A method, system, computer device and medium for complementing measurement data of a distribution network

Abstract

The present invention provides a method, a system, a computer device and a medium for completing measurement data of a distribution network, belonging to the technical field of distribution system state estimation, including: Step S1, constructing a standard matrix completion model according to the problem of missing measurement data of the distribution network; Step S2, based on the analysis of the data characteristics of the distribution network, adding linear constraints to the constructed standard matrix completion model to construct a complete measurement data completion model for the distribution network; Step S3, using the alternating minimization method to solve the complete measurement data completion model for the distribution network to obtain the measurement data matrix of the distribution network after completion at a single moment; Step S4, using the measurement data matrix of the distribution network after completion and combining with the moving average method to perform state estimation on the next moment of the unknown distribution system state. The present invention can better adapt to a new type of distribution network with a relatively high proportion of missing measurement data, and still has a good completion result under heavy load conditions, with a relatively high credibility.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution system state estimation, and in particular to a method, system, computer device and medium for completing measurement data of a distribution network. Background Art

[0002] Guided by mathematics, control theory and other emerging theories, and combined with the characteristics of the power system itself, the distribution system state estimation technology has become one of the key technologies to ensure the stable operation of the distribution system. With the popularization of distributed energy resources, due to the scarcity of sensors and the low quality of measurements, traditional state estimation technologies are difficult to cope with the current low-measurement distribution system.

[0003] In view of the above situation, some research has proposed an algorithm for distribution system state estimation using low-rank matrix completion, which can operate under low-measurement conditions with large-scale data missing. This method flexibly combines the characteristics of measurement values to estimate and complete the power flow data of the distribution system at a single moment, but the algorithm cannot estimate the power flow data situation on the time scale and cannot perform state estimation on the distribution network with unknown measurements at adjacent moments in practical applications. Summary of the Invention

[0004] The purpose of the present invention is to provide a method, system, computer device and medium for completing measurement data of a distribution network, which can better adapt to a new type of distribution system with a high proportion of missing measurement data, and still have good completion results and high credibility under heavy load conditions.

[0005] To achieve the above purpose, the present invention provides a method for completing measurement data of a distribution network, including the following steps:

[0006] Step S1: Construct a standard matrix completion model according to the problem of missing measurement data of the distribution network;

[0007] Step S2: Based on the constructed standard matrix completion model and according to the analysis of the data characteristics of the distribution network, add linear constraints to construct a complete measurement data completion model of the distribution network;

[0008] Step S3: Use the alternating minimization method to solve the complete measurement data completion model of the distribution network to obtain the measurement data matrix of the distribution network after completion at a single moment;

[0009] Step S4: Use the measurement data matrix of the distribution network after completion at a single moment and combine it with the moving average method to estimate the state of the next moment of the distribution system with unknown state.

[0010] Preferably, in step S1, a standard matrix completion model is constructed according to the problem of missing measurement data of the distribution network, and the standard matrix completion model is solved. The specific operations are as follows:

[0011] Let is a real-valued data matrix, and Ω is the set of known elements in M. represents the data matrix containing the problem of missing measurement data in the distribution network, where if (i0, j0) ∈ Ω and the rest are 0 here, then the problem of completing the data matrix containing the problem of missing measurement data in the distribution network is expressed as:

[0012]

[0013] where X is the completed matrix; (i0, j0) represents the position of a certain data point in the matrix as the i0-th row and the j0-th column; m represents the number of rows of M; n represents the number of columns of M; represents M Ω the data at the i0-th row and the j0-th column; represents the data at the i0-th row and the j0-th column of M;

[0014] Solve the non-convex NP-hard problem in formula (1) by minimizing the nuclear norm of the matrix through a heuristic algorithm:

[0015]

[0016] where ||X|| * represents the sum of the singular values in X, that is, the nuclear norm of the matrix;

[0017] Modify the equality constraint in formula (2) to obtain the standard matrix completion model:

[0018] ||X Ω -M Ω || F ≤ δ (3);

[0019] where ||·|| * is the Frobenius norm of the matrix, and the parameter δ ≥ 0.

