3.8).

[0114] ρ′ ij = Ηρ ij (3.8)

[0115] H is Φ i (q i ), Φ j (q j ) and ρ ij For example, when q i and q jWhen both wind speeds follow the Weibull distribution, we can obtain equation (3.9).

[0116]

[0117] (II) Randomness Analysis of Single-Input Random Variables Based on Gauss-Hermite Integral

[0118] For a single variable response function f = S (q), the mean and standard deviation of f can be calculated by definite integral. In practical engineering applications, the analytical expression of the function S (q) is unknown, but the value of f under a certain q value can be obtained through simulation, so numerical integration can be used to calculate the mean and standard deviation of f.

[0119] Table 1 Some Gauss-Hermitian integration points and corresponding integration weights

[0120]

[0121] When q is a normal random variable, Gauss-Hermite integration has the highest algebraic accuracy under the same number of integration points. When using Gauss-Hermite integration to perform numerical integration of normal random variables, it is first necessary to determine the sampling points and integration weights on the standard normal space. The sampling points and integration weights on the standard normal space can be determined based on the Hermite polynomials. The sampling points and integration weights are constants under a fixed number of integration points. Therefore, the sampling points and integration weights can be directly obtained through table lookup without repeatedly calculating the sampling points, thereby reducing the calculation time. Table 1 shows the sampling points and corresponding integration weights for 3, 5, and 7 sampling points. In Table 1, z j is the jth sampling point, P is the number of samples, A j is the integral weight corresponding to the jth sampling point. The sum of the integral weights corresponding to all integral points is 1, and the integral weight corresponding to the mean 0 is the largest. The integral weight corresponding to the integral point closer to the mean 0 is also larger. In the actual calculation process, an odd number of integral points is usually used. This is because the sampling points contain a mean of 0 under an odd number of integral points, which is conducive to the application of subsequent generalized dimensionality reduction methods.

[0122] If the inverse Nataf transform is expressed as N -1 , then the response function f can be converted into formula (3.10).

[0123] f=S(q)=S(N -1 (z)) = F(z)(3.10)

[0124] In equation (3.10), z represents an independent standard normal random variable. According to the Gauss-Hermite quadrature formula, the mean μ of the output random variable f can be obtained: S and standard deviation σ S, as shown in formula (3.11).

[0125]

[0126] 3. Randomness analysis based on Gauss-Hermite integral and generalized dimensionality reduction method

[0127] When there is only one input random variable, equation (3.11) can calculate the probability characteristics of the output random variable such as the mean and standard deviation. In practical applications, the number of input random variables is usually greater than 1, and the response function S is the input random variable Q = [q 1 ,q 2 ,...,q d ] T The function can be expressed as f = S Σ (Q). In this case, the simplest and most accurate method is to use P integration points for each input random variable, and the sample is composed of P integration points one by one. Then, a total of P d input random variables are required. d This method is simple to implement and can accurately obtain the probability characteristics such as the mean and standard deviation of the output random variable, but it requires P d In time domain simulation, as the number of input random variables increases, the amount of calculation increases exponentially, and there is a serious dimensionality curse problem.

[0128] In order to reduce the number of time-domain simulations and reduce the impact of the dimensionality curse, a quadratic dimensionality reduction method is proposed based on the generalized dimensionality reduction method to approximate the target response function, thereby improving the computational efficiency:

[0129] The bivariate dimension reduction method (BDRM) approximates the high-dimensional target function as a linear combination of a one-dimensional function and a two-dimensional function, and uses the one-dimensional Gauss-Hermite integral and the two-dimensional Gauss-Hermite integral to calculate the probability characteristics of the one-dimensional function (i.e., the one-dimensional probability characteristics) and the probability characteristics of the two-dimensional function (i.e., the two-dimensional probability characteristics), respectively. Finally, the probability characteristics of the high-dimensional target function (i.e., the target probability characteristics) are calculated based on the probability characteristics of the one-dimensional function and the two-dimensional function. The input random variable Q is converted into a set of independent standard normal random variables Z through the Nataf transformation, and the BDRM can be expressed by formula (3.15).

[0130]

[0131] In formula (3.15), F i (z i ) is S Σ (Q) relative to z i A univariate function of F, where the remaining random variables Z are averaged.ij (z i ,z j ) is about z i and z j The remaining random variables Z are all averaged.

