Power system probabilistic power flow method and system based on polynomial proxy and graph parallelism

Abstract

The invention discloses a power system probabilistic power flow method and system based on polynomial proxy and graph parallelism, and belongs to the technical field of power system planning and operation optimization. The method comprises the following steps: establishing a probability distribution model of a bus load prediction error to obtain sample distribution of predicted power; representing the output response quantity of the system as an input polynomial function, and establishing an initial polynomial agent model; determining an optimal configuration point set; mapping all the selected configuration points to an input sample space to obtain a small number of sample points of an input variable; performing deterministic load flow calculation on the sample points to obtain a sample vector of output response; calculating an undetermined coefficient in the proxy model according to the configuration point matrix and the sample vector; and solving the statistical characteristic quantity of the power flow response to obtain the probability distribution of the response. According to the calculation method provided by the invention, the probability distribution of the power flow response can be accurately and efficiently estimated, and convenience is provided for probabilistic power flow calculation of a novel power system under the access of a distributed power supply.

Description

Technical Field

[0001] The present invention relates to a probabilistic power flow method and system for power systems based on polynomial surrogate and graph parallelism, belonging to the technical field of power system planning and operation optimization. Background Art

[0002] There are always random factors such as load uncertainty in power systems. In recent years, renewable energy has developed rapidly and been integrated into power systems, with an increasing penetration rate. Due to the change of weather conditions, the behavior of renewable energy, including photovoltaic power generation (PV) and wind power generation, is random and intermittent, resulting in an increase in the uncertainty of node injection power. Therefore, new challenges are posed to the operation and control of power systems, and uncertainty analysis methods become very important in the operation and planning of power systems. How to quantitatively analyze the impact of the uncertainty brought by the large-scale access of renewable energy on the operation and dispatch of power systems has become an important research direction in power systems.

[0003] Probabilistic power flow is one of the important tools for analyzing the uncertainty of power systems, which can effectively reflect the operation of the system in various scenarios of random factors and obtain analysis results that are more in line with the actual situation. Existing probability assessment methods, such as the Monte Carlo simulation method, although can provide certain assessment results, are very time-consuming and inefficient in calculation because a large number of samples are required to obtain statistical accuracy. In addition, this method often has difficulty in accurately capturing and processing random inputs with different probability distributions, thus limiting its application value in the actual design and operation of distribution networks. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art, and provide a probabilistic power flow method and system for power systems based on polynomial surrogate and graph parallelism, so as to solve the problems that existing probabilistic power flow calculations require a large number of samples to obtain statistical accuracy, are very time-consuming and inefficient in calculation.

[0005] To achieve the above object / To solve the above technical problems, the present invention is implemented by the following technical solutions: First aspect: A probabilistic power flow method for power systems based on polynomial surrogate and graph parallelism, the method includes: Establish a probability distribution model of bus load prediction error to obtain the sample distribution of predicted power; Express the output response quantity of the distribution network system as a polynomial function of the input, and establish an initial polynomial surrogate model; Construct collocation points, and determine the optimal set of collocation points based on a linearly independent method, and further obtain a collocation point matrix; According to the principle of equiprobable transformation, map all selected collocation points in the set of collocation points to the sample distribution to obtain sample points of the input quantity; Perform deterministic power flow calculation on sample points based on the distributed graph parallel functional module to obtain the sample vector of the output response; Construct a linear equation system according to the determined configuration point matrix and the sample vector of the output response to calculate the undetermined coefficients in the initial polynomial surrogate model, and obtain the polynomial surrogate model based on the undetermined coefficients; Solve the statistical characteristic quantities of the power flow response according to the polynomial surrogate model to obtain the probability distribution of the response.

[0006] Optionally, the establishment of the probability distribution model of the bus load prediction error to obtain the sample distribution of the predicted power includes: According to the real-time operation data of the th bus load collected , obtain the ultra-short-term bus load prediction data set for the next hours , where N is the number of historical operation data sets, Obtain the power prediction error data set of the th bus load, and establish the probability distribution model of the bus load prediction error . The prediction error follows a normal Gaussian distribution ; ; Take the bus load power prediction at the future moment as the input random variable of the distribution network system, and it follows a mean value of ; Transform the predicted power input variable that satisfies the normal distribution into a standard normal distribution according to the standardization process to obtain the standardized normal variable ; where, is the random variable in the original normal distribution, is the mean value of the normal distribution, is the standard deviation of the normal distribution, is the transformed standard normal distribution, , N = 1, 2, 3...; is the actual value, the mean value , tends to 0, unbiased prediction, and the standard deviation ; represents the input random variable, is the bus predicted power value at the future moment, and the normal distribution with a standard deviation of , , represents the power prediction error of the bus load of the th data set, represents Index of a historical operation data set.

