Power distribution network modeling method based on shallow physical information neural network

Abstract

The invention relates to the technical field of power distribution networks, in particular to a power distribution network modeling method based on a shallow physical information neural network, and the method comprises the following steps: S1, building a modeling basic model: building a power distribution network power flow model, and building an ICNN network through employing a non-negative weight and a ReLU activation function; s2, modeling of a power distribution network topological structure based on the ICNN: discretizing the weight of the ICNN network through a clustering method, estimating a cost-saving incidence matrix and solving an inverse matrix of the cost-saving incidence matrix, thereby obtaining the topological structure of the power distribution network through inversion; s3, ICNN-based power distribution network line parameter modeling: estimating a line resistance and reactance diagonal matrix through an ICNN network, and introducing a regular term for optimization to realize inversion modeling of power distribution network line parameters; according to the method, joint inversion of the structure and the parameters of the power distribution network is realized, and the practicability and the robustness of modeling are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution networks, and particularly to a distribution network modeling method based on a shallow physics-informed neural network. Background Art

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

[0003] The model-driven method depends on accurate system parameters and structure information, and it is difficult to adapt to complex conditions such as sparse measurement equipment and frequent parameter changes in practice, resulting in limited applicability. Although the data-driven method has flexibility, it has problems such as poor parameter interpretability and low training efficiency. Especially under the condition of lacking prior topology or line parameters, it is difficult to realize the joint identification of the distribution network structure and parameters. In addition, although some methods can invert network information from measurement data, there is no clear corresponding relationship between the model results and the physical properties of the power grid, which affects the credibility and generalization ability of the modeling results. Summary of the Invention

[0004] The present invention provides a distribution network modeling method based on a shallow physics-informed neural network, which realizes the efficient identification of the distribution network structure and parameter estimation, and at the same time has good computational efficiency and model generalization ability.

[0005] A distribution network modeling method based on a shallow physics-informed neural network includes the following steps:

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

[0007] S2. Modeling of the distribution network topology structure based on ICNN: Train a single-layer ICNN network, using 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 a clustering method, estimate the inverse of the branch-saving incidence matrix and find its inverse matrix, thereby inversely obtaining the topology structure of the distribution network;

[0008] S3. Modeling of the distribution network line parameters based on ICNN: Based on the obtained topology structure, train the ICNN network, using the relationship between the node injection power and the node voltage as the input, learn the voltage sensitivity matrix, estimate the diagonal matrices of line resistance and reactance through the ICNN network, and introduce a regularization term for optimization to achieve the inverse modeling of the distribution network line parameters.

[0009] Optionally, the construction of the modeling basic model in S1 includes:

[0010] S11. Linear modeling of the distribution network power flow: Use the linearized DistFlow equation to establish the mapping relationship between the bus voltage, active / reactive power, and line power flow, introduce the branch-saving incidence matrix and the voltage sensitivity matrix, and establish the distribution network power flow model;

[0011] S12. ICNN structure design: Provide an ICNN model suitable for the inversion of the distribution network topology structure and parameters through non-negative weights and the ReLU activation function.

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

[0013] S111. Construction of the radial distribution network structure: Assume that the distribution network consists of N + 1 buses, and the bus set is The set of distribution lines is Bus 0 is the point of common coupling;

[0014] S112. Definition of each node and line parameters: For each bus i, define the bus voltage amplitude as V i , the active / reactive power injection of the bus is p i / q i , for each distribution line (i, j), the line resistance and reactance are r ij and x ij , the active / reactive power flow from bus i to bus j is P ij and Q ij , the set of adjacent buses of bus j far from the feeder head is

[0015] S113. Calculation of the power flow equation: Calculate the DistFlow equation of the power flow of each distribution line (i, j) in the distribution network, expressed as:

[0016]

[0017] Among them, represents the line power loss;

[0018] S114, linearized power flow model: ignoring the line power loss Obtain the linearized power flow model, expressed as:

[0019]

[0020] V i -V j = r ij P ij + x ij Q ij ;

[0021] S115, introducing the graph theory matrix expression form: expressing the LinDistFlow model based on the matrix form of the graph, expressed as:

[0022] (M 0 ) T [V0 V T T = m0 + M T V = D r P + D x Q;

[0023] Among them, D r , D x are diagonal matrices, M 0 = [m0 M T T represents the sectional connection matrix of the distribution network;

[0024] S116, power balance relationship expression: expressing the power balance relationship in matrix form, expressed as:

[0025] -MP = -p;

[0026] -MQ = -q;

[0027] M T V = D r M -1 p + D x M -1 q - m0;

[0028] S117, derivation expression of voltage sensitivity relationship: constructing the final expression form of the relationship between the voltage vector and power, expressed as:

[0029] V = Rp + Xq - M -T m0; ​​

[0030] Among them, R = M -T D r M -1 and X = M -T D x M -1 represents the voltage sensitivity matrix.