[0132] According to the generalized dimensionality reduction method, the high-dimensional objective function can be approximated as a linear combination of a one-dimensional function and a two-dimensional function according to formula (3.15), where F i (z i ) the average value u Fi and the second-order origin moment λ 2 Fi It can be calculated by formula (3.16), where z i j is the random variable z i The jth sample of .

[0133]

[0134] At this time F ij (z i ,z j ) the average value u Fij and the second-order origin moment λ 2 Fij It can be calculated by formula (3.17), where z i k The kth sample z of the two-dimensional Gaussian integral i The value of z j k The kth sample z of the two-dimensional Gaussian integral j The value of E k is the integral weight of the kth sample of the two-dimensional Gaussian integral. The samples of the two-dimensional Gaussian integral are composed of one-dimensional Gaussian integral samples. The integral weight is the product of the one-dimensional Gaussian integral. Some two-dimensional Gaussian integral points and integral weights are shown in Table 2.

[0135]

[0136] Table 2 Some two-dimensional Gauss-Hermitian integration points and corresponding integration weights

[0137]

[0138] In getting F i (z i ) and F ij (z i ,z j ) and the second-order origin moment, the target response function S ΣThe mean and standard deviation of can be expressed by formula (3.18).

[0139]

[0140] According to the above idea, the target response function S can be calculated Σ When calculating the k-order origin moment of the objective function, it is only necessary to convert S Σ The kth power of (Q) is used as the new objective function, and the new objective function is subjected to secondary dimensionality reduction. The mean of the new objective function calculated using equations (3.16), (3.17) and (3.18) is S Σ The k-th origin moment of (Q).

[0141] Take 3 input random variables and 3 integration points as an example, Figure 3 A schematic diagram of the sample points reduced by the two dimensionality reduction methods is given, where the red bubbles represent the reduced sample points, and the green bubbles represent the retained sample points. The bubble size is proportional to the probability of the sample point. It can be seen that the above dimensionality reduction methods ignore low-probability samples and retain high-probability samples. When calculating the k-th moment, the quadratic dimensionality reduction uses the k-th power of the target response function as the new target function.

[0142] (IV) Specific process

[0143] The mathematical essence of time-domain simulation of power systems is to solve a set of nonlinear differential-algebraic equations (DAEs). The general DAEs of power systems can be expressed by formula (3.19).

[0144]

[0145] In equation (3.19), x is the power system state variable vector, such as generator power angle, generator speed, excitation voltage of the exciter, output power of the turbine, etc. y represents the algebraic variable vector of the power system, such as voltage amplitude, voltage phase angle, current, etc. f and g are both nonlinear function vectors of x and y. When there are random parameters in the power system, DAEs are expressed as equation (3.20).

[0146]

[0147] In formula (3.20), Q is the input random variable. This application studies the randomness of wind farm output and load power. Wind speed varies with time and location, and its probability density function (PDF) is usually a Weibull distribution function. Therefore, the wind speed model adopts the Weibull distribution function, as shown in formula (3.21). In formula (3.21), s wis the wind speed, β is the shape parameter, and η is the scale parameter. The wind turbine output can be calculated based on the wind speed at the wind turbine installation location and the wind turbine output model. Specifically, the wind turbine active output model can be expressed by formula (3.22).

[0148]

[0149] In formula (3.22), ω is the wind speed, P N is the rated power of the fan, ω k is the wind turbine cut-in wind speed, ω s is the rated wind speed, ω c is the fan cut-out wind speed, k 1 =P N / (ω s -ω k ), k 2 =-k 1 ω k Unlike the random characteristics of wind speed, load power usually obeys a normal distribution. Considering the input random variable Q, the target response function can be obtained as shown in formula (3.23).

[0150]

[0151] In formula (3.23), ζ t and τ t are the values ​​of ζ and τ at time t respectively. t and G t is similar to S in equation (3.10) Σ The target response function is thus t and τ t The mean and standard deviation can be calculated using the formulas described above.

[0152] See also Figure 4 As shown in FIG. 1 , a specific process of a possible power system transient stability analysis method is provided, which is described as follows:

[0153] (1) Input the correlation coefficient matrix C Q , the number of input random variables d, the number of Gauss-Hermite integration points P and other parameters.