[0007] Optionally, representing the output response quantity of the distribution network system as a polynomial function of the input and establishing an initial polynomial surrogate model includes: Representing the output response quantity of the distribution network system in the form of a polynomial expansion: ; where is the output response quantity of the distribution network system, is the number of buses with load fluctuations selected in the distribution network system, i.e., the dimension of the random variable; is a standard normal variable, ; , , ... are the undetermined coefficients of the polynomial; is a multi-dimensional Hermite polynomial of order , takes 1, 2, 3,..., The calculation formula of ; Input different random variable dimensions and orders The Hermite polynomials are all obtained from Equation (2); According to Equation (1) and Equation (2), expand and represent the output response quantity using a 2nd-order Hermite polynomial: ; where , , and are the undetermined coefficients of , and the number of them , represents the transpose matrix, is the sample vector, represents taking the partial derivative with respect to the variable, , are both standard normal variables.

[0008] Optionally, the constructing of the collocation points includes: For the standard normal variable , its collocation points are a combination of a set of zeros and the roots of high-order Hermite polynomials, and its 2nd-order Hermite polynomial collocation points are obtained by combining the zeros and the roots of the 3rd-order Hermite polynomial.

[0009] Optionally, an optimal set of configuration points is determined based on a linearly independent method, and a configuration point matrix is further obtained, including: Determining the optimal set of configuration points includes: (1) Randomly combine the roots of the zero- and (m + 1)-order Hermite polynomials to generate an initial set of configuration points ; (2) Randomly select groups of configuration points from the initial set as a subset, and delete the selected configuration points from the initial set to obtain a new set of configuration points , and the th group of configuration points is denoted as ; (3) Establish a coefficient matrix , and solve for the rank of the coefficient matrix =Rank( ), with a random variable dimension of and an order = 2 Hermite polynomial, whose coefficient matrix is : ; where the subscript M represents the number of configuration points, ; (4) If the rank of the coefficient matrix is , then take the current subset as the final set of configuration points and end the selection process; otherwise, combine the groups of linearly independent configuration points and the newly selected groups of configuration points from the set of configuration points to form a new subset of configuration points, and return to (3) to continue the iteration until the condition is satisfied, is the number of undetermined coefficients of the Hermite polynomial.

[0010] Optionally, according to the principle of equiprobable transformation, all selected configuration points in the set of configuration points are mapped to the sample distribution to obtain sample points of the input quantity, including: According to the principle of equiprobable transformation of formula (4), map all selected groups of optimal configuration points to the bus load prediction power space to obtain groups of sample points of the bus load prediction power variable (i = 1, 2,... ); ; Among them, is the cumulative probability distribution function CDF of the standard normal variable , is the input random variable 's CDF, is 's inverse function.

[0011] Optionally, the deterministic power flow calculation is performed on the sample points based on the distributed graph parallel functional module to obtain a sample vector of the output response, including: (1) Distributed graph calculation framework construction: The power grid topology is abstracted as an undirected graph , where represents the set of power grid bus nodes, and voltage amplitude and phase angle state variables are assigned to each node, represents the set of edges connected by branches, and admittance values and are assigned as the attributes of the edges; (2) Task assignment and execution: Divide the groups of sample points of the input random variable predicted power into several subsets, and based on the load balancing strategy, distribute the sample point subsets to different processing cores. For the input samples on each computing core, initialize the initial conditions of the bus voltage and branch power flow for each sample point, and use the iterative power flow calculation algorithm to parallelly solve the node voltage and branch power flow in the scenario of each sample point; According to the power injection of the node, define the active power and reactive power balance equations. For the power flow equation of node , it is expressed as , where is the active power of node , is the reactive power of node , is the conductance matrix element between node and , is the susceptance matrix element between node and , is the phase angle difference between node and , is the voltage of node , is 's voltage, is the number of network nodes; (3) The update formula of the Newton-Raphson method is: , is the The voltage vector of the next iteration; is the Jacobian matrix, whose elements are the partial derivatives of the power equation with respect to the voltage variables, defined as ; is the power imbalance vector, indicating the active and reactive power imbalances at the th iteration, defined as , , are the active and reactive powers obtained by iterative calculation, , are the predicted power samples; (4) The calculation core updates the bus voltage through parallel matrix solution in each iteration , until the convergence condition is met: , is the preset convergence threshold; (5) After calculating the voltage at each bus node, the voltage information is transmitted to adjacent nodes, and based on the message passing function of the distributed graph calculation framework, the power flow information interaction and update of each bus are realized, and the parallel calculation results of each calculation core are summarized to the CPU main unit for integration to obtain the sample vector of the output response quantity Y .

