Power System Probabilistic Power Flow Method and System Based on Polynomial Surrogate and Graph Parallelism

Abstract

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. It includes establishing a probability distribution model of the bus load prediction error to obtain the sample distribution of the predicted power; representing the output response quantity of the system as a polynomial function of the input and establishing an initial polynomial surrogate model; determining the optimal set of collocation points; mapping all selected collocation points to the input sample space to obtain a small number of sample points of the input variables; performing deterministic power flow calculations on the sample points to obtain the sample vector of the output response; calculating the undetermined coefficients in the surrogate model according to the collocation point matrix and the sample vector; and solving the statistical characteristic quantities of the power flow response to obtain the probability distribution of the response. The calculation method provided by the present invention can accurately and efficiently estimate the probability distribution of the power flow response, facilitating the probabilistic power flow calculation of a new power system under the access of distributed power sources.

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 the penetration rate continuously increasing. 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 have 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 scheduling 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 adopting the following technical solutions:

[0006] In the first aspect: A probabilistic power flow method for power systems based on polynomial surrogate and graph parallelism, the method includes:

[0007] Establish a probability distribution model of the bus load prediction error to obtain the sample distribution of the predicted power;

[0008] Express the output response quantity of the distribution network system as a polynomial function of the input, and establish an initial polynomial surrogate model;

[0009] Construct collocation points, and determine the optimal set of collocation points based on a linearly independent method, and further obtain a collocation point matrix;

[0010] According to the principle of equiprobable transformation, map all selected configuration points in the set of configuration points to the sample distribution to obtain the sample points of the input quantity;

[0011] Based on the distributed graph parallel functional module, perform deterministic power flow calculation on the sample points to obtain the sample vector of the output response;

[0012] According to the determined configuration point matrix and the sample vector of the output response, construct a linear equation system to calculate the undetermined coefficients in the initial polynomial surrogate model, and obtain the polynomial surrogate model based on the undetermined coefficients;

[0013] According to the polynomial surrogate model, solve the statistical characteristic quantities of the power flow response to obtain the probability distribution of the response.

[0014] Optionally, the establishment of the probability distribution model of the bus load prediction error to obtain the sample distribution of the predicted power includes:

[0015] According to the real-time operation data of the load of the th bus collected , obtain the ultra-short-term load prediction data set of the bus for the next hours, N is the number of historical operation data sets, ;

[0016] Obtain the data set of the predicted power error of the load of the th bus, and establish the probability distribution model of the bus load prediction error , and the prediction error follows a normal Gaussian distribution ; ;

[0017] Take the predicted power of the bus load at the next moment as the input random variable of the distribution network system, and it follows a mean value of ;

[0018] Input the predicted power variable that satisfies the normal distribution into the standardization process of to transform it into a standard normal distribution, and obtain the standard normal variable ;

[0019] Among them, 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 , approaches 0, unbiased prediction, the standard deviation ; represents the input random variable, For the future The predicted bus power value at the moment is Normal distribution , Indicates the The bus load power prediction error of the data set is express The index of the historical run dataset.

[0020] Optionally, expressing the output response of the distribution network system as a polynomial function of the input to establish an initial polynomial proxy model includes:

[0021] The output response of the distribution network system is expressed as a polynomial expansion:

[0022] ;

[0023] 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 Multidimensional Hermite polynomials of Take 1, 2, 3..., The calculation formula is:

[0024] ;

[0025] Input different random variable dimensions and order The Hermite polynomials of are obtained from formula (2);

[0026] According to formula (1) and formula (2), the output response Expressed as a 2nd-order Hermite polynomial expansion:

[0027] ;

[0028] 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.

[0029] Optionally, the construction configuration point includes:

[0030] For standard normal variables , its collocation points are a combination of a set of zeros and roots of higher-order Hermite polynomials, and its second-order Hermite polynomial collocation points are obtained by combining zeros and roots of third-order Hermite polynomials.