[0154] (2) Calculate the matrix C according to formula (3.4) W , calculate the matrix L according to formula (3.5).

[0155] (3) According to the Gauss-Hermite integral points and corresponding integral weights listed in Tables 1 and 2, the samples and integral weights corresponding to Z are determined in the normal space.

[0156] (4) Based on the samples corresponding to Z, determine the samples corresponding to the input random variable Q through formula (3.7).

[0157] (5) Solve equation (3.23) for each sample in Q to obtain the values ​​of ζ and τ at time t.

[0158] (7) Under quadratic dimensionality reduction, the mean and standard deviation of the target response function under the action of multiple random variables Z are calculated according to equations (3.16) and (3.17).

[0159] In some embodiments, a specific implementation scheme based on the above-mentioned power system transient stability analysis is provided. In this scheme, the IEEE39 node system (a standard test system for power system analysis and research) is used for simulation analysis. The dynamic data of the synchronous generator, exciter and prime mover in the IEEE39 node system can be set by referring to existing literature. The load constant impedance, constant current and constant power ratios are 90%, 10% and 0% respectively. The IEEE39 node system topology is as follows: Figure 6 As shown. Figure 6 It can be seen that the IEEE39-bus system has a total of 39 buses, 10 synchronous generators and 21 loads.

[0160] In this example, it is assumed that the fluctuation value of the static active output of generator 1 and generator 2 satisfies the relationship shown in formula (3.22), and the static active power of load 1 and load 3 and the wind speed corresponding to the fluctuation value of the static active output of generator 1 and generator 2 are the input random variables to be studied. Assume that the active power of load 1 obeys Gaussian distribution, with the mean being the original load active power and the standard deviation being 10% of the mean; the active power of load 3 also obeys Gaussian distribution, with the mean being the original load active power and the standard deviation being 10% of the mean, and the correlation coefficient between the active power of load 1 and load 3 is 1 / 2. Assume that the wind speed corresponding to the fluctuation value of the static active output of generator 1 and generator 2 obeys Weibull distribution with a scale parameter of 9 and a shape parameter of 2.15, and the correlation coefficient between the two is 1 / 2. The implicit Euler method is used in the time domain simulation method, with a simulation step size of 0.01 seconds and a total simulation time of 10 seconds. At 1s, a three-phase metallic short circuit occurs on bus 5, and 0.1 seconds later, line 4-5 is cut off to end the short circuit fault. The abbreviations of various methods involved in the present invention are shown in Table 3, wherein BDRM3 represents the quadratic dimensionality reduction when the number of integral points is 3, and the standard value of the simulation result adopts the calculated value of 20,000 Monte Carlo simulation method.

[0161] Table 3 Abbreviations of various random time-domain simulation methods

[0162]

[0163] Select the speed of synchronous generator 2 to analyze the results. Figure 5.1The mean error of the speed of synchronous generator 2 calculated by LHS and BDRM5 is shown. Figure 5.2 The variance of the speed of synchronous generator 2 calculated by the three methods of MCS, LHS and BDRM5 is shown.

[0164] from Figure 5.1 and Figure 5.2 It can be seen that the average values ​​of the synchronous generator 2 speed calculated by the BDRM5 and LHS methods are very close to the calculated value of MCS. In addition, the accuracy of the variance of the synchronous generator 2 speed calculated by the BDRM5 and LHS methods is slightly lower than that of MCS, which can be ignored in practical engineering applications. It is worth noting that the error always increases at the top and bottom of the peak. In addition, it can be seen that the average values ​​and variances of the synchronous generator 2 speed calculated by the BDRM5 and LHS methods are very close.

[0165] Table 4 Mean and variance of generator 1 power angle calculated by various methods at 10s

[0166]

[0167] In order to further verify the effectiveness of the proposed method, the mean and variance of the generator 1 power angle calculated by each method at 10s are given in Table 4. It can be seen from Table 4 that the mean and variance calculated by BDRM5 and LHS have the same accuracy.

