A power distribution network modeling method based on a shallow physical information neural network

Abstract

The present application relates to power distribution network technical field, specifically to a kind of power distribution network modeling method based on shallow physical information neural network, comprising the following steps: S1, constructing modeling base model: establishing power flow model of distribution network, while using non-negative weight and ReLU activation function, ICNN network is constructed;S2, ICNN-based distribution network topological structure modeling: the weight of ICNN network is discretized by clustering method, the inverse of branch association matrix is estimated and its inverse matrix is solved, so that the topological structure of distribution network is obtained by inversion;S3, ICNN-based distribution network line parameter modeling: the line resistance and reactance diagonal matrix are estimated by ICNN network, and a regularization term is introduced for optimization, to realize the inversion modeling of distribution network line parameters;The present application realizes the joint inversion of distribution network structure and parameter, significantly improves the practicability and robustness of modeling.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of power distribution networks, and in particular to a power distribution network modeling method based on a shallow physical information neural network. BACKGROUND

[0002] With the development of smart grids and the access of multiple types of loads, the structure of power distribution networks is increasingly complex, and the operating environment is also more variable. Emerging applications such as distributed energy, electric vehicle charging and demand response have put forward higher modeling and regulation requirements for power distribution networks. In order to realize power quality optimization, operating cost reduction and power supply reliability guarantee, the modeling accuracy of power distribution networks is a key foundation. At present, power distribution network modeling methods are mainly divided into model-driven and data-driven methods. The model-driven method is based on graph theory and power flow equations, and establishes a power flow model and deduces the sensitivity relationship through physical laws. The data-driven method extracts features or identifies structures through large-scale measurement data, and constructs a mapping model or a parameter inversion model, gradually breaking the strong dependence on power grid structure information.

[0003] The model-driven method relies on accurate system parameters and structure information, and is difficult to adapt to complex conditions such as sparse measurement equipment and frequent parameter changes in practice, resulting in limited applicability. The data-driven method has flexibility, but has problems such as poor parameter interpretability and low training efficiency. In particular, under the condition of lacking prior topology or line parameters, it is difficult to realize the joint identification of the structure and parameters of the power distribution network. In addition, although some methods can invert network information from measurement data, there is a lack of clear correspondence between the model results and the physical properties of the power grid, affecting the credibility and generalization ability of the modeling results. SUMMARY

[0004] The application provides a power distribution network modeling method based on a shallow physical information neural network, which realizes efficient identification and parameter estimation of the power grid structure, and has good calculation efficiency and model generalization ability.

[0005] A power distribution network modeling method based on a shallow physical information neural network comprises the following steps:

[0006] S1, constructing a modeling base model: establishing a power distribution network power flow model, introducing a branch-node association matrix and a voltage sensitivity matrix, constructing a relationship model between node voltage and injected power and line power flow, and using non-negative weights and ReLU activation functions to construct an ICNN network;

[0007] S2, ICNN-based power distribution network topology modeling: a single-layer ICNN network is trained, taking the relationship between node active power injection and active line flow as input and output pairs, so that the weight of the ICNN network reflects the path matrix information, the weight of the ICNN network is discretized by clustering method, the node-branch incidence matrix inverse is estimated and its inverse matrix is solved, and thus the topology of the power distribution network is inversely obtained;

[0008] S3, ICNN-based power distribution network line parameter modeling: based on the obtained topology, an ICNN network is trained, taking the relationship between node injection power and node voltage as input to learn the voltage sensitivity matrix, estimating the line resistance and reactance diagonal matrix through the ICNN network, and introducing a regularization term for optimization to realize the inverse modeling of the line parameters of the power distribution network.

[0009] Optionally, the S1 includes constructing a modeling base model, which includes:

[0010] S11, power distribution network flow linear modeling: a linear DistFlow equation is used to establish the mapping relationship between bus voltage, active / reactive power and line flow, and the node-branch incidence matrix and voltage sensitivity matrix are introduced to establish the power distribution network flow model.

[0011] S12, ICNN structure design: through non-negative weight and ReLU activation function, an ICNN model suitable for power distribution network topology and parameter inversion is provided.