[0031] Optionally, the optimal configuration point set is determined based on a linear independence method, and a configuration point matrix is further obtained, including:

[0032] Determining the optimal configuration point set includes:

[0033] (1) Randomly combine the roots of zero and (m+1) order Hermite polynomials to generate the initial configuration point set ;

[0034] (2) From the initial set Random selection Group the configuration points as a subset and delete the selected configuration points from the initial set to obtain a new configuration point set , No. The group configuration point is recorded as ;

[0035] (3) Establish coefficient matrix , and solve the coefficient matrix Rank =Rank( ), with the random variable dimension as , order =2 Hermite polynomial, its coefficient matrix is :

[0036] ;

[0037] Wherein, the subscript M represents the number of configuration points, ;

[0038] (4) If the coefficient matrix Rank , then the current subset is taken as the final configuration point set and the selection process ends; otherwise, Group linearly independent collocation points and sets of collocation points The new selection Group configuration points to 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.

[0039] Optionally, mapping all selected configuration points in the configuration point set to a sample distribution according to an equal probability transformation principle to obtain sample points of the input quantity includes:

[0040] 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,… );

[0041] ;

[0042] in, is a standard normal variable The cumulative probability distribution function CDF is, is the input random variable CDF, for The inverse function of .

[0043] Optionally, the distributed graph parallel function module is used to perform deterministic power flow calculation on the sample points to obtain a sample vector of the output response, including:

[0044] (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;

[0045] (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 assigned 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 node voltage and branch power flow are solved in parallel using an iterative power flow calculation algorithm for each sample point scenario.

[0046] Define the active power and reactive power balance equations according to the power injection of nodes. For node the power flow equation is expressed as , where is the active power of node , is the reactive power of node , is the element of the conductance matrix between nodes and , is the element of the susceptance matrix between nodes and , is the phase angle difference between nodes and , is the voltage of node , is 's voltage, is the number of network nodes;

[0047] (3) The update formula of the Newton-Raphson method is: , is the voltage vector at the -th 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, representing 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;

[0048] (4) The calculation core updates the bus voltage by parallel matrix solving in each iteration until the convergence condition is satisfied: , is the preset convergence threshold;

[0049] (5) After each bus node calculates the voltage, it transmits the voltage information to adjacent nodes, and based on the message passing function of the distributed graph calculation framework, realizes the interaction and update of the power flow information of each bus. The parallel calculation results of each calculation core are aggregated to the CPU main unit for integration to obtain the sample vector of the output response quantity Y.

[0050] Optionally, based on the determined configuration point matrix and the sample vector of the output response, a system of linear equations is constructed to calculate the undetermined coefficients in the polynomial surrogate model, and the polynomial surrogate model is obtained based on the undetermined coefficients, including:

[0051] 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 system of linear equations in Equation (5) , and finally the polynomial approximation expression of the output response quantity Y is obtained;

[0052] , where Sample vector.

[0053] 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:

[0054] Through the obtained polynomial surrogate model coefficients of the output response quantity , the statistical characteristic quantities of are calculated. At the same time, a large number of output samples are calculated through the surrogate model, the probability distribution of the node voltage or branch power flow is obtained, and the out-of-limit situation of the system response quantity is evaluated;

[0055] ;

[0056] ;

[0057] where and are the mean and variance of the output response quantity Y, respectively.

[0058] Second aspect: A power system probabilistic power flow system based on polynomial surrogate and graph parallelism, the system includes:

[0059] A sample prediction module, configured to: establish a probability distribution model of the bus load prediction error to obtain the sample distribution of the predicted power;

[0060] 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;

[0061] A configuration point matrix optimization module, configured to: construct configuration points and determine an optimal set of configuration points based on a linearly independent method, and further obtain a configuration point matrix;

[0062] A sample mapping conversion module, configured to: map all selected configuration points in a set of configuration points to a sample distribution according to the principle of equiprobable transformation, so as to obtain sample points of an input quantity;