[0012] Optionally, according to the determined configuration point matrix and the sample vector of the output response, a linear equation system is constructed to calculate the undetermined coefficients in the polynomial surrogate model, and based on the undetermined coefficients, a polynomial surrogate model is obtained, including: According to the configuration point coefficient matrix and the sample vector, the undetermined coefficients of the second-order Hermite polynomial are obtained by constructing the linear equation system of formula (5) , and finally the polynomial approximation expression of the output response quantity Y is obtained; , where sample vector.

[0013] Optionally, according to the polynomial surrogate model, the statistical characteristic quantities of the power flow response are solved to obtain the probability distribution of the response, including: Through the coefficients of the polynomial surrogate model of the output response quantity calculated, the statistical characteristic quantities of are obtained, and at the same time, a large number of output samples are calculated through the surrogate model to obtain the probability distribution of the node voltage or branch power flow, and the out-of-limit situation of the system response quantity is evaluated; ; ; where and are the mean and variance of the output response quantity Y, respectively.

[0014] Second aspect: A probabilistic power flow system based on polynomial surrogate and graph parallelism, the system comprising: A sample prediction module, configured to: establish a probability distribution model for the prediction error of bus load, and obtain the sample distribution of the predicted power; A model construction module, configured to: represent the output response quantity of the distribution network system as a polynomial function of the input, and establish an initial polynomial surrogate model; A collocation point matrix optimization module, configured to: construct collocation points, and determine an optimal set of collocation points based on the method of linear independence, and further obtain a collocation point matrix; A sample mapping transformation module, configured to: map all selected collocation points in the set of collocation points to the sample distribution according to the principle of equiprobable transformation, and obtain sample points of the input quantity; A parallel power flow calculation module, configured to: perform deterministic power flow calculation on the sample points based on a distributed graph parallel functional module, and obtain a sample vector of the output response; A coefficient solving module, configured to: construct a linear equation system according to the determined collocation point matrix and the sample vector of the output response, calculate the undetermined coefficients in the polynomial surrogate model, and obtain the polynomial surrogate model based on the undetermined coefficients; A statistical distribution calculation module, configured to: solve the statistical characteristic quantities of the power flow response according to the polynomial surrogate model, and obtain the probability distribution of the response.

[0015] Compared with the prior art, the beneficial effects achieved by the present invention are: 1. The method provided by the present invention highly accurately considers the randomness of load, photovoltaic power generation, and wind power following different distributions. It can not only simulate random variables with a normal distribution, but also efficiently process variables with a non-normal distribution, making the application more extensive.

[0016] 2. The method for selecting a set of collocation points provided by the present invention can effectively capture the high-probability region by the selected collocation points, improving the accuracy of the analysis results. The method based on linear independence avoids unnecessary deterministic power flow calculations, improving the calculation efficiency. At the same time, this method does not depend on specific power flow calculations when selecting collocation points, and only relates to the order of the polynomial and the number of input variables, having strong adaptability.