[0012] Optionally, the S11 includes power distribution network flow linear modeling, which includes:

[0013] S111, constructing a radial power distribution network structure: assuming that the power distribution network is composed of N + 1 bus lines, the bus set is , the set of power distribution lines is , and bus 0 is the common coupling point.

[0014] S112, defining node and line parameters: for each bus i, the bus voltage amplitude is defined as , the active / reactive power injection of the bus is defined as / , for each power distribution line , the line resistance and reactance are and , the active / reactive flow from bus i to bus j is and , and the set of adjacent buses far away from the feeder head in bus is .

[0015] S113, Computing the power flow equation: Compute the DistFlow equation of the power flow of each distribution line of the distribution network, denoted as:

[0016] ;

[0017] ;

[0018] ;

[0019] wherein, represents the line power loss;

[0020] S114, Linearizing the power flow model: Ignoring the line power loss , obtain the linearized power flow model, denoted as:

[0021] ;

[0022] ;

[0023] ;

[0024] S115, Introducing the graph theory matrix expression form: Based on the matrix form of the graph, the LinDistFlow model is expressed, denoted as:

[0025] ;

[0026] wherein, , is a diagonal matrix, represents the node-branch incidence matrix of the distribution network;

[0027] S116, Power balance relationship expression: Express the power balance relationship as a matrix form, denoted as:

[0028] ;

[0029] ;

[0030] ;

[0031] S117, Derivation of the voltage sensitivity relationship: Construct the final expression form of the voltage vector and power relationship, denoted as:

[0032] ;

[0033] wherein, , represents the voltage sensitivity matrix.

[0034] ​Optionally, the ICNN structure design in S12 comprises:

[0035] S121, defining the ICNN network structure: the ICNN network is a neural network whose output is convex relative to the input by designing the weight and activation function of the neural network, considering a neural network composed of k fully connected layers, denoted as:

[0036] ;

[0037] ;

[0038] wherein, represents the weight parameter, represents the nonlinear activation function of the i-th layer;

[0039] S122, activation function selection: selecting ReLU function as the activation function, denoted as:

[0040] ;

[0041] S123, matrix expression form: analyzing the properties of ReLU function and introducing the matrix expression form, denoted as:

[0042] ;

[0043] ;

[0044] wherein, , ;

[0045] S124, constructing a single-layer bias-free ICNN structure: constructing a single-layer bias-free ICNN network, including an input layer, a ReLU activation layer, an output layer and a weight matrix.

[0046] Optionally, the ICNN-based power distribution network topology structure modeling in S2 comprises:

[0047] S21, the core task of power distribution network topology inversion: the essence of power distribution network topology inversion is to solve the branch-node incidence matrix M, and the relationship between the node incidence matrix and the power distribution network line active power flow and the node injection power is represented by the LinDistFlow model:

[0048] ;

[0049] S22, derivation of the inverse matrix of the node incidence matrix: the inverse matrix of the node incidence matrix is denoted as:

[0050] ;

[0051] wherein, an inverse matrix of the branch incidence matrix;

[0052] S23, the core expression of the inversion process: the topology inversion of the power distribution network is realized by using the characteristics of the ICNN network, which is expressed as:

[0053] ;

[0054] S24, constructing the topology matrix: the topology matrix A is composed of the power grid topology information of the power distribution network, which is expressed as:

[0055] ;

[0056] wherein, denotes the path matrix;

[0057] S25, matrix calculation of network topology inversion: based on the topology matrix A, the power distribution network topology matrix is calculated, which is expressed as:

[0058] ;

[0059] wherein, denotes the augmented branch incidence inverse matrix;

[0060] S26, the relationship between the ICNN network and the power distribution network topology structure: the relationship between the weight of the ICNN network and the power distribution network topology structure is expressed as:

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] wherein, all denote the topology structure information matrix, denotes taking the i-th column to the j-th column of the matrix.