[0031] Optionally, the ICNN structure design in S12 includes:

[0032] S121, defining the ICNN network structure: The ICNN network is a neural network that makes the output convex with respect to the input by designing the weights and activation functions of the neural network. Consider a neural network composed of k fully connected layers, expressed as:

[0033]

[0034] Among them, represents the weight parameter, and δ i represents the non-linear activation function of the i-th layer;

[0035] S122, activation function selection: The ReLU function is selected as the activation function, expressed as:

[0036] ReLU(x) = max(x, 0);

[0037] S123, matrix expression form: Analyze the properties of the ReLU function and introduce the matrix expression form, expressed as:

[0038] |x| = -x + 2ReLU(x);

[0039] |z| = |Wx| = -Wx + 2ReLU(Wx)

[0040] = W (x) x + ReLU(W (z) x);

[0041] Among them, W (x) = -W, W (z) = 2W;

[0042] S124, constructing a single-layer ICNN structure without bias terms: Construct a single-layer, bias-free ICNN network, including an input layer, a ReLU activation layer, an output layer, and a weight matrix.

[0043] Optionally, the modeling of the distribution network topology structure based on ICNN in S2 includes:

[0044] S21, the core task of distribution network topology inversion: The essence of distribution network topology inversion is to solve for the branch-node incidence matrix M. Through the LinDistFlow model, the relationship between the node incidence matrix and the active power flow of distribution network lines and the node injection power is expressed as:

[0045] p = MP;

[0046] S22, derivation of the inverse matrix of the node incidence matrix: The inverse matrix of the node incidence matrix is expressed as:

[0047] P = M -1 p = Ap;

[0048] where A = M -1 represents the inverse matrix of the branch-node incidence matrix;

[0049] S23, the core expression of the inversion process: Utilize the characteristics of the ICNN network to achieve the topology inversion of the distribution network, expressed as:

[0050] |P| = -Ap + 2ReLU(Ap);

[0051] S24, constructing the topology matrix: The topology matrix A is composed of the power grid topology information of the distribution network, expressed as:

[0052] A = M -1 = -Γ;

[0053] where Γ represents the path matrix;

[0054] S25, matrix calculation of network topology inversion: Based on the topology matrix A, calculate the distribution network topology matrix, expressed as:

[0055]

[0056] where A' ∈ R N×2N represents the augmented branch-node incidence inverse matrix;

[0057] S26, the connection between the ICNN network and the distribution network topology structure: The relationship between the weights of the ICNN network and the distribution network topology structure is expressed as:

[0058] W (x) = [A - A + N×2N ;

[0059] W (z) = [2A + 2A - N×2N ;

[0060] W T1 = W (x) ​​[N + 1:2N] - W (x) [1:N] ≈ A;

[0061] W T2 = (W (z) [1:N] - W (z) [N + 1:2N]) / 2 ≈ A;

[0062] where W T1 , W T2 ∈R N×N both represent the topological structure information matrix, and [i:j] represents taking the i-th column to the j-th column of the matrix.

[0063] Optionally, the ICNN-based distribution network line parameter modeling in S3 includes:

[0064] S31, constructing the impedance parameter solution objective: The objective of line parameter inversion is to solve the line resistance diagonal matrix D r and the reactance diagonal matrix D x , expressed as:

[0065] D r = M T RM;

[0066] D x = M T XM;

[0067] S32, establishing the voltage and power relationship expression: Based on the LinDistFlow model, define the relationship between the matrices R and X and the node injection power and the distribution network node voltage, expressed as:

[0068] V′ = V + M -T m0 = Rp + Xq;

[0069] where V′ represents the transformed node voltage phasor;

[0070] S33, constructing the mapping structure: Construct the mapping structure of the ICNN network, expressed as:

[0071] |V′| = -(Rp + Xq) + 2ReLU(Rp + Xq);

[0072] S34, variable transformation: Through variable transformation to meet the non-negative weight constraint, expressed as:

[0073]

[0074] S35, augmented matrix expression: Convert the mapping relationship between node voltage and power into the augmented matrix form, expressed as:

[0075]

[0076] where \(R', X' \in R\) N×2N represents the augmented voltage sensitivity matrix;

[0077] S36. Establish the relationship between the weight and the parameter matrix: Train a single-layer unbiased ICNN network, and its weight parameter \(W\) (x) and \(W\) (z) reflect the topological structure and line parameter information of the distribution network, and are expressed as:

[0078] W (x) = [R - X - R + X + N×4N ;

[0079] W (z) = [2R + 2X + 2R - 2X - N×4N ;

[0080] W TR1 = W (x) [2N + 1:3N] - W (x) [1:N] \(\approx R\);

[0081] W TR2 = (W (z) [1:N] - W (z) [2N + 1:3N]) / 2 \(\approx R\);

[0082] W TX1 = W (x) [3N + 1:4N] - W (x) [N + 1:2N] \(\approx X\);

[0083] W TX2 = (W (z) [N + 1:2N] - W (z) [3N + 1:4N]) / 2 \(\approx X\);

[0084] where \(W\) TR1 , \(W\) TR2 , \(W\) TX1 , \(W\) TX2 \(\in R\) N×N represents the voltage sensitivity information matrix;

[0085] S37. Invert the line impedance matrix: Based on the M matrix, realize the inversion of the line parameters of the distribution network, and it is expressed as:

[0086] D' r = M T R'M = M​​T (R + -R - )M;

[0087] D′ x = M T X′M = M T (X + -X - )M;

[0088] where D r ′ and D x ′ respectively represent the line resistance estimation matrix and the line reactance estimation matrix;

[0089] S38, Weight matrix symmetric design and optimization expression: By introducing sub - weight blocks to represent the weight structure, it is expressed as:

[0090]

[0091]

[0092] where W1 to W8 are a set of trainable weight parameter diagonal matrices;

[0093]

[0094] S39, Introduce regularization term constraints and virtual nodes: Introduce a regularization term loss function, construct a total loss function including mean - square error and regularization penalty term, and introduce a virtual PCC node to normalize the voltage.

[0095] Optionally, the sub - weight block is expressed as:

[0096]

[0097] Optionally, the regularization term loss function is expressed as:

[0098]

[0099] The total loss function is expressed as:

[0100]

[0101] where z and respectively represent the voltage label value and the voltage prediction value output by the ICNN, MSE(·) represents mean - square error calculation, and α represents the weight coefficient.

[0102] Optionally, the introduction of a virtual PCC node to normalize the voltage is expressed as:

[0103] ΔV k = V k ′ - Vk0 ;

[0104] V i,new =V i '-ΔV k , i ∈ S i,A ;

[0105] where V i,new and V' respectively represent the new voltage magnitude and the original voltage magnitude of node i.

[0106] Advantages of the present invention:

[0107] In the present invention, by introducing a shallow physical information neural network and combining the physical modeling method and the data-driven method of the distribution network, it not only overcomes the problems of strong dependence on accurate parameters and poor adaptability of the traditional model-driven method, but also makes up for the defects of weak model interpretability and low training efficiency in the existing data-driven methods. By constructing a voltage-power mapping relationship based on the linearized DistFlow model and introducing a branch-node association matrix and a voltage sensitivity matrix, the weights of the neural network have clear physical meanings. The ICNN network based on the ReLU activation function not only ensures the convexity and interpretability of the model output, but also can effectively learn the topological structure and line parameters. Under the condition of unknown topology and parameters, the joint inversion of the distribution network structure and parameters is realized through SCADA measurement data, significantly improving the practicability and robustness of the modeling.

[0108] In the present invention, through a shallow network structure, the number of neural network layers is reduced, the model training complexity is reduced, and the modeling efficiency is improved. At the same time, a linkage mechanism for topology recognition and line parameter estimation is proposed, and a virtual PCC node and a voltage normalization method are introduced in large-scale distribution network modeling to improve the modeling stability of the model in the area without a reference point. A regular term loss function is introduced to further constrain the physical rationality of the weight parameters and ensure that the inversion results conform to the electrical engineering characteristics. Description of the drawings

[0109] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the embodiments or the description of the prior art. Obviously, the following drawings are only for the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0110] Figure 1 It is a schematic diagram of a radial distribution network with node and line related variables in an embodiment of the present invention;

[0111] Figure 2 It is a schematic diagram of the ICNN structure in an embodiment of the present invention;

[0112] Figure 3 Schematic diagram of the ReLU activation function according to an embodiment of the present invention;

[0113] Figure 4 Schematic diagram of the single - layer ICNN structure according to an embodiment of the present invention;

[0114] Figure 5 Schematic diagram of the process flow of the modeling method according to an embodiment of the present invention. Detailed implementation manners

[0115] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. At the same time, it should be noted here that in order to make the embodiments more detailed, the following embodiments are the best and preferred embodiments. For some well - known technologies, those skilled in the art can also adopt other alternative methods for implementation; moreover, the accompanying drawings are only for more specifically describing the embodiments and are not intended to specifically limit the present invention.

[0116] It should be pointed out that in the specification, when referring to "an embodiment", "embodiment", "exemplary embodiment", "some embodiments", etc., it indicates that the described embodiment may include specific features, structures or characteristics, but not necessarily every embodiment includes such specific features, structures or characteristics. Additionally, when combining an embodiment to describe a specific feature, structure or characteristic, implementing such a feature, structure or characteristic in combination with other embodiments (whether explicitly described or not) should be within the knowledge of those skilled in the relevant art.

[0117] Generally, terms can be understood at least in part from their use in the context. For example, at least in part depending on the context, the term "one or more" used herein can be used to describe any feature, structure or characteristic in a singular sense, or can be used to describe a combination of features, structures or characteristics in a plural sense. Additionally, the term "based on" can be understood as not necessarily aiming to convey a set of exclusive factors, but rather, at least in part depending on the context, allowing for the existence of other factors that may not be explicitly described.

[0118] As Figures 1-5 shown, a power distribution network modeling method based on a shallow physical - information neural network includes the following steps:

[0119] 1. Basic model:

[0120] 1.1 Power flow model of the distribution network:

[0121] Considering a distribution network composed of N + 1 buses, the set of buses is The set of distribution lines is The radial distribution feeder is as Figure 1As shown in the figure. For a radial distribution network, the number of distribution lines |L| = N + 1 - 1 = N. Bus 0 is called the point of common coupling, which is usually located at the distribution substation and provides the reference voltage for the distribution network. For each bus, V i represents the bus voltage magnitude, p i and q i represent the active / reactive injection power of the bus respectively; for each distribution line (i, j), r ij and x ij represent the line resistance and reactance respectively, and P ij and Q ij represent the active / reactive power flow from bus i to bus j respectively. Additionally, represents the set of adjacent buses in bus j that are far from the feeder head. The DistFlow equation for calculating the power flow of each distribution line (i, j) in the distribution network is:

[0122]

[0123] In the above formula, represents the line power loss. Assuming that this loss can be ignored compared to the line power flow, the above power flow equation can be linearized.

[0124] Under a relatively flat voltage distribution, V i ≈ 1, and at this time there is The linearized DistFlow (LinDistFlow) model for the power flow of each distribution line (i, j) is as follows:

[0125]

[0126] V i - V j = r ij P ij + x ij Q ij (6)

[0127] Express the LinDistFlow model in a graph-based matrix form.

[0128] Let M 0 = [m0 M T T represent the branch-node incidence matrix of the distribution network, and m0 represents the first row of M 0 . Since the radial distribution network is a typical tree structure, the rank of M 0 is equal to (N + 1) - 1 = N, that is, M ∈ R N×N is a full-rank invertible matrix.

[0129] ​Let the voltage of the power supply node V0 = 1, then the voltages of each node in the distribution network can be expressed by the LinDistFlow model as:

[0130] (M 0 ) T [V0 V T T =m0+M T V=D r P+D x Q (7)

[0131] In the formula, D r is an N×N diagonal matrix, and the diagonal elements represent the resistance of the line. Similarly, D x is also a diagonal matrix, and the diagonal elements represent the reactance of the line. At this time, the power balance equation can be expressed as:

[0132] -MP=-p (8)

[0133] -MQ=-q (9) By solving P and Q respectively and substituting them into formula (7), we can get:

[0134] M T V=D r M -1 p+D x M -1 q-m0 (10)

[0135] Or equivalently:

[0136] V=Rp+Xq-M -T m0 (11)

[0137] In the formula, R=M -T D r M -1 ,X=M -T D x M -1 ,both represent the voltage sensitivity matrix. It is easy to prove that both R and X are symmetric positive definite matrices.

[0138] 1.2、ICNN model:

[0139] ICNN (Input Convex Neural Network, ICNN) is a neural network that makes the output convex with respect to the input by cleverly designing the weights and activation functions of the neural network. Consider a neural network composed of k fully connected layers, as follows Figure 2 shown, this model is as follows:

[0140]

[0141] In the formula, δ​i represents the activation function of each layer (where z0=0, ), represents the weight parameter, δ i Represents the nonlinear activation function of the i-th layer.

[0142] when Non-negative, and the activation function of each layer δ i are both convex and non-decreasing, then f(x;θ) is a convex function of the input x.

[0143] To satisfy the activation function δ i The condition of "is convex and non-decreasing", the ReLU function is usually selected as the activation function, and its expression is as follows:

[0144] ReLU(x)=max(x,0) (14)

[0145] Analyzing the properties of the ReLU function, it is easy to know:

[0146] |x|=-x+2ReLU(x) (15)

[0147] Multiplying x on both sides of the equation by the coefficient matrix W gives the following matrix expression:

[0148]

[0149] Where W (x) =-W, W (z) =2W. Considering the network structure of ICNN, formula (16) can be expressed by a single-layer ICNN network without bias, as follows: Figure 4 shown.

[0150] 2. Distribution network topology inversion modeling based on shallow interpretable ICNN:

[0151] The essence of distribution network topology inversion is to solve the branch-saving association matrix M. From the LinDistFlow model, we can know that the relationship between the M matrix and the active power flow of the distribution network line and the active power injected into the node is:

[0152] p=MP (17)

[0153] Since M is a full-rank reversible matrix, the above formula can be written as:

[0154] P=M -1 p=Ap (18)

[0155] Where A = M -1 Represents the inverse of the branch incidence matrix.

[0156] Substituting formula (18) into formula (15), we can obtain:

[0157] |P| = -Ap + 2ReLU(Ap) (19)

[0158] A = M -1 = -Γ (20)

[0159] In the formula, Γ represents the path matrix, and its column vector Γ i represents a set of lines that form a path from Bus 0 to Bus i. The elements of the lines in the path are 1, and the elements of the lines outside the path are 0. Therefore, the elements in matrix A only contain 0 and -1. At this time, the weight matrix W (z) in formula (19) does not satisfy the non - negative property required by ICNN.

[0160] For this reason, consider making the following transformation:

[0161]

[0162] A = A + - A - (22)

[0163] In the formula, A + and A - are both non - negative matrices.

[0164] At this time, formula (19) becomes:

[0165]

[0166] In the formula, A' ∈ R N×2N represents the augmented node - branch incidence inverse matrix.

[0167] It is easy to know that formula (23) is equivalent to formula (19). Observation shows that formula (16) and formula (23) have exactly the same form, which indicates that the neural network parameters of ICNN are related to the topological structure parameters of the distribution network. If a set of power measurements {P1,...P i ,...,P T} and {p1,...p i ,...,p T} (the subscript T represents the number of time sections of the measurements) are given, training a single - layer ICNN network without bias terms, its weight parameters W (x) and W (z) can reflect the topological structure information of the distribution network, and the specific expression is:

[0168] W (x) = [A - A + N×2N (24) ​

[0169] W (z) = [2A + 2A - N×2N (25)

[0170] W T1 = W (x) [N + 1:2N] - W (x) [1:N] ≈ A (26)

[0171] W T2 = (W (z) [1:N] - W (z) [N + 1:2N]) / 2 ≈ A (27)

[0172] Wherein, W T1 , W T2 ∈R N×N both represent the topological structure information matrix, and [i:j] represents taking the i-th column to the j-th column of the matrix. The reason for using the approximate equal sign instead of the equal sign in the above formula is that the elements in matrix A only contain two discrete values, 0 and -1, while W T1 , W T2 transformed from the neural network weight parameter matrix usually takes continuous values. To ensure the accurate inversion of the topological structure, for each column of elements in W T1 or W T2 , the K-means clustering method

[18] is used. They are clustered into two categories according to the absolute value size of the matrix elements. All elements in the category with smaller absolute values are assigned 0, and all elements in the category with larger absolute values are assigned -1, obtaining the estimated inverse matrix of the section-saving correlation matrix, denoted as D.

[0173] If 100% inversion can be achieved (i.e., D = A), then the D matrix is also a full-rank invertible matrix, and the estimated section-saving correlation matrix satisfies M' = D -1 = M, which means obtaining the true topology of the system. Note that this is a strict requirement. Once the D matrix and the M -1 matrix cannot match 100%, it will cause the D matrix to be non-invertible, resulting in the failure of inversion.

[0174] Suppose the power measurements {P L1 ,...P Li ,..., P LT} and {p L1 ,...p Li ,..., p LT} of a local area of a distribution network are selected for topological inversion (the subscript L represents the local area). To ensure that the local measurements still satisfy the KCL and KVL laws, it is necessary to merge the measurements of the boundary buses of the distribution sub-network.

[0175] ​

[0176] Wherein, S i,A and S i,N respectively represent the sets of nodes inside and outside the local area connected to node i, p i,B and q i,B respectively represent the active power injection and reactive power injection of node i of the merged boundary nodes.

[0177] After the measurement merging, the topology of the local area of the distribution network can be estimated according to the method in this section. In the next chapter, based on the topology inversion results of this chapter, the inversion modeling of the line parameters of the distribution network is further realized.

[0178] 3. Inversion Modeling of Distribution Network Line Parameters Based on Shallowly Interpretable ICNN:

[0179] The essence of line parameter inversion is to solve for D r and D x . Since the M matrix is invertible, according to Equation (11), the resistance diagonal matrix and reactance diagonal matrix of the distribution line can be obtained from the following equations (32) and (33) respectively:

[0180] D r = M T RM (32)

[0181] D x = M T XM (33)

[0182] The above equations show that the distribution network line parameter information is contained in the voltage sensitivity matrices R and X. According to the LinDistFlow model, the relationship between the matrices R and X, the node injection power, and the distribution network node voltage is:

[0183] V' = V + M -T m0 = Rp + Xq (34)

[0184] Wherein, V' represents the transformed node voltage phasor.

[0185] Substituting Equation (34) into Equation (15) gives:

[0186] |V'| = -(Rp + Xq) + 2ReLU(Rp + Xq) (35)

[0187] Since both 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:

[0188]

[0189] At this time, Equation (31) becomes:

[0190]

[0191] where \(R', X'\in R\) N×2N represents the augmented voltage sensitivity matrix.

[0192] It is easy to know that formula (38) is equivalent to formula (34). It is observed that formulas (16) and (38) have exactly the same form, which indicates that a connection is established between the weight parameters of the ICNN and the voltage sensitivity matrix of the distribution network. From formula (11), it can be seen that the voltage sensitivity parameters are related to both the topological structure and line parameters. If a set of power and voltage measurements \(\{p_1,...p\) i ,...,p T \}, \(\{q_1,...q\) i ,...,q T \}, and \(\{V_1',...V\) i ',...,V T '\} are given, a single-layer ICNN network without bias terms is trained, and its weight parameters \(W\) (x) and \(W\) (z) can reflect the topological structure and line parameter information of the distribution network, and the specific expressions are:

[0193] W (x) = [R - X - R + X + N×4N (39)

[0194] W (z) = [2R + 2X + 2R - 2X - N×4N (40)

[0195] W TR1 = W (x) [2N + 1:3N] - W (x) [1:N] ≈ R (41)

[0196] W TR2 = (W (z) [1:N] - W (z) [2N + 1:3N]) / 2 ≈ R (42)

[0197] W TX1 = W (x) [3N + 1:4N] - W (x) [N + 1:2N] ≈ X (43)

[0198] W TX2 ​​=(W (z) [N + 1:2N] - W (z) [3N + 1:4N]) / 2 ≈ X (44)

[0199] Wherein, W TR1 , W TR2 , W TX1 , W TX2 ∈R N×N all represent the voltage sensitivity information matrix. Among them, W TR1 , W TR2 can reflect the information of line resistance, and W TX1 , W TX2 can reflect the information of line reactance.

[0200] Assume that the weight parameters of the ICNN network trained in the second chapter have been inversely obtained to get the topological structure of the target distribution network, that is, the M matrix. On this basis, the line parameter inversion of the distribution network can be realized according to the following formula.

[0201] D r ′ = M T R′M = M T (R + - R - )M (45)

[0202] D x ′ = M T X′M = M T (X + - X - )M (46)

[0203] Wherein, D r ′ and D x ′ respectively represent the line resistance estimation matrix and the line reactance estimation matrix.

[0204] It should be noted that R + , R - , X + and X - are all neural network weight parameters. It is very difficult to directly inversely obtain the voltage sensitivity matrices R and X with symmetry and positive definiteness by training a single-layer ICNN network. The essence of line parameter inversion is to solve for the diagonal matrices D r and D x . Therefore, we redesigned the weight matrix structure to directly learn a diagonal weight matrix, thereby reducing the learning difficulty.

[0205] Assume that the weight matrix consists of four square matrices:

[0206]

[0207]

[0208] Among them, the expressions of each sub-square matrix are as follows:

[0209]

[0210] In the formula, W1 to W8 are a group of trainable weight parameter diagonal matrices, and the diagonal elements are all non-negative numbers.

[0211] At this time, D r ′ and D x ′ can be obtained by the following formula:

[0212]

[0213] The above formula shows that D r ′ and D x ′ are obtained by subtracting W1 to W8 pairwise. However, in mathematics, the difference between any two non-negative numbers is not necessarily non-negative, which contradicts the fact that the resistance and reactance parameters of the actual distribution network are all non-negative (that is, all diagonal elements of D r and D x are non-negative). To ensure the reasonable accuracy of line parameter inversion, it is hoped that during the neural network training process, the diagonal elements of W1, W2, W7, and W8 tend to zero as much as possible. This is equivalent to adding a loss function to the neural network weight parameters as follows:

[0214]

[0215] Adding the above loss function as a penalty term to the original loss function, the following expression can be obtained:

[0216]

[0217] In the formula, z and respectively represent the voltage label value and the voltage prediction value output by the ICNN. MSE(·) represents the mean square error calculation, and α 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.

[0218] When the scale of the distribution network is large, the fitting accuracy of the single-layer ICNN is limited, and the estimation errors of D r ′ and D x ′ are large. To ensure the line parameter inversion accuracy, it is necessary to limit the scale of the distribution network for training. The measurement merging method described in Chapter 2 can be used to equivalent the distribution network in the local area. It should be noted that when the local area does not contain the PCC of the distribution network, a virtual PCC needs to be set manually (generally, the node closest to the real PCC is selected, and assume the node number is k), so as to ensure the training accuracy of the ICNN. Let the voltage amplitude of this node be 1, that is, Vk0 = 1. At this time, the deviation of the node voltage amplitude is ΔV k = V k ′ - V k0 . Let the voltage amplitudes of other nodes in the local area be subtracted by ΔV k . Ensure that the differences in voltage amplitudes between nodes in the local area are the same. The formula is expressed as follows:

[0219] V i,new = V i ′ - ΔV k , i ∈ S i,A (53)

[0220] In the formula, V i,new and V′ respectively represent the new voltage amplitude and the original voltage amplitude of node i.

[0221] The present invention covers any substitutions, modifications, equivalent methods, and solutions made to the essence and scope of the present invention. For the public to have a thorough understanding of the present invention, specific details are described in detail in the following preferred embodiments of the present invention. However, those skilled in the art can fully understand the present invention without the description of these details. In addition, well-known methods, processes, procedures, components, and circuits are not described in detail to avoid unnecessary confusion to the essence of the present invention.

[0222] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A distribution network modeling method based on a shallow physics-informed neural network, characterized in that, It includes the following steps: S1. Build a basic modeling model: Establish a power flow model for the distribution network, introduce a savings-correlation matrix and a voltage sensitivity matrix, build a relationship model between node voltages, injected powers, and line power flows. At the same time, adopt non-negative weights and the ReLU activation function to build an ICNN network; S2. Model the topology structure of the distribution network based on ICNN: Train a single-layer ICNN network, use the relationship between the active power injection of nodes and the active line power flow 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 a clustering method, estimate the inverse of the savings-correlation matrix and find its inverse matrix, thereby inversely obtaining the topology structure of the distribution network; S3. Model the line parameters of the distribution network based on ICNN: Based on the obtained topology structure, train the ICNN network, use the relationship between the node injection power and the node voltage as the input, learn the voltage sensitivity matrix, estimate the diagonal matrices of line resistance and reactance through the ICNN network, and introduce a regularization term for optimization to realize the inverse modeling of the line parameters of the distribution network.

2. The method for modeling a distribution network based on a shallow physics-informed neural network according to claim 1, wherein The construction of the basic modeling model in S1 includes: S11. Linear modeling of the distribution network power flow: Use the linearized DistFlow equation to establish the mapping relationship between bus voltages, active / reactive powers, and line power flows, introduce a savings-correlation matrix and a voltage sensitivity matrix, and establish a power flow model for the distribution network; S12. ICNN structure design: Provide an ICNN model applicable to the inversion of the topology structure and parameters of the distribution network through non-negative weights and the ReLU activation function.

3. The method for modeling a distribution network based on a shallow physics-informed neural network according to claim 2, wherein The linear modeling of the distribution network power flow in S11 includes: S111, construct a radial distribution network structure: assume that the distribution network consists of N + 1 buses, and the bus set is The set of distribution lines is Bus 0 is the point of common coupling; S112. Define the parameters of each node and line: For each bus i, define the bus voltage magnitude as V i , the active / reactive injection power of the bus as p i / q i , for each distribution line (i, j), the line resistance and reactance as r ij and x ij , the active / reactive power flow from bus i to bus j as P ij and Q ij , the set of adjacent buses of bus j far from the feeder head is S113. Calculate the power flow equation: Calculate the DistFlow equation for the power flow of each distribution line (i, j) in the distribution network, expressed as: Among them, represents the line power loss; S114, Linearized power flow model: ignoring line power losses Obtain a linearized power flow model, expressed as: V i -V j = r ij P ij + x ij Q ij ; S115. Introduce the graph theory matrix expression form: Express the LinDistFlow model based on the matrix form of the graph, expressed as: (M 0 ) T [V0 V T T = m0 + M T V = D r P + D x Q;​ Among them, D r , D x are diagonal matrices, M 0 = [m0 M T T represents the savings-related incidence matrix of the distribution network;​ S116. Express the power balance relationship in matrix form, expressed as: -MP = -p; -MQ = -q; M T V = D r M -1 p + D x M -1 q - m0; S117. Derive and express the voltage sensitivity relationship: Construct the final expression form of the relationship between the voltage vector and the power, expressed as: V = Rp + Xq - M -T m0; Among them, R = M -T D r M -1 and X = M -T D x M -1 denote the voltage sensitivity matrix.

4. A method for modeling a distribution network based on a shallow physics-informed neural network according to claim 3, characterized in that, The ICNN structure design in S12 includes: S121. Define the ICNN network structure: The ICNN network is a neural network that makes the output convex with respect to the input by designing the weights and activation functions of the neural network. Consider a neural network composed of k fully connected layers, expressed as: Among them, represents the weight parameter, δ i represents the non-linear activation function of the i-th layer; S122. Select the activation function: Select the ReLU function as the activation function, expressed as: ReLU(x) = max(x, 0); S123. Matrix expression form: Analyze the properties of the ReLU function and introduce the matrix expression form, expressed as: |x| = -x + 2ReLU(x); |z| = |Wx| = -Wx + 2ReLU(Wx) = W (x) x + ReLU(W (z) x); Among them, W (x) = -W, W (z) = 2W; S124. Construct a single-layer ICNN structure without bias terms: Construct a single-layer, bias-free ICNN network, including an input layer, a ReLU activation layer, an output layer, and a weight matrix.

5. A power distribution network modeling method based on a shallow physics-informed neural network according to claim 4, characterized in that, The modeling of the distribution network topology 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 the branch-node incidence matrix M. Through the LinDistFlow model, the relationship between the node incidence matrix and the active power flow of the distribution network lines and the node injection power is expressed as: p = MP; S22, derivation of the inverse matrix of the node incidence matrix: The inverse matrix of the node incidence matrix is expressed as: P = M -1 p = Ap; where A = M -1 denotes the inverse matrix of the cost-saving incidence matrix; S23, the core expression of the inversion process: Utilize the characteristics of the ICNN network to achieve the topology inversion of the distribution network, expressed as: |P| = -Ap + 2ReLU(Ap); S24, constructing the topology matrix: The topology matrix A is composed of the grid topology information of the distribution network, expressed as: A = M -1 = -Γ; where Γ 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: where \(A'\in R\) N×2N denotes the augmented cost-saving incidence inverse matrix; S26, the connection between the ICNN network and the distribution network topology structure: The relationship between the weights of the ICNN network and the distribution network topology structure is expressed as: W (x) = [A - A + N×2N ;​ W (z) = [2A + 2A - N×2N ;​ W T1 = W (x) [N + 1:2N] - W (x) [1:N] ≈ A; W T2 = (W (z) [1:N] - W (z) [N + 1:2N]) / 2 ≈ A; Among them, W T1 , W T2 ∈R N×N both represent the topological structure information matrix, and [i:j] represents taking the i-th column to the j-th column of the matrix.

6. A method for modeling a distribution network based on a shallow physics-informed neural network according to claim 5, characterized in that, The modeling of the distribution network line parameters based on ICNN in S3 includes: S31. Construct the impedance parameter solution objective: The objective of line parameter inversion is to solve the line resistance diagonal matrix D r and the reactance diagonal matrix D x , which is expressed as: D r = M T RM; D x = M T XM; S32, establishing the expression of the voltage-power relationship: Based on the LinDistFlow model, define the relationship between the matrices R and X and the node injection power and the distribution network node voltage, expressed as: V′ = V + M -T m0 = Rp + Xq; where V′ represents the transformed node voltage phasor; S33, constructing the mapping structure: Construct the mapping structure of the ICNN network, expressed as: |V′| = -(Rp + Xq) + 2ReLU(Rp + Xq); S34, variable transformation: Perform variable transformation to meet the non-negative weight constraint, expressed as: S35, augmented matrix expression: Convert the mapping relationship between the node voltage and power into the augmented matrix form, expressed as: where \(R', X' \in R\) N×2N denotes the augmented voltage sensitivity matrix; S36, establish the relationship between the weight and the parameter matrix: Train a single-layer unbiased ICNN network, and its weight parameter W (x) and W (z) reflect the topological structure and line parameter information of the distribution network, and are expressed as: W (x) = [R - X - R + X + N×4N ;​ W (z) = [2R + 2X + 2R - 2X - N×4N ;​ W TR1 = W (x) [2N + 1:3N] - W (x) [1:N] ≈ R; W TR2 =(W (z) [1:N] - W (z) [2N + 1:3N]) / 2 ≈ R; W TX1 = W (x) [3N + 1:4N] - W (x) [N + 1:2N] ≈ X; W TX2 = (W (z) [N + 1:2N] - W (z) [3N + 1:4N]) / 2 ≈ X; Among them, W TR1 , W TR2 , W TX1 , W TX2 ∈ R N×N represents the voltage sensitivity information matrix; S37, inverting the line impedance matrix: Based on the M matrix, achieve the inversion of the distribution network line parameters, expressed as: D r ′ = M T R′M = M T (R + - R - )M; D x ′ = M T X′M = M T (X + - X - )M; Among them, D r ' and D x ' respectively represent the line resistance estimation matrix and the line reactance estimation matrix; S38, symmetric design and optimization expression of the weight matrix: Represent the weight structure by introducing sub-weight blocks, expressed as: W (z) = [W5 (z) W6 (z) W7 (z) W8 (z) N×4N ;​ where W1 to W8 are a group of trainable weight parameter diagonal matrices; S39, introducing the regularization term constraint and virtual nodes: Introduce the regularization term loss function, construct the total loss function including the mean square error and the regularization penalty term, and introduce the virtual PCC node to normalize the voltage.

7. A power distribution network modeling method based on a shallow physics-informed neural network according to claim 6, characterized in that, The sub-weight block is expressed as:

8. A method for modeling a distribution network based on a shallow physics-informed neural network according to claim 7, characterized in that, The regularization term loss function is expressed as: The total loss function is expressed as: where z and represent the voltage tag value and the voltage prediction value output by ICNN respectively, MSE(·) represents the mean square error calculation, and α represents the weight coefficient.

9. A method for modeling a distribution network based on a shallow physics-informed neural network according to claim 8, characterized in that, The introduction of the virtual PCC node to normalize the voltage is expressed as: ΔV k = V k ′ - V k0 ; V i,new = V i ′ - ΔV k , i ∈ S i,A ; where V i,new and V′ represent the new voltage magnitude and the original voltage magnitude of node i, respectively.

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