[0063] A parallel power flow calculation module, configured to: perform deterministic power flow calculation on sample points based on a distributed graph parallel functional module, so as to obtain a sample vector of an output response;

[0064] A coefficient solving module, configured to: construct a linear equation set according to a determined configuration point matrix and a sample vector of an output response to calculate undetermined coefficients in a polynomial surrogate model, and obtain a polynomial surrogate model based on the undetermined coefficients;

[0065] A statistical distribution calculation module, configured to: solve statistical characteristic quantities of a power flow response according to a polynomial surrogate model, so as to obtain a probability distribution of the response.

[0066] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0067] 1. The method provided by the present invention highly accurately considers the randomness of loads, 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.

[0068] 2. The method for selecting a set of configuration points provided by the present invention can effectively capture high-probability regions with the selected configuration points, improving the accuracy of analysis results. The method based on linear independence avoids unnecessary deterministic power flow calculations, improving calculation efficiency. At the same time, this method does not depend on specific power flow calculations when selecting configuration points, only related to the order of the polynomial and the number of input variables, and has strong adaptability.

[0069] 3. The method for graph parallel power flow calculation provided by the present invention models a distribution network as independent sub-regions, enabling parallel calculation of nodes and edges within each region, and achieving data consistency between regions through boundary node information synchronization. This method makes full use of the independence and hierarchical characteristics of the graph structure, greatly reducing calculation time, improving the efficiency and scalability of large-scale distribution network power flow calculation, while maintaining calculation accuracy, and is especially suitable for power system analysis with high complexity and a large number of nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 The figure shows a flowchart of a power system probabilistic power flow method and system based on polynomial surrogate and graph parallel provided by the present invention;

[0071] Figure 2 The figure shows a schematic diagram of cumulative distribution functions of node voltage magnitudes calculated by two methods, namely MCS and polynomial approximation, in an embodiment of the present invention;

[0072] Figure 3 The figure shows a schematic diagram of the probability density function of calculating the node voltage amplitude by two methods of MCS and polynomial approximation in the embodiment of the present invention. Specific embodiments

[0073] In order to make the technical means, creative features, achieved purposes and effects of the present invention easy to understand, the present invention will be further described below in conjunction with specific embodiments.

[0074] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. It 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, so it cannot be understood as a limitation to 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 indicating the quantity of the indicated technical features. Thus, the 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 "plurality" is two or more.

[0075] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the terms "installation", "connection", "connection" 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 elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.

[0076] 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, its method flow is Figure 1 It can be seen that this method includes:

[0077] S1. Establish a probability distribution model of the bus load prediction error to obtain the sample distribution of the predicted power;

[0078] 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;

[0079] 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;

[0080] S4. According to the principle of equiprobable transformation, map all the selected configuration points in the set of configuration points to the sample distribution to obtain the sample points of the input quantity;

[0081] S5. Based on the distributed graph parallel functional module, perform deterministic power flow calculation on the sample points to obtain the sample vector of the output response;

[0082] S6. According to the determined configuration 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;

[0083] 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.

[0084] 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, load demand, etc., and determining the main uncertainty sources affecting the system operation state, such as renewable energy power generation, load demand changes, etc.

[0085] According to the real-time operation data of the load of the th bus (including renewable energy and electrical load) collected (N is the number of historical operation data sets, N = 1, 2, 3...), obtain the very short-term load prediction data set of the bus for the future ( ), and obtain the load power prediction error data set of the th bus (N = 1, 2, 3...) ( is the actual value). (N = 1, 2, 3...) ( is the actual value).

[0086] Establish a probability distribution model for the load prediction error of the bus . From the perspective of engineering application, the prediction error follows a normal (Gaussian) distribution, that is . Among them, the mean value ( approaches 0, unbiased prediction), and the standard deviation . At this time, the load power prediction of the bus at the future moment is taken 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 bus prediction power value at the future moment) and a standard deviation of , that is .