[0066] Optionally, the ICNN-based power distribution network line parameter modeling in S3 comprises:

[0067] S31, constructing impedance parameter solving target: the target of line parameter inversion is to solve the line resistance diagonal matrix and the reactance diagonal matrix , which is expressed as:

[0068] ;

[0069] ;

[0070] S32, establish the voltage and power relationship expression: based on the LinDistFlow model, define the matrix R and X The relationship between the node injection power and the distribution network node voltage is represented as:

[0071] ;

[0072] wherein, represents the transformed node voltage phasor;

[0073] S33, construct the mapping structure: construct the mapping structure of the ICNN network, represented as:

[0074] ;

[0075] S34, variable transformation: through variable transformation to meet the non-negative weight constraint, represented as:

[0076] ;

[0077] ;

[0078] S35, augmented matrix expression: convert the mapping relationship between node voltage and power into an augmented matrix form, represented as:

[0079] ;

[0080] wherein, represents the augmented voltage sensitivity matrix;

[0081] S36, establish the relationship between the weight and the parameter matrix: train the single-layer bias-free ICNN network, and the weight parameters and reflect the topological structure and line parameter information of the distribution network, represented as:

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] ;

[0088] wherein, represents the voltage sensitivity information matrix;

[0089] S37, inverse line impedance matrix: based on the M matrix, the line parameter inversion of the power distribution network is realized, which is represented as:

[0090] ;

[0091] ;

[0092] wherein, and respectively represent the line resistance estimation matrix and the line reactance estimation matrix;

[0093] S38, weight matrix symmetry design and optimization expression: by introducing a sub-weight block to represent the weight structure, which is represented as:

[0094] ;

[0095] ;

[0096] wherein, ~ is a set of trainable weight parameter diagonal matrices;

[0097] ;

[0098] S39, introduction of regularization term constraint and virtual node: a regularization term loss function is introduced, a total loss function including mean square error and regularization penalty term is constructed, and a virtual PCC node is introduced to normalize the voltage.

[0099] Optionally, the sub-weight block is represented as:

[0100] .

[0101] Optionally, the regularization term loss function is represented as:

[0102] ;

[0103] The total loss function is represented as:

[0104] ;

[0105] wherein, and respectively represent the voltage label value and the voltage prediction value of the ICNN output, represents the mean square error calculation, represents the weight coefficient.

[0106] Optionally, the introduction of the virtual PCC node to normalize the voltage is represented as:

[0107] ;

[0108] ;

[0109] wherein, and denote the new voltage magnitude and the original voltage magnitude of node i, respectively.

[0110] Advantages of the present application:

[0111] The present application combines the physical modeling method of the power distribution network with the data-driven method by introducing a shallow physical information neural network, overcomes the problem of strong dependence on accurate parameters and poor adaptability of the traditional model-driven method, makes up for the defects of weak model interpretability and low training efficiency in the existing data-driven method, constructs a voltage-power mapping relationship based on the linearized DistFlow model, introduces the branch-node correlation matrix and the voltage sensitivity matrix, so that the neural network weight has a clear physical meaning, the ICNN network based on the ReLU activation function not only ensures the convexity and interpretability of the model output, but also effectively learns the topology structure and line parameters, and under the condition of unknown topology and parameters, the joint inversion of the power distribution network structure and parameters is realized through the SCADA measurement data, which significantly improves the practicality and robustness of modeling.

[0112] The present application reduces the number of neural network layers through a shallow network structure, reduces the model training complexity, improves the modeling efficiency, at the same time, proposes a linkage mechanism of topology identification and line parameter estimation, introduces a virtual PCC node and a voltage normalization method in large-scale power distribution network modeling, improves the modeling stability of the model in the local reference point area, introduces a regularization term loss function to further constrain the physical rationality of the weight parameter, and ensures that the inversion result meets the electrical engineering characteristics. BRIEF DESCRIPTION OF DRAWINGS

[0113] In order to more clearly illustrate the technical solutions in the present application or prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only illustrate the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0114] Figure 1 It is a schematic diagram of a radial power distribution network with node and line related variables of an embodiment of the present application;

[0115] Figure 2 It is a schematic diagram of an ICNN structure of an embodiment of the present application;

[0116] Figure 3 It is a schematic diagram of a ReLU activation function of an embodiment of the present application;

[0117] Figure 4 A single-layer ICNN structure diagram of an embodiment of the present application;

[0118] Figure 5 A modeling method flow diagram of an embodiment of the present application. DETAILED DESCRIPTION

[0119] The present application will be described in detail below with reference to the drawings and specific embodiments. It should be noted that, in order to make the embodiments more detailed, the following embodiments are the best, preferred embodiments, and other alternative ways can also be implemented by those skilled in the art for some known technologies; and the drawings are only used to more specifically describe the embodiments, and are not intended to specifically limit the present application.