[0017] 3. The method for graph-parallel power flow calculation provided by the present invention models the distribution network as independent sub-regions, enabling parallel calculation of the nodes and edges within each region, and achieving data consistency between regions through the synchronization of boundary node information. This method makes full use of the independence and hierarchical characteristics of the graph structure, significantly reducing the calculation time, improving the efficiency and scalability of large-scale distribution network power flow calculation, while maintaining the calculation accuracy, and is particularly suitable for power system analysis with high complexity and a large number of nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The figure shows a flowchart of the power system probabilistic power flow method and system based on polynomial surrogate and graph parallel provided by the present invention; Figure 2 The figure shows a schematic diagram of the cumulative distribution function of the node voltage magnitude calculated by two methods, namely MCS and polynomial approximation, in an embodiment of the present invention; Figure 3 The figure shows a schematic diagram of the probability density function of the node voltage magnitude calculated by two methods, namely MCS and polynomial approximation, in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] To make the technical means, creative features, achieved objectives, and functions of the present invention easy to understand, the present invention will be further described below in conjunction with specific embodiments.

[0020] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0021] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the terms "installation", "connection", and "coupling" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0022] Embodiment 1, as Figure 1 shown, the power system probabilistic power flow method based on polynomial surrogate and graph parallelism provided by the present invention has a method flow consisting of Figure 1 It can be seen that this method includes: S1. Establish a probability distribution model for the bus load prediction error to obtain the sample distribution of the predicted power; S2. Establish an initial polynomial surrogate model and represent the output response quantity of the distribution network system as a polynomial function of the input; S3. Construct collocation points and determine the optimal set of collocation points based on the method of linear independence, and further obtain the collocation point matrix; S4. According to the principle of equiprobability transformation, map all selected collocation points in the collocation point set to the sample distribution to obtain the sample points of the input quantity; S5. Perform deterministic power flow calculations on the sample points based on the distributed graph parallel functional module to obtain the sample vector of the output response; S6. According to the determined collocation point matrix and the sample vector of the output response, construct a linear equation system to calculate the undetermined coefficients in the polynomial surrogate model, and obtain the polynomial surrogate model based on the undetermined coefficients; S7. According to the polynomial surrogate model, solve the statistical characteristic quantities of the power flow response to obtain the probability distribution of the response.

[0023] In the specific implementation process of this embodiment: Step S1 includes: collecting basic data such as the topological structure of the power grid, generator parameters, and load demands, and determining the main uncertainty sources affecting the system operation state, such as renewable energy power generation and load demand changes.

[0024] According to the real-time operation data of the th bus load (including renewable energy and power load) collected (N is the number of historical operation data sets, N = 1, 2, 3...), obtain the ultra-short-term bus load prediction data set for the future ( ) hours (N = 1, 2, 3...), and obtain the prediction error data set of the th bus load power. (N = 1, 2, 3...), (N = 1, 2, 3 …) ( is the actual value).

[0025] Establish a probability distribution model for the bus load prediction error From the perspective of engineering applications, the prediction error follows a normal (Gaussian) distribution, that is . Among them, the mean ( approaches 0, unbiased prediction), and the standard deviation . At this time, the predicted bus load power at the future moment is used as the input random variable of the distribution network system, and is represented by the symbol , and this variable follows a normal distribution with a mean of ( is the predicted power value of the bus at the future moment), and a standard deviation of , that is .

[0026] The predicted power input variable that satisfies the normal distribution is transformed into a standard normal distribution according to the standardization process.

[0027] In the specific implementation process of this embodiment: in step S2, the output response quantity ( is the node voltage or the branch power flow ) is expressed in the form of a polynomial expansion: (1), where is the number of buses with load fluctuations selected in the distribution network system (i.e., the dimension of the random variable); is the standard normal variable, ; , , … are the undetermined coefficients of the polynomial; is the multi-dimensional Hermite polynomial of order , and the calculation formula of is: (2).

[0028] The Hermite polynomials with different random variable dimensions and orders are all obtained from formula (2); According to formulas (1) and (2), the output response quantity is expanded and expressed by a 2nd-order Hermite polynomial: ; Among them, , , and are undetermined coefficients, and the number of them , represents the transpose matrix, is the sample vector, represents taking the partial derivative with respect to the variable, , are both standard normal variables.

[0029] In the specific implementation process of this embodiment: Step S3 includes: constructing collocation points: for the standard normal variable , its collocation points are a combination of a set of zeros and the roots of the higher-order Hermite polynomial. Then, the optimal collocation point set is determined based on the method of linear independence.