[0087] The predictive power input variables that satisfy the normal distribution are transformed into the standard normal distribution according to the standardization process.

[0088] In the specific implementation process of this embodiment: in step S2, the output response quantity of the system ( being the node voltage or the branch power flow ) is expressed in the form of polynomial expansion:

[0089] (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).

[0090] The Hermite polynomials with different random variable dimensions and orders are all obtained from formula (2);

[0091] According to formulas (1) and (2), the output response quantity is expanded and expressed by the Hermite polynomial of order 2:

[0092] ;

[0093] where , , and are the undetermined coefficients of , and the number of them , represents the transposed matrix, is the sample vector, represents taking the partial derivative of the variable, , are both standard normal variables.

[0094] 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 high-order Hermite polynomial. Then, the optimal set of collocation points is determined based on the method of linear independence.

[0095] In the specific implementation process of this embodiment: Step S3 further includes: determining an optimal set of collocation points based on a linearly independent method, and further obtaining a collocation point matrix, including:

[0096] Determining the optimal set of collocation points includes:

[0097] (1) Randomly combine the roots of the zero - sum (m + 1) - order Hermite polynomial to generate an initial set of collocation points ;

[0098] (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 set of collocation points , and the th group of collocation points is denoted as ;

[0099] (3) Establish a coefficient matrix , and solve the rank of the coefficient matrix = Rank( ), for a Hermite polynomial with variable dimension and order = 2, its coefficient matrix is :

[0100] ;

[0101] Where the subscript M represents the number of collocation points, ;

[0102] (4) 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, combine groups of linearly independent collocation points and newly selected groups of collocation points from the set of collocation points to form a new subset of collocation points, and return to (3) to continue the iteration until the condition is satisfied, where

[0103] In the specific implementation process of this embodiment: Step S4 includes: using formula (4): the equiprobable transformation formula (4), mapping all selected groups of optimal collocation points (in the standard normal space) to the space of the original input variables (bus load prediction errors), to obtain groups of sample points of the bus prediction error variables ( = 1, 2, … ). Among them, is the cumulative probability distribution function (CDF) of the standard normal variable ; is the CDF of the input random variable , and is the inverse function of .

[0104] In the specific implementation process of this embodiment: Step S5 includes: obtaining the sample vector of the output response quantity Y (node voltage or branch power) based on the graph parallel computing framework.

[0105] In the specific implementation process of this embodiment: Step S6 includes: according to the collocation point coefficient matrix determined in Step S3 and the sample vector obtained in Step S5, through Equation (5) , obtaining the undetermined coefficients of the second-order Hermite polynomial, and finally obtaining the polynomial approximation expression of the output response quantity Y.

[0106] 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 , such as mean value, variance, etc., can be quickly calculated. 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 evaluate the out-of-limit situation of the system response quantity;

[0107] ;

[0108] ;

[0109] Among them, and are the mean value and variance of the output response quantity Y respectively.

[0110] Embodiment 2, the present invention selects the IEEE 33-node system as a case to verify the feasibility of the proposed method:

[0111] ​​​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 being the original node power and the standard deviation being 5% of the mean. 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, with the power values being the means and the standard deviations being 15%, 10%, 10%, 13%, 12% of the means respectively. Take the power of these 15 nodes as random input variables, and the variable dimension \(n = 15\).

[0112] Output response quantity ( For the node voltage ) is expanded and expressed by a 2 - order Hermite polynomial: . 、 、 and are the undetermined coefficients of, and the number of them .

[0113] Construct collocation points: Each set of collocation points is a vector of , and each element in it is any one of 0, , three numbers. Determine the optimal collocation points:

[0114] (1) First, generate an initial set of collocation points , by randomly combining 0, ;

[0115] (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 ;

[0116] (3) Establish a coefficient matrix \(H\), \(H\) is a square matrix of order, and solve the rank of this matrix =Rank( );

[0117] (4) 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, take 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 then returning to (3) to continue iteration until the condition is satisfied , and the optimal set of 136 configuration points can be obtained.