[0120] It should be noted that in the specification, "one embodiment", "embodiment", "exemplary embodiment", "some embodiments" and the like indicate that the described embodiments can include a specific feature, structure or property, but not necessarily every embodiment includes the specific feature, structure or property. In addition, when a specific feature, structure or property is described in combination with an embodiment, it should be within the knowledge of those skilled in the related art to implement such a feature, structure or property in combination with other embodiments (whether or not explicitly described).

[0121] Generally, the terms can be understood at least in part from the context of their use. For example, depending on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in the singular or can be used to describe combinations of features, structures, or characteristics that are combinable into one or more instances. In addition, the term "based on" can be understood as not necessarily intended to convey a set of exclusive factors, but can instead, depending on the context, allow for the existence of other factors that are not necessarily explicitly described.

[0122] As shown in Figures 1-5 , a power distribution network modeling method based on a shallow physical information neural network includes the following steps:

[0123] 1. Basic model:

[0124] 1.1. Power flow model of power distribution network:

[0125] Consider a power distribution network composed of N + 1 busbars, the busbar set is , the set of power distribution lines is , and the radial power distribution feeder is as shown in Figure 1 . For a radial power distribution network, the number of power distribution lines bus 0, which is usually located at the distribution substation, provides reference voltage for the distribution network. For each bus, denotes the bus voltage magnitude, and denote the active / reactive power injection at bus i, respectively. For each distribution line, , and denote the line resistance and reactance, respectively, and denote the active / reactive power flow from bus i to bus j. In addition, denotes the set of neighboring buses of bus i that are far away from the feeder head. The DistFlow equation for calculating the power flow on each distribution line is given by:

[0126] (1)

[0127] (2)

[0128] (3)

[0129] In the above equations, denotes the line power loss, which can be neglected compared to the line power flow, and thus the power flow equation can be linearized.

[0130] Under a relatively flat voltage profile, , where , the linearized DistFlow (LinDistFlow) model for each distribution line is given by:

[0131] (4)

[0132] (5)

[0133] (6)

[0134] The LinDistFlow model can be represented in a graph-based matrix form.

[0135] Let denote the incidence matrix of the distribution network, denote the first row of . Since the radial distribution network is typically a tree structure, the rank of is equal to , i.e. is a full rank invertible matrix.

[0136]

[0136] Let the voltage of the power supply node The voltage of each node in the distribution network can be represented by the LinDistFlow model as follows:

[0137] (7)

[0138] where, is a diagonal matrix whose diagonal elements represent the resistance of the line, and similarly is also a diagonal matrix whose diagonal elements represent the line reactance. At this time, the power balance equation can be expressed as:

[0139] (8)

[0140] (9)

[0141] Solve P and Q and substitute them into equation (7) to get:

[0142] (10)

[0143] or equivalently:

[0144] (11)

[0145] where, , , all represent the voltage sensitivity matrix. It is easy to prove that R and X are symmetric positive definite matrices.

[0146] 1.2, ICNN model:

[0147] ICNN (Input Convex Neural Network, ICNN) is a neural network that cleverly designs the weights and activation functions of the neural network, so that the output is convex with respect to the input. Consider a neural network composed of k fully connected layers, as shown below Figure 2 The model is as follows:

[0148] (12)

[0149] (13)

[0150] where, represents the activation function of each layer (where, , ), represents the weight parameter, ​The nonlinear activation function representing the i-th layer.

[0151] When the activation function of each layer is non-negative and convex and non-decreasing , then is a convex function of the input .