[0030] In the specific implementation process of this embodiment: Step S3 also includes: determining the optimal collocation point set based on the method of linear independence, and further obtaining the collocation point matrix, including: Determining the optimal collocation point set includes: (1) Randomly combine zeros and the roots of the (m + 1)-th order Hermite polynomial to generate the initial collocation point set ; (2) Randomly select groups of collocation points from the initial set as a subset, and delete the selected collocation points from the initial set to obtain a new collocation point set , and the -th group of collocation points is denoted as ; (3) Establish the coefficient matrix , and solve the rank of the coefficient matrix = Rank( ), for the Hermite polynomial with the variable dimension of and the order = 2, its coefficient matrix is : ; Among them, the subscript M represents the number of collocation points, ; (4) If the rank of the coefficient matrix , then take the current subset as the final collocation point set and end the selection process; otherwise, combine the groups of linearly independent collocation points and the newly selected from the collocation point set The group of configuration points jointly form a new subset of configuration points and return to (3) for continued iteration until the conditions are met , is the number of undetermined coefficients of the Hermite polynomial.

[0031] In the specific implementation process of this embodiment: Step S4 includes: Using formula (4): the equiprobability transformation formula (4), map all selected group of optimal configuration points (standard normal space) to the space of the original input variables (bus load prediction error) to obtain group of sample points ( = 1, 2,... ). Among them, is the cumulative distribution function (CDF) of the standard normal variable ; is the CDF of the input random variable , is 's inverse function.

[0032] In the specific implementation process of this embodiment: Step S5 includes: Based on the graph parallel computing framework, obtain the sample vector of the output response quantity Y (node voltage or branch power).

[0033] In the specific implementation process of this embodiment: Step S6 includes: According to the configuration point coefficient matrix determined in step S3 and the sample vector obtained in step S5, through formula (5) , obtain the undetermined coefficients of the second-order Hermite polynomial, and finally obtain the polynomial approximation expression of the output response quantity Y.

[0034] In the specific implementation process of this embodiment: Step S7 includes: Through the coefficients of the polynomial surrogate model of the obtained output response quantity , a series of statistical characteristic quantities of can be quickly calculated, such as the mean, variance, etc. At the same time, a large number of output samples are obtained through the surrogate model calculation to obtain the probability distribution of the node voltage or branch power flow, and evaluate the out-of-limit situation of the system response quantity; ; ; Among them, and are respectively the mean and variance of the output response quantity Y.

[0035] Example 2. The IEEE 33 - node system is selected as a case in the present invention to verify the feasibility of the proposed method: In the IEEE 33 - node system, assume that the load powers of nodes 3, 4, 9, 11, 16, 19, 23, 25, 27, 29 follow a normal distribution, with the mean value being the original node power and the standard deviation being 5% of the mean value. Assume that after nodes 5, 10, 15, 20, 30 are respectively connected to wind turbines with rated powers of 0.050, 0.055, 0.045, 0.060, 0.080 MW, the load powers of these nodes also follow a normal distribution, the power values being the mean values, and the standard deviations being 15%, 10%, 10%, 13%, 12% of the mean values respectively. Take the power of these 15 nodes as random input variables, and the variable dimension n = 15.

[0036] Output response quantity ( For the node voltage ) is expanded and expressed by a 2 - order Hermite polynomial: . , , and are undetermined coefficients of .

[0037] Construct collocation points: Each group of collocation points is a vector, and each element in it is either 0, , any one of the three numbers. Determine the optimal collocation points: (1) First, generate an initial set of collocation points , by randomly combining 0, ; (2) Randomly select 136 groups of collocation points from the initial set as a subset, and delete these selected collocation points from the initial set of collocation points to obtain a new set of collocation points ; (3) Establish a coefficient matrix H, H is a square matrix of order , and solve the rank of this matrix = Rank( ) If the rank of the coefficient matrix , then take the current subset as the final set of collocation points and end the selection process; otherwise, add groups of linearly independent collocation points (selected from groups of collocation point subsets) and from the set of collocation points Newly selected Group configuration points, jointly forming a new subset of configuration points, and returning to (3) to continue iteration until the condition is met , and the optimal set of 136 configuration points can be obtained.