[0168] In order to compare the accuracy of high-order moments of output variables under different methods, Figure 5.3 and Figure 5.4 The third-order central moment of the balancing machine speed and the fourth-order central moment of the generator 2 power angle calculated by the three methods are shown respectively. BDRM5 and LHS can be used to calculate the third-order and fourth-order moments of the output variables with higher accuracy. The third-order central moment of the balancing machine speed calculated by BDRM5 is comparable to that of LHS in accuracy, while the fourth-order central moment of the generator 2 power angle calculated by BDRM5 is higher in accuracy than LHS. In addition, it is worth noting that the third-order and fourth-order moments of the bus voltage amplitude are very small in this case analysis, which means that the voltage amplitude is less affected by the input random variables, and the system voltage amplitude deviates from the mean very little when the input random variables change.

[0169] Figure 5.5 The error of BDRM in balancing the generator speed variance at different integration points is shown. The results show that there is no significant difference between the results obtained by BDRM5 and BDRM7, while the accuracy of BDRM3 is lower than that of BDRM5 and BDRM7.

[0170] The error of the BDRM method mainly comes from the approximate errors of equations (3.16), (3.17) and (3.18). Different integration points only affect the approximate errors of equations (3.16) and (3.17). As can be seen from the figure, in this example, when the number of integration points is 5, the approximate errors of equations (3.16) and (3.17) have basically met the requirements. Usually, BDRM uses 5 integration points to better balance the calculation efficiency and calculation accuracy.

[0171] Figure 5.6 The variance error of bus 20 voltage amplitude calculated by three different methods is shown. Figure 5.2 and Figure 5.6 It can be seen that the voltage amplitude is much less affected by the input random variables than the speed. This is because dynamic components such as synchronous generators are the root cause of the change in the state of the drive system, and the voltage amplitude changes with the change of the system state to balance the network power. In addition, Figure 5.6 It shows that the variance of the voltage amplitude calculated by BDRM and LHS is very close to the standard result (MCS).

[0172] Table 5 shows the number of time domain simulations under various scenarios. It can be seen from Table 5 that compared with MCS and LHS, BDRM can reduce the number of time domain simulations, thereby improving the computational efficiency. The results in Table 5 indicate that BDRM can effectively reduce the number of time domain simulations compared with LHS and other simulation methods. Figure 5.1 to Figure 5.6 The results show that BDRM is comparable to LHS in computational accuracy, which indicates that BDRM can better balance computational efficiency and accuracy.

[0173] Table 5 Time domain simulation times in various scenarios

[0174]

[0175] In summary, compared with MCS and LHS, BDRM can improve the calculation efficiency while ensuring high calculation accuracy. BDRM is suitable for situations where both high calculation accuracy and calculation efficiency are required for high-order moments.

[0176] This application uses the implicit Euler method as the time domain simulation kernel, converts the related input random variables into independent standard normal variables through the Nataf transform, and then uses the Gauss-Hermite integral to calculate the probability characteristics of the output random variables, and proposes two methods to improve the computational efficiency based on the generalized dimensionality reduction method to reduce the impact of the dimensionality curse. The following characteristics are obtained through the simulation results of the IEEE39 node system: First, the proposed method is non-invasive, and the time domain simulation method based on the implicit Euler method can be used as the simulation kernel. At the same time, the proposed method can handle the correlation between the input random variables. Second, the BDRM method proposed based on the generalized dimensionality reduction method can accurately calculate the first two order moments of the output random variables, where the accuracy of BDRM is equivalent to LHS, and BDRM can be used to calculate more accurate high-order moments of the output random variables. Third, in terms of computational efficiency, the computational efficiency of BDRM is higher than that of LHS. BDRM is suitable for occasions where both the accuracy and efficiency of high-order moment calculations are required.

[0177] The above technical solution is non-invasive and can adapt to complex power system models; at the same time, it does not require a large number of samples, the number of samples is small and precise, and the strategy for obtaining samples is stable; the original input random variables are converted into independent standard normal random variables by using Nataf transform, which can more accurately handle the correlation between input random variables; randomness analysis of power system time domain simulation based on Nataf transform and Gauss-Hermite integral can improve computational efficiency; for multiple input random variables, a dimensionality reduction method is used to reduce the impact of the curse of dimensionality.

[0178] It should be understood that, although the various steps in the flowcharts involved in the above-mentioned embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-mentioned embodiments can include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0179] Based on the same inventive concept, an embodiment of the present application further provides a power system transient stability analysis device for implementing the power system transient stability analysis method involved above. The solution provided by this device for solving problems is similar to the solution described in the above method. Therefore, the specific limitations in one or more embodiments of the power system transient stability analysis device provided below can refer to the limitations on the power system transient stability analysis method in the above text, and will not be repeated here.