[0152] To meet the condition that the activation function is convex and non-decreasing, the ReLU function is usually selected as the activation function, and its expression is as follows:

[0153] (14)

[0154] Analyzing the properties of the ReLU function, it is easy to know that:

[0155] (15)

[0156] Multiplying x on both sides of the equation by the coefficient matrix W, the matrix expression is as follows:

[0157] (16)

[0158] In the formula, , . In connection with the network structure of ICNN, formula (16) can be expressed by a single-layer ICNN network without bias, as shown in Figure 4 .

[0159] 2. Power distribution network topology inversion modeling based on shallow interpretable ICNN:

[0160] The essence of power distribution network topology inversion is to solve the branch-node incidence matrix M. According to the LinDistFlow model, the relationship between the M matrix and the line active power flow and the node active power injection of the distribution network is:

[0161] (17)

[0162] Since is a full-rank invertible matrix, the above formula can be written as:

[0163] (18)

[0164] In the formula, represents the inverse matrix of the branch-node incidence matrix.

[0165] Substituting formula (18) into formula (15), we can get:

[0166] (19)

[0167] (20)

[0168] where, denotes the path matrix, whose column vector denotes a set of lines that constitute a path from Bus 0 to Bus i, and the corresponding element is 1 for a line in the path and 0 for a line out of the path. Therefore, the elements in matrix A only contain 0 and In this case, the weight matrix in formula (19) does not satisfy the non-negative characteristic required by ICNN.

[0169] To this end, consider the following transformation:

[0170] (21)

[0171] (22)

[0172] where, and are both non-negative matrices.

[0173] In this case, formula (19) becomes:

[0174] (23)

[0175] where, denotes the augmented branch incidence inverse matrix.

[0176] It is easy to know that formula (23) is equivalent to formula (19). It is observed that formula (16) and formula (23) have exactly the same form, which shows that the neural network parameters of ICNN are related to the topological structure parameters of the power distribution network. If a set of power measurements and (the subscript T represents the number of time sections of the measurements), a single-layer ICNN network without bias is trained, and the weight parameters and of the ICNN network can reflect the topological structure information of the power distribution network, and the specific expression is:

[0177] (24)

[0178] (25)

[0179] (26)

[0180] (27)

[0181] where, both denote the topological structure information matrix, denotes the firsti Listed to number j The reason why the above formula uses an approximate equality sign instead of an equal sign is because of the matrix. A The elements in the only contain 0 and These two discrete values ​​are derived from the transformation of the neural network weight parameter matrix. Typically, values ​​are taken continuously. To ensure accurate inversion of the topological structure, for or The elements in each column are clustered using the K-means clustering method

[18] . The elements are clustered into two classes according to the absolute value of the matrix elements. All elements in the class with smaller absolute values ​​are assigned the value 0, and all elements in the class with larger absolute values ​​are assigned the value 1. The estimated inverse of the branch correlation matrix is ​​obtained, denoted as . .

[0182] If 100% inversion can be achieved (i.e.) ),but If the matrix is ​​also a full-rank invertible matrix, then the estimated branch correlation matrix satisfies This means that the true topology of the system has been obtained. Note that this is a stringent requirement; once... Matrix and Matrix mismatch will result in The matrix is ​​not invertible, thus the inversion fails.

[0183] Assuming power measurement is selected in a local area of ​​a power distribution network and To perform topology inversion (where the subscript L indicates a local region), and to ensure that local measurements still satisfy the KCL and KVL laws, measurements of the boundary buses of the distribution network need to be merged.

[0184] (28)

[0185] (29)

[0186] (30)

[0187] (31)

[0188] In the formula, and Representing the nodes respectively i The set of nodes within and outside a connected local region. and These represent the merged boundary nodes. i The node active power injection and the node reactive power injection.

[0189] After the measurement is merged, the topology of the partial area of the distribution network can be estimated according to the method of this section, and on the basis of the topology inversion result, the inversion modeling of the line parameters of the distribution network is further realized.

[0190] 3. Inversion modeling of line parameters of distribution network based on shallow interpretable ICNN:

[0191] The essence of line parameter inversion is to solve and Since the M matrix is invertible, according to formula (11), the resistance diagonal matrix and the reactance diagonal matrix of the distribution line can be obtained by the following formula (32) (33):

[0192] (32)

[0193] (33)

[0194] The above formula shows that the line parameter information of the distribution network is contained in the voltage sensitivity matrix R and X According to the LinDistFlow model, the relationship between the matrix R and X and the node injection power and the node voltage of the distribution network is:

[0195] (34)

[0196] In the formula, denotes the transformed node voltage phasor.