[0038] After obtaining the full-rank coefficient matrix H and the optimal set of 136 configuration points, using the equiprobability transformation formula (4), map all the selected 136 optimal configuration points (in the standard normal space) to the original input variable space to obtain 136 sample points of the node load prediction power variable (i = 1, 2,... 136).

[0039] Perform iterative power flow calculations on the 136 sample points using the computer graph parallel function module to obtain the sample vector of the output response quantity Y (node voltage) .

[0040] According to the obtained full-rank coefficient matrix H and the sample vector of the output response quantity Y (node voltage), the undetermined coefficients of the second-order Hermite polynomial can be obtained using formula (5) , and obtain the polynomial expansion expression of the output response quantity Y (node voltage).

[0041] Set the calculation result of the 10,000-time Monte Carlo simulation method (MCS) as the exact value and use it as a benchmark to test the accuracy of the polynomial approximation algorithm (PCE). Figure 2 and Figure 3 respectively give the comparison diagrams of the CDF curve and PDF curve of the voltage amplitude at node 3 under the two methods. It can be seen from the figure that the calculation accuracies of the two methods are very close.

[0042] Table 1. Comparison of the expectations and standard deviations of the voltage amplitude at node 3 under the two methods:

[0043] Table 1 gives the expectations and standard deviations of the voltage amplitude at node 3 calculated under the Monte Carlo simulation method (MCS) and polynomial approximation (PCE). The calculated expected values of the two methods are equal, and the standard deviations are also basically equal, with an error of only about 1%. It can be seen from this that the polynomial approximation method can accurately estimate the probability statistical characteristics of the node voltage amplitude.

[0044] Table 2. Comparison of the calculation times under the two methods:

[0045] Table 2 lists the time for selecting configuration points , the time for solving coefficients , the time for sample estimation and the total time Compared with the Monte Carlo simulation method (MCS), the time spent by the polynomial approximation method (PCE) in solving coefficients and evaluating statistical samples can be ignored. Obviously, the polynomial approximation method (PCE) is more computationally efficient than the Monte Carlo simulation method (MCS).

[0046] Example 3, a power system probabilistic power flow system based on polynomial surrogate and graph parallelism, the system includes: A sample prediction module, configured to: establish a probability distribution model of the bus load prediction error and obtain the sample distribution of the predicted power; A model construction module, configured to: represent the output response quantity of the distribution network system as a polynomial function of the input and establish an initial polynomial surrogate model; A collocation point matrix optimization module, configured to: construct collocation points, determine the optimal set of collocation points based on a linearly independent method, and further obtain a collocation point matrix; A sample mapping transformation module, configured to: map all selected collocation points in the collocation point set to the sample distribution according to the principle of equiprobable transformation to obtain the sample points of the input quantity; A parallel power flow calculation module, configured to: perform deterministic power flow calculations on the sample points based on a distributed graph parallel functional module to obtain the sample vector of the output response; A coefficient solving module, configured to: construct a linear equation system according to the determined collocation point matrix and the sample vector of the output response to calculate the undetermined coefficients in the polynomial surrogate model, and obtain the polynomial surrogate model based on the undetermined coefficients; A statistical distribution calculation module, configured to: solve the statistical characteristic quantities of the power flow response according to the polynomial surrogate model to obtain the probability distribution of the response.

[0047] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and deformations can be made, and these improvements and deformations should also be regarded as the protection scope of the present invention.

Claims

1. A probabilistic power flow method for power systems based on polynomial agents and graph parallelism, characterized in that: The method comprises: Establish a probability distribution model for bus load forecasting error and obtain sample distribution of predicted power; The output response of the distribution network system is expressed as a polynomial function of the input, and an initial polynomial proxy model is established; Constructing the configuration points, and determining the optimal configuration point set based on the linear independence method, and further obtaining the configuration point matrix; According to the principle of equal probability transformation, all selected configuration points in the configuration point set are mapped to the sample distribution to obtain the sample points of the input quantity; Based on the distributed graph parallel function module, the deterministic power flow calculation is performed on the sample points to obtain the sample vector of the output response; According to the determined configuration point matrix and the sample vector of the output response, a linear equation group is constructed to calculate the undetermined coefficients in the initial polynomial proxy model, and the polynomial proxy model is obtained based on the undetermined coefficients; According to the polynomial proxy model, the statistical characteristic quantities of the power flow response are solved and the probability distribution of the response is obtained.