[0180] In an exemplary embodiment, as Figure 7 shown, a power system transient stability analysis device 700 is provided, including:

[0181] An acquisition module 701, configured to acquire at least two random variables in the power system;

[0182] A dimension reduction module 702, configured to determine corresponding independent standard normal random variables based on the random variables, and acquire response functions corresponding to the independent standard normal random variables; perform dimension reduction processing on the response functions to obtain a one-dimensional function and a two-dimensional function corresponding to the response functions;

[0183] A determination module 703, configured to determine one-dimensional probability characteristics corresponding to the independent standard normal random variables based on the one-dimensional function, and determine two-dimensional probability characteristics corresponding to the independent standard normal random variables based on the two-dimensional function; determine the target probability characteristics of the response function according to the one-dimensional probability characteristics and the two-dimensional probability characteristics; determine the transient stability of the power system according to the target probability characteristics.

[0184] In one embodiment, the determination module 703 is further configured to determine one-dimensional probability characteristics corresponding to the independent standard normal random variables based on the one-dimensional function, and determine two-dimensional probability characteristics corresponding to the independent standard normal random variables based on the two-dimensional function, including: determining the one-dimensional probability characteristics based on the one-dimensional function and the one-dimensional Gauss-Hermite integral; determining the two-dimensional probability characteristics based on the two-dimensional function and the two-dimensional Gauss-Hermite integral; wherein, the samples corresponding to the two-dimensional Gauss-Hermite integral are determined based on the one-dimensional samples corresponding to the one-dimensional Gauss-Hermite integral; the integral weights corresponding to the two-dimensional Gauss-Hermite integral are the product of the one-dimensional integral weights corresponding to the one-dimensional Gauss-Hermite integral.

[0185] In one embodiment, the determination module 703 is further configured to determine one-dimensional probability characteristics based on the one-dimensional function and the one-dimensional Gauss-Hermite integral, including: determining one-dimensional samples and one-dimensional integral weights based on the independent standard normal random variables; wherein, the one-dimensional samples include at least three sampling points, and the sum of the one-dimensional integral weights corresponding to each sampling point is equal to 1; determine the one-dimensional probability characteristics corresponding to the one-dimensional function based on the one-dimensional samples and the one-dimensional integral weights, and based on the one-dimensional Gauss-Hermite integral.

[0186] In one embodiment, the one-dimensional sample includes sampling points with a value of 0, the total number of sampling points included in the one-dimensional sample is an odd number, and the sum of the values ​​corresponding to the sampling points is 0.

[0187] In one of the embodiments, the determination module 703 is also used to determine the transient stability of the power system based on the target probability characteristics, including: when the target probability characteristics are within a preset probability characteristic range, determining that the power system is transiently stable; when the target probability characteristics are greater than or less than the preset probability characteristic range, determining that the power system is transiently unstable.

[0188] In one of the embodiments, the target probability characteristics include a mean and a standard deviation; the determination module 703 is also used to determine the transient stability of the power system based on the target probability characteristics, including: based on the mean and the standard deviation, determining the fluctuation of the power system under the influence of random factors corresponding to the random variables; the random factors include at least one of the following: renewable energy generation data, load power, parameters of power equipment and environmental information of the power system; based on the fluctuation, determining the transient stability of the power system.

[0189] Each module in the above-mentioned power system transient stability analysis device can be implemented in whole or in part by software, hardware and a combination thereof. Each of the above-mentioned modules can be embedded in or independent of the processor in the power equipment in the form of hardware, or can be stored in the memory in the power equipment in the form of software, so that the processor can call and execute the operations corresponding to each of the above modules.

[0190] In an exemplary embodiment, a power device is provided. The power device may be a server, and its internal structure diagram may be as shown in FIG. Figure 8 As shown. The power equipment includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the power equipment is used to provide computing and control capabilities. The memory of the power equipment includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the power equipment is used to store data required for transient stability analysis of the power system, for example, independent standard normal random variables. The input / output interface of the power equipment is used to exchange information between the processor and an external device. The communication interface of the power equipment is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for transient stability analysis of the power system is implemented.