[0197] Substituting formula (34) into formula (15) gives:

[0198] (35)

[0199] Since R and X are symmetric positive definite matrices, in order to ensure that the weight matrix of the ICNN is non-negative, the following transformation is made:

[0200] (36)

[0201] (37)

[0202] At this time, formula (31) becomes:

[0203] (38)

[0204] In the formula, denotes the augmented voltage sensitivity matrix.

[0205] It is easy to know that formula (38) is equivalent to formula (34). It is observed that formula (16) and formula (38) have the same form, which shows that the weight parameters of ICNN are related to the voltage sensitivity matrix of the power distribution network, and the voltage sensitivity parameters are related to the topological structure and line parameters according to formula (11). If a set of power and voltage measurements 、 、 are given, a single-layer ICNN network without bias is trained, and the weight parameters 、 of the ICNN network can reflect the topological structure and line parameter information of the power distribution network, and the specific expression is as follows:

[0206] (39)

[0207] (40)

[0208] (41)

[0209] (42)

[0210] (43)

[0211] (44)

[0212] In the formula, all represent the voltage sensitivity information matrix, wherein can reflect the information of line resistance, can reflect the information of line reactance.

[0213] Assuming that the topological structure of the target power distribution network is obtained by inverting the weight parameters of the trained ICNN network, i.e., the M matrix, the line parameter inversion of the power distribution network can be realized according to the following formula.

[0214] (45)

[0215] (46)

[0216] In the formula, and respectively represent the line resistance estimation matrix and the line reactance estimation matrix.

[0217] It is worth noting that 、 、 and These are all neural network weight parameters. The goal is to directly invert and obtain a voltage sensitivity matrix with symmetry and positive definiteness by training a single-layer ICNN network. R and X It is extremely difficult. The essence of line parameter inversion is solving for the diagonal matrix. and Therefore, we redesigned the weight matrix structure and directly learned a diagonal weight matrix, thereby reducing the learning difficulty.

[0218] Assume the weight matrix consists of four square matrices:

[0219] (47)

[0220] (48)

[0221] The expressions for each submatrix are as follows:

[0222] (49)

[0223] In the formula, ~ It is a set of trainable weight parameters in a diagonal matrix, where all diagonal elements are non-negative.

[0224] at this time, and It can be obtained from the following formula:

[0225] (50)

[0226] The above formula shows that, and Depend on ~ The difference between any two non-negative numbers is obtained by subtracting them pairwise. However, mathematically, the difference between any two non-negative numbers is not necessarily non-negative. This leads to a discrepancy with the fact that the resistance and reactance parameters of actual power distribution networks are all non-negative (i.e., ...). and All diagonal elements are non-negative. To ensure the reasonable accuracy of line parameter inversion, it is hoped that during the neural network training process, , , and The diagonal elements are made as close to zero as possible, which is equivalent to adding a loss function to the neural network weight parameters as follows:

[0227] (51)

[0228] Adding the above loss function as a penalty term to the original loss function, we get the following expression:

[0229] (52)

[0230] In the formula, and respectively represent the voltage label value and the voltage prediction value of the ICNN output, represents the mean square error calculation, represents the weight coefficient, which is used to adjust the proportion of the additional loss in the total loss, and can be set to 0.01.

[0231] When the power distribution network is large, the fitting accuracy of the single-layer ICNN is limited, and The estimation error is large, in order to ensure the line parameter inversion accuracy, it is necessary to limit the training scale of the power distribution network, and the measurement merging method can be used for equivalent of the local area of the power distribution network. It is worth noting that when the local area does not contain the PCC of the power distribution network, a virtual PCC (generally selected as the node closest to the real PCC, assuming that the node number is k ), so as to ensure the training accuracy of the ICNN. Let the voltage amplitude of the node be 1, that is, At this time, the node voltage amplitude deviation is Let the voltage amplitudes of other nodes in the local area be reduced by , so as to ensure that the voltage amplitude difference between nodes in the local area is the same, and the formula is as follows:

[0232] (53)

[0233] In the formula, and respectively represent the new voltage amplitude and the original voltage amplitude of the node i .