[0020] Preferably, in step S2, before constructing the complete distribution network measurement data completion model, it also includes constructing a matrix model based on the polyphase distribution system;

[0021] Among them, the specific operation of constructing a matrix model based on the polyphase distribution system is as follows:

[0022] Construct a matrix model based on the polyphase distribution system based on the branch index. During the process of constructing the matrix model based on the polyphase distribution system, M is constructed such that each row represents a power system branch and each column represents the measurement quantity related to that branch. For each branch the corresponding row in

[0023]

[0024] In the formula, represents the real part, represents the imaginary part; |v f | represent the real part, imaginary part and absolute value of the voltage at the branch endpoint f respectively; represent the active power and reactive power injected at the branch endpoint f respectively; |v t | represent the real part, imaginary part and absolute value of the voltage at the branch endpoint t respectively; represent the active power and reactive power injected at the branch endpoint t respectively; represent the real part and imaginary part of the current flowing through the branch (f, t) respectively;

[0025] Among them, the specific operation of constructing a matrix model based on a polyphase distribution system is as follows:

[0026] Construct a matrix model based on a polyphase distribution system based on node indexing. During the process of constructing a matrix model based on a polyphase distribution system based on node indexing, M is constructed such that each row represents a node and each column represents the measured quantity related to that node. For each node the corresponding row in

[0027]

[0028] Among them, represents the real part of the node voltage; represents the imaginary part of the node voltage; |v ε represents the absolute value of the node voltage; represents the active power injected at the node; represents the reactive power injected at the node;

[0029] Let represent the set of nodes, where node 1 is the slack node and the remaining nodes are all PQ nodes, and are the voltage and injected power phasors at each node respectively. The slack node voltage and injected power phasors are represented as v1 and s1 respectively, and the unslack node voltage and injected power phasors are represented as v -1 and s -1 respectively; i ft represents the current in the branch ; represents the set of lines; The electrical characteristics between different nodes are expressed in mathematical form through the nodal admittance matrix :

[0030]

[0031] Among them, Υ 11 represents the self-admittance of node 1; Υ LL represents the self-admittance of node L; Υ 1L represents the mutual admittance between node 1 and node L; Υ L1 represents the mutual admittance between node L and node 1.

[0032] Preferably, in step S2, the linear constraints include repetition constraints, noise-adaptive Ohm's law constraints, and linear power flow constraints;

[0033] Among them, the repetition constraint is as follows:

[0034]

[0035] Among them, Λ is a set containing all repeated measurement pairs in M; represents the measured value located in the i1-th row and j1-th column of X; represents the measured value located in the i1'-th row and j1'-th column of X;

[0036] The noise-adaptive Ohm's law constraint is as follows:

[0037]

[0038] Among them, ξ r,ft , ξ c,ft are respectively the error tolerances of the real and imaginary parts of Ohm's law on the branch; represents the real part of Ohm's law; represents the imaginary part of Ohm's law;

[0039] The linear power flow constraint is as follows:

[0040] For unbalanced node voltages and injection powers, the following form of approximation is adopted:

[0041]

[0042] Among them, is the real part of the phasor of the injection power of the unbalanced node; is the imaginary part of the phasor of the injection power of the unbalanced node; the absolute value of the unbalanced node voltage is |v -1 |; the absolute value of the no-load voltage of the unbalanced node is |w|;

[0043] Let be the phasor of the no-load voltage of the unbalanced node, and define When estimating the unbalanced node voltage it is:

[0044]

[0045] Among them, \(j\) represents the general form in complex numbers;

[0046] The accurate power flow equation is used to relate the voltage to the injected power at the slack bus:

[0047]

[0048] Since \(v_1\) is known, Equation (13) is linear with respect to the voltage;

[0049] Next, Equation (9), Equation (10), and Equation (13) are respectively modified to Equation (14), Equation (15), and Equation (16):

[0050]

[0051] Among them, \(\tau\) r , \(\tau\) c , \(\gamma\), \(\alpha\) r , \(\alpha\) c are all error tolerances;

[0052] In Equations (9) - (10), let Let \(w\) (T) , \(h\) (T) , \(B\) (T) , \(C\) (T) represent \(s\) -1 , \(v\) -1 , \(w\), \(h\), \(B\), \(C\) corresponding to time \(T\);

[0053] Equation (17) is used to express Equations (14) and (15):

[0054] \(y\approx Ax + b\) (17);

[0055] Among them, \(x = [h\) (T) ;

[0056] Preferably, in step S2, the complete distribution network measurement data complementation model is as follows:

[0057]

[0058] Among them, such that \(\mu>0\), \(\nu>0\) are penalty parameters; is a constant;

[0059] \(z_1,\cdots,z\) 2T , \(c_1,\cdots,c\) 2T The values of are obtained from the following specific forms of \(X\), \(y\), and \(x\):

[0060]

[0061] Preferably, in step S3, the alternating minimization method is used to solve the complete distribution network measurement data completion model, and the system measurement data matrix after completion at a single moment is obtained. The specific operations are as follows:

[0062] Any matrix of rank r is expressed as and in the form of a matrix product, that is, X = UV, and its nuclear norm is expressed in terms of the Frobenius norms of U and V as follows:

[0063]

[0064] The matrix completion model (18) is reformulated using formula (20) as follows:

[0065]

[0066] such that

[0067] The alternating minimization algorithm alternately solves for U and V with the rank r of the matrix fixed and the number of iterations k = 1,..., N:

[0068]

[0069] When the iteration result satisfies , stop the iteration, and the residual threshold σ ∈ [0, 1);

[0070] The solved matrix X after completion at time T is X = U N V N .

[0071] Preferably, in step S4, the sliding average method is used in combination with the completed distribution network measurement data matrix to perform state estimation for the next moment of the unknown distribution system state. The specific operations are as follows:

[0072] For a data sequence of length n, with a window size of l, the matrix X = U N V N after completion at time T is substituted into formula (24) to calculate the sliding average value:

[0073]

[0074] where X q is the data matrix of the q-th time section in the original data sequence; X T+1 is the data matrix at time T + 1 with unknown state obtained after calculation.

[0075] The present invention also provides a device for completing distribution network measurement data, comprising:

[0076] A standard matrix completion module, configured to construct a standard matrix completion model according to the problem of missing distribution network measurement data;

[0077] A characteristic adaptability constraint module for distribution network measurement data, configured to add linear constraints based on the constructed standard matrix completion model according to the analysis of distribution network data characteristics, and construct a complete distribution network measurement data completion model;

[0078] A single-moment distribution network measurement data completion module based on alternating minimization, configured to use the alternating minimization method to solve the complete distribution network measurement data completion model, and obtain the completed distribution network measurement data matrix at a single moment;

[0079] A distribution network measurement data completion module based on a sliding average time series, configured to use the completed distribution network measurement data matrix at a single moment and combine it with the sliding average method to estimate the state of the next moment of the unknown distribution system.

[0080] A computer device, comprising: a memory and a processor; the memory stores a computer program, and when the processor executes the computer program, the steps of the above-mentioned method for completing distribution network measurement data are implemented.

[0081] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned method for completing distribution network measurement data are implemented.

[0082] Therefore, the present invention adopts the above-mentioned method, system, computer device and medium for completing distribution network measurement data, and the beneficial technical effects are as follows:

[0083] (1) In the present invention, by combining the alternating minimization matrix completion algorithm with the sliding average algorithm to estimate the state of the next moment of the unknown distribution system, it makes up for the limitation that it is difficult to analyze time series data in the process of estimating the distribution network state using the traditional matrix completion method;

[0084] (2) In the present invention, through repeated constraints, noise self-adaptive Ohm's law constraints and linear power flow constraints, it can better adapt to a new type of distribution system with a relatively high proportion of missing measurement data, and still has a good completion result and high credibility under heavy load conditions;

[0085] (3) The process of the present invention is simpler than artificial intelligence algorithms, without the need to divide the training set and the test set, and has a high accuracy and credibility, which proves its effectiveness and broad prospects for analyzing the data of actual distribution systems. Description of the Drawings

[0086] Figure 1 It is the flowchart of a method for completing measurement data of a distribution network according to the present invention;

[0087] Figure 2 It is a schematic diagram of the alternating minimization combined with the sliding average matrix completion model;

[0088] Figure 3 It is the operation process of the alternating minimization combined with the sliding average algorithm;

[0089] Figure 4 It is the completion result of the power flow data of the IEEE-33 and IEEE-118 node systems;

[0090] Figure 5 It is the completion result diagram of the voltage amplitude of the IEEE-118 node;

[0091] Figure 6 It is the completion situation of a heavily loaded node in the IEEE-33 node system; among them, Figure 6 In (a), the active power injected into the node when 30% is missing; Figure 6 In (b), the reactive power injected into the node when 30% is missing; Figure 6 In (c), the active power injected into the node when 60% is missing; Figure 6 In (d), the reactive power injected into the node when 60% is missing;

[0092] Figure 7 It is the structural schematic diagram of a device for completing measurement data of a distribution network. Specific implementation manners

[0093] The technical solution of the present invention will be further described below through the accompanying drawings and embodiments.