2. The power system probabilistic power flow method based on polynomial proxy and graph parallelism according to claim 1 is characterized in that: The method of establishing a probability distribution model of bus load prediction error to obtain a sample distribution of predicted power includes: According to the collected Real-time operation data of bus loads , get the future Hourly bus ultra-short-term load forecasting dataset , N is the number of historical operation data sets; Find the first Bus load power prediction error dataset , establish the bus load prediction error The probability distribution model of the prediction error follows the normal Gaussian distribution ; The future The bus load power forecast at the moment is used as the input random variable of the distribution network system, and its mean is ; The predicted power input variable that satisfies the normal distribution is The standardization process is transformed into a standard normal distribution, and the obtained standard normal variable ; in, is a random variable from the original normal distribution, is the mean of the normal distribution, is the standard deviation of the normal distribution, is the transformed standard normal distribution, , N=1,2,3…; is the actual value, mean , Approaching 0, unbiased prediction, standard deviation ; represents the input random variable, For the future The predicted bus power value at the moment, the standard deviation is Normal distribution , Indicates The bus load power prediction error of the data set is express The index of the historical run data set.

3. The power system probabilistic power flow method based on polynomial proxy and graph parallelism according to claim 1 is characterized in that: The output response of the distribution network system is expressed as an input polynomial function to establish an initial polynomial proxy model, including: The output response of the distribution network system is expressed as a polynomial expansion: ； in, is the output response of the distribution network system, is the number of buses with load fluctuations selected in the distribution network system, that is, the dimension of the random variable; is a standard normal variable, ; , , …are the unknown coefficients of the polynomial; The order is The multidimensional Hermite polynomials of Take 1, 2, 3..., The calculation formula is: ； Input different random variable dimensions and order The Hermite polynomials of are obtained from formula (2); According to equations (1) and (2), the output response Expressed as a 2nd-order Hermite polynomial expansion: ； in, , , and for The number of undetermined coefficients , represents the transposed matrix, is the sample vector, It means to find the partial derivative of the variable. , All are standard normal variables.

4. The power system probabilistic power flow method based on polynomial proxy and graph parallelism according to claim 1 is characterized in that: The construction configuration point includes: For standard normal variables , whose configuration points are a combination of a set of zero points and roots of higher-order Hermite polynomials, and its second-order Hermite polynomial configuration points are obtained by combining zero points and roots of third-order Hermite polynomials.

5. The power system probabilistic power flow method based on polynomial proxy and graph parallelism according to claim 4 is characterized in that: Based on the linear independence method, the optimal configuration point set is determined, and the configuration point matrix is ​​further obtained, including: Determining the optimal configuration point set includes: (1) Randomly combine the roots of zero and (m+1) order Hermite polynomials to generate an initial configuration point set ; (2) From the initial set Random selection The group configuration points are taken as a subset and the selected configuration points are deleted from the initial set to obtain a new configuration point set. , No. The group configuration point is denoted as ; (3) Establish coefficient matrix , and solve the coefficient matrix Rank =Rank( ), with random variable dimension , order =2 Hermite polynomial, its coefficient matrix is : ； Wherein, the subscript M represents the number of configuration points, ; (4) If the coefficient matrix Rank , the current subset is taken as the final configuration point set and the selection process ends; otherwise, Set of linearly independent collocation points and from the set of collocation points Newly selected The group configuration points together form a new set of configuration point subsets, and return to (3) to continue iterating until the condition is met , is the number of undetermined coefficients of the Hermite polynomial.

6. The power system probabilistic power flow method based on polynomial proxy and graph parallelism according to claim 5 is characterized in that: According to the equal probability transformation principle, all selected configuration points in the configuration point set are mapped to the sample distribution to obtain the sample points of the input quantity, including: According to the equal probability transformation principle of formula (4), all selected The optimal configuration point of the group is mapped to the bus load forecast power space to obtain the bus load forecast power variable Group sample points (i=1,2,… ); ； in, is a standard normal variable The cumulative probability distribution function CDF is The input random variable The CDF of for The inverse function of .