[0234] The present application covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present application. In order to make the public have a thorough understanding of the present application, specific details are described in the following preferred embodiments of the present application, and the present application can also be fully understood without the description of these details to those skilled in the art. In addition, in order to avoid unnecessary confusion to the essence of the present application, well-known methods, processes, procedures, elements and circuits, etc. are not described in detail.

[0235] The above only describes the preferred embodiments of the present application, and it should be pointed out that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can also be made, and these improvements and refinements should be regarded as the protection scope of the present application.

Claims

1. A method for modeling power distribution networks based on shallow physical information neural networks, characterized in that, Includes the following steps: S1. Constructing the basic model: Establishing a power flow model of the distribution network, introducing the node correlation matrix and voltage sensitivity matrix, constructing the relationship model between node voltage and injected power and line power flow, and simultaneously using non-negative weights and ReLU activation function to construct an ICNN network; S2, Distribution network topology modeling based on ICNN: Train a single-layer ICNN network, take the relationship between the active power injection of nodes and the active power flow of lines as the input-output pair, so that the weights of the ICNN network reflect the path matrix information, discretize the weights of the ICNN network through clustering method, estimate the inverse of the branch correlation matrix and find its inverse matrix, thereby inverting the topology of the distribution network. S3, Distribution network line parameter modeling based on ICNN: Based on the obtained topology, an ICNN network is trained, and the relationship between node injected power and node voltage is used as input to learn the voltage sensitivity matrix. The line resistance and reactance diagonal matrix are estimated through the ICNN network, and a regularization term is introduced for optimization to achieve inverse modeling of distribution network line parameters. The ICNN-based distribution network line parameter modeling in S3 includes: S31, Constructing the objective for impedance parameter solution: The objective of line parameter inversion is to solve the diagonal matrix of line resistance. and reactance diagonal matrix , is represented as: ； ； S32, Establishing the relationship between voltage and power: Based on the LinDistFlow model, define the matrix. R and X The relationship between node injected power and distribution network node voltage is expressed as follows: ； in, Represents the transformed node voltage phasor; S33, Constructing the mapping structure: Construct the mapping structure of the ICNN network, represented as: ； S34, Variable Transformation: Satisfying the non-negative weight constraint through variable transformation, expressed as: ； ； S35, Augmented Matrix Representation: The mapping relationship between node voltage and power is converted into an augmented matrix form, expressed as: ； in, Represents the augmented voltage sensitivity matrix; S36, Establish the relationship between weights and parameter matrices: Train a single-layer unbiased ICNN network, its weight parameters and Information reflecting the topology and line parameters of the distribution network is represented as follows: ； ； ； ； ； ； in, Represents the voltage sensitivity information matrix; S37, Inverting the Line Impedance Matrix: Based on the M matrix, the line parameters of the distribution network are inverted, expressed as: ； ； in, and These represent the line resistance estimation matrix and the line reactance estimation matrix, respectively. S38, Symmetric Design and Optimization of Weight Matrix: The weight structure is represented by introducing sub-weight blocks, as follows: ； ； in, ~ It is a set of trainable weight parameter diagonal matrices; ； S39, Introducing regularization constraints and virtual nodes: Introducing a regularization loss function, constructing a total loss function including mean square error and regularization penalty term, and introducing virtual PCC nodes to normalize the voltage.

2. The power distribution network modeling method based on shallow physical information neural networks according to claim 1, characterized in that, The basic model for constructing the modeling system in S1 includes: S11, Linear modeling of power flow in distribution network: Using the linearized DistFlow equation, the mapping relationship between bus voltage, active / reactive power and line power flow is established. The branch correlation matrix and voltage sensitivity matrix are introduced to establish the power flow model of distribution network. S12, ICNN architecture design: Through non-negative weights and the ReLU activation function, an ICNN model suitable for distribution network topology and parameter inversion is provided.