[0191] Those skilled in the art will understand that Figure 8 The structure shown in the figure is only a block diagram of a part of the structure related to the scheme of the present application, and does not constitute a limitation on the power equipment to which the scheme of the present application is applied. The specific power equipment may include more or fewer components than shown in the figure, or combine certain components, or have a different arrangement of components.

[0192] In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0193] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0194] In one embodiment, a computer program product is provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0195] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, an artificial intelligence (AI) processor, etc., but are not limited to this.

[0196] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0197] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for analyzing transient stability of a power system, characterized in that: The method comprises: obtaining at least two random variables in the power system; Determine a corresponding independent standard normal random variable based on the random variable, and obtain a response function corresponding to the independent standard normal random variable; Performing dimensionality reduction processing on the response function to obtain a one-dimensional function and a two-dimensional function corresponding to the response function; Determine the one-dimensional probability feature corresponding to the independent standard normal random variable based on the one-dimensional function, and determine the two-dimensional probability feature corresponding to the independent standard normal random variable based on the two-dimensional function; Determining a target probability feature of the response function according to the one-dimensional probability feature and the two-dimensional probability feature; The transient stability of the power system is determined according to the target probability characteristics.

2. The method according to claim 1, characterized in that The determining of the one-dimensional probability feature corresponding to the independent standard normal random variable based on the one-dimensional function, and the determining of the two-dimensional probability feature corresponding to the independent standard normal random variable based on the two-dimensional function, include: Determining the one-dimensional probability feature based on the one-dimensional function and the one-dimensional Gauss-Hermite integral; Based on the two-dimensional function and the two-dimensional Gauss-Hermite integral, the two-dimensional probability feature is determined; wherein, The samples corresponding to the two-dimensional Gauss-Hermite integral are determined based on the one-dimensional samples corresponding to the one-dimensional Gauss-Hermite integral; the integral weight corresponding to the two-dimensional Gauss-Hermite integral is the product of the one-dimensional integral weight corresponding to the one-dimensional Gauss-Hermite integral.

3. The method according to claim 2, characterized in that The determining the one-dimensional probability feature based on the one-dimensional function and the one-dimensional Gauss-Hermite integral includes: Based on the independent standard normal random variable, determine the one-dimensional sample and the one-dimensional integral weight; wherein the one-dimensional sample includes at least three sampling points, and the sum of the one-dimensional integral weights corresponding to each sampling point is equal to 1; According to the one-dimensional sample and the one-dimensional integral weight, and based on the one-dimensional Gauss-Hermite integral, a one-dimensional probability feature corresponding to the one-dimensional function is determined.

4. The method according to claim 3, characterized in that: The one-dimensional sample includes sampling points with a value of 0, the total number of sampling points included in the one-dimensional sample is an odd number, and the sum of the values ​​corresponding to the sampling points is 0.

5. The method according to any one of claims 1 to 4, characterized in that: Determining the transient stability of the power system according to the target probability characteristics includes: When the target probability characteristic is within a preset probability characteristic range, determining that the power system is in transient stability; When the target probability characteristic is greater than or less than the preset probability characteristic range, it is determined that the power system is in transient instability.

6. The method according to any one of claims 1 to 4, characterized in that: The target probability characteristics include mean and standard deviation; Determining the transient stability of the power system according to the target probability characteristics includes: Based on the mean and the standard deviation, determining the fluctuation of the power system under the influence of the random factors corresponding to the random variables; the random factors include at least one of the following: renewable energy power generation data, load power, parameters of power equipment and environmental information of the power system; According to the fluctuation conditions, the transient stability of the power system is determined.

7. A power system transient stability analysis device, characterized in that: The device comprises: An acquisition module, used for acquiring at least two random variables in the power system; A dimension reduction module is used to determine a corresponding independent standard normal random variable based on the random variable, obtain a response function corresponding to the independent standard normal random variable; perform dimension reduction processing on the response function to obtain a one-dimensional function and a two-dimensional function corresponding to the response function; A determination module is used to determine the one-dimensional probability characteristics corresponding to the independent standard normal random variables based on the one-dimensional function, and to determine the two-dimensional probability characteristics corresponding to the independent standard normal random variables based on the two-dimensional function; determine the target probability characteristics of the response function according to the one-dimensional probability characteristics and the two-dimensional probability characteristics; and determine the transient stability of the power system according to the target probability characteristics.

8. An electric power device, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

Images