7. The power system probabilistic power flow method based on polynomial proxy and graph parallelism according to claim 1 is characterized in that: The distributed graph parallel function module is used to perform deterministic power flow calculation on the sample points to obtain the sample vector of the output response, including: (1) Construction of distributed graph computing framework: the power grid topology is abstracted as an undirected graph ,in Represents the set of busbar nodes in the power grid, and each node is assigned voltage amplitude and phase angle state. A set of edges representing branch connections, each edge is assigned an admittance value and As an attribute of an edge; (2) Task allocation and execution: Input random variables to predict power of The sample points are divided into several subsets. Based on the load balancing strategy, the sample point subsets are allocated to different processing cores. For the input samples on each computing core, the initial conditions of the bus voltage and branch power flow are initialized for each sample point. The iterative power flow calculation algorithm is used to solve the node voltage and branch power flow in parallel in the scenario of each sample point. According to the power injection of the node, the active power and reactive power balance equations are defined. The power flow equation is expressed as ,in, Is a node The active power, Is a node The reactive power, For Node and The conductivity matrix elements between For Node and The susceptance matrix elements between Is a node and The phase angle difference between Is a node The voltage, yes The voltage, is the number of network nodes; (3) The update formula of the Newton-Raphson method is: , For the The voltage vector of the iteration; is the Jacobian matrix whose elements are the partial derivatives of the power equation with respect to the voltage variable, defined as ; is the power imbalance vector, indicating that The active and reactive power imbalance at the iteration is defined as , , is the active and reactive power calculated iteratively, , is the predicted power sample; (4) The computing core updates the bus voltage by solving the parallel matrix in each iteration , until the convergence condition is met: , is the preset convergence threshold; (5) After each bus node calculates the voltage, it transmits the voltage information to the adjacent nodes. Based on the message passing function of the distributed graph computing framework, the flow information of each bus is interacted and updated. The parallel calculation results of each computing core are aggregated to the CPU main unit for integration to obtain the sample vector of the output response quantity Y. .

8. The power system probabilistic power flow method based on polynomial proxy and graph parallelism according to claim 1, characterized in that: According to the determined configuration point matrix and the sample vector of the output response, a linear equation group is constructed to calculate the undetermined coefficients in the polynomial proxy model, and the polynomial proxy model is obtained based on the undetermined coefficients, including: According to the configuration point coefficient matrix and sample vector, the unknown coefficients of the second-order Hermite polynomial are obtained by constructing the linear equation system of formula (5): , and finally obtain the polynomial approximation expression of the output response quantity Y; ,in, Sample vector.

9. The power system probabilistic power flow method based on polynomial proxy and graph parallelism according to claim 1, characterized in that: The method of solving the statistical characteristic quantity of the power flow response according to the polynomial proxy model to obtain the probability distribution of the response includes: The output response is obtained by The coefficients of the polynomial proxy model are calculated to obtain The statistical characteristic quantity of the system is calculated by the agent model to obtain a large number of output samples, obtain the probability distribution of node voltage or branch power flow, and evaluate the over-limit situation of the system response quantity; ； ； in, and are the mean and variance of the output response Y respectively.

10. A probabilistic power flow system based on polynomial agents and graph parallelism, characterized by: The system comprises: The sample prediction module is configured to: establish a probability distribution model of bus load prediction error to obtain a sample distribution of predicted power; The model building module is configured to: represent the output response quantity of the distribution network system as a polynomial function of the input, and establish an initial polynomial agent model; The configuration point matrix optimization module is configured to: construct configuration points, determine the optimal configuration point set based on a linear independence method, and further obtain a configuration point matrix; The sample mapping conversion module is configured to: map all selected configuration points in the configuration point set to the sample distribution according to the equal probability transformation principle to obtain the sample points of the input quantity; The parallel power flow calculation module is configured to: perform deterministic power flow calculation on the sample points based on the distributed graph parallel function module to obtain a sample vector of the output response; The coefficient solving module is configured to: construct a linear equation group to calculate the undetermined coefficients in the polynomial proxy model according to the determined configuration point matrix and the sample vector of the output response, and obtain the polynomial proxy model based on the undetermined coefficients; The statistical distribution calculation module is configured to solve the statistical characteristic quantity of the power flow response according to the polynomial proxy model to obtain the probability distribution of the response.

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