3. The power distribution network modeling method based on shallow physical information neural networks according to claim 2, characterized in that, The linear power flow modeling of the distribution network in S11 includes: S111, Construct a radial distribution network structure: Assume the distribution network consists of... N + 1 It consists of several busbars, and the busbar set is as follows: The collection of power distribution lines is Bus 0 is the common coupling point; S112, Define the parameters for each node and line: For each bus i, define the bus voltage amplitude as... The active / reactive power injected into the bus is / For each power distribution line The line resistance and reactance are and The active / reactive power flow from bus i to bus j is and busbar The set of adjacent busbars furthest from the feeder head is ; S113, Calculate the power flow equations: Calculate the power flow equations for each distribution line in the distribution network. The DistFlow equation for the power flow is expressed as: ； ； ； in, Indicates line power loss; S114, Linearized power flow model: Ignoring line power losses The linear power flow model is obtained, which is expressed as: ； ； ； S115 introduces a graph-theoretic matrix representation: the LinDistFlow model is expressed in graph-based matrix form as follows: ； in, , It is a diagonal matrix. Represents the branch correlation matrix of the power distribution network; S116, Power Balance Relationship Expression: The power balance relationship is expressed in matrix form as follows: ； ； ； S117, Derivation of the voltage sensitivity relationship: Construct the final expression of the voltage vector-power relationship, as follows: ； in, , This represents the voltage sensitivity matrix.

4. The power distribution network modeling method based on shallow physical information neural networks according to claim 3, characterized in that, The ICNN architecture design in S12 includes: S121, Define the ICNN network structure: The ICNN network is a neural network whose output is convex relative to the input by designing the weights and activation functions of the neural network. Consider a neural network consisting of k fully connected layers, represented as: ； ； in, Represents the weight parameters. This represents the nonlinear activation function of the i-th layer; S122, Activation Function Selection: The ReLU function is selected as the activation function, expressed as: ； S123, Matrix Representation: Analyzing the properties of the ReLU function and introducing a matrix representation, it is expressed as follows: ； ； in, , ; S124, Construct a single-layer unbiased ICNN structure: Construct a single-layer, unbiased ICNN network, including an input layer, a ReLU activation layer, an output layer, and a weight matrix.

5. The power distribution network modeling method based on a shallow physical information neural network according to claim 4, characterized in that, The distribution network topology modeling based on ICNN in S2 includes: S21, the core task of distribution network topology inversion: The essence of distribution network topology inversion is to solve for the node correlation matrix M. Through the LinDistFlow model, the relationship between the node correlation matrix and the active power flow and node injected power of the distribution network is expressed as follows: ； S22, Derivation of the inverse matrix of the node incidence matrix: The inverse matrix of the node incidence matrix is ​​represented as: ； in, The matrix representing the inverse of the branch correlation matrix; S23, the core expression of the inversion process: Utilizing the characteristics of ICNN networks to achieve topology inversion of the distribution network, expressed as: ； S24, Construct the topology matrix: The topology matrix A is composed of the power grid topology information of the distribution network, and is represented as follows: ； in, Represents the path matrix; S25, Matrix calculation for network topology inversion: Based on the topology matrix A, calculate the distribution network topology matrix, expressed as: ； in, Represents the augmented branch correlation inverse matrix; S26, The relationship between the ICNN network and the distribution network topology: The relationship between the weights of the ICNN network and the distribution network topology is expressed as follows: ； ； ； ； in, Each represents a topological information matrix. This indicates taking columns i to j of the matrix.

6. The power distribution network modeling method based on a shallow physical information neural network according to claim 5, characterized in that, The sub-weighted block is represented as follows: 。 7. The power distribution network modeling method based on shallow physical information neural networks according to claim 6, characterized in that, The regularization loss function is expressed as follows: ； The total loss function is expressed as: ； in, and These represent the voltage label value and the voltage prediction value output by ICNN, respectively. This indicates the calculation of the mean square error. This represents the weighting coefficient.

8. The power distribution network modeling method based on a shallow physical information neural network according to claim 7, characterized in that, The normalization of voltage by introducing virtual PCC nodes is expressed as follows: ； ； in, and These represent the new voltage amplitude and the original voltage amplitude at node i, respectively.

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