[0118] After obtaining the full-rank coefficient matrix H and the optimal set of 136 configuration points, using the equiprobable 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).

[0119] Use the computer graphics parallel function module to perform iterative power flow calculations on the 136 sample points to obtain the sample vector of the output response quantity Y (node voltage) .

[0120] 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).

[0121] Assume that the calculation result of the 10,000-time Monte Carlo simulation method (MCS) is 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 of node 3 under the two methods. It can be seen from the figure that the calculation accuracies of the two methods are very close.

[0122] Table 1 Comparison of the expectations and standard deviations of the voltage amplitude of node 3 under the two methods:

[0123]

[0124] Table 1 gives the expectations and standard deviations of the voltage amplitude of node 3 calculated by the Monte Carlo simulation method (MCS) and the 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.

[0125] Table 2 Comparison of the calculation times under the two methods:

[0126]

[0127] Table 2 lists the time for selecting configuration points , the time for solving coefficients , sample estimation time and 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).

[0128] Example 3, a power system probabilistic power flow system based on polynomial surrogate and graph parallelism, the system includes:

[0129] 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;

[0130] 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;

[0131] A collocation point matrix optimization module, configured to: construct collocation points and determine the optimal set of collocation points based on a linearly independent method, and further obtain a collocation point matrix;

[0132] A sample mapping conversion module, configured to: map all selected collocation points in the collocation point set to the sample distribution according to the equal probability transformation principle to obtain sample points of the input quantity;

[0133] 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 a sample vector of the output response;

[0134] 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;

[0135] 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.

[0136] The above is only the preferred embodiment 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 power system probabilistic power flow method based on polynomial agents and graph parallelism, characterized by: The method comprises: Establish a probability distribution model for bus load forecast error and obtain the 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 agent 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, 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 system 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 characteristics 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 agent 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 busbar loads , get the future Hourly bus ultra-short-term load forecasting dataset , N is the number of historical running data sets; Get 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 is Normal distribution , Indicates the The bus load power prediction error of the data set is express The index of the historical run dataset.

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

5. The power system probabilistic power flow method based on polynomial agent and graph parallelism according to claim 4 is characterized in that: The optimal configuration point set is determined based on the linear independence method, 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 the initial configuration point set ; (2) From the initial set Random selection Group the configuration points as a subset and delete the selected configuration points from the initial set to obtain a new configuration point set , No. The group configuration point is recorded as ; (3) Establish coefficient matrix , and solve the coefficient matrix Rank =Rank( ), with the random variable dimension as , order =2 Hermite polynomial, its coefficient matrix is : ； Wherein, the subscript M represents the number of configuration points, ; (4) If the coefficient matrix Rank , then 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 The new selection Group configuration points to 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 agent and graph parallelism according to claim 5 is characterized in that: 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, 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, is the input random variable CDF, for The inverse function of .

7. The power system probabilistic power flow method based on polynomial agent and graph parallelism according to claim 1 is characterized in that: The distributed graph parallel function module performs 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 assigned 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 node voltage and branch power flow are solved in parallel using an iterative power flow calculation algorithm for each sample point scenario. 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 nodes and The conductivity matrix elements between For nodes 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 , 、 are the active and reactive powers obtained by iterative calculation, 、 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 busbar 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 busbar is interactively 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 agent and graph parallelism according to claim 1 is characterized in that: 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 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 undetermined 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 agent and graph parallelism according to claim 1, characterized in that: The method of solving the statistical characteristic quantity of the power flow response based on the polynomial proxy model and obtaining the probability distribution of the response includes: The output response is obtained The coefficients of the polynomial surrogate model are calculated to obtain The statistical characteristics of the system are calculated and a large number of output samples are obtained through the proxy model to obtain the probability distribution of node voltage or branch power flow, and to 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 to 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 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 system 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 agent model and obtain the probability distribution of the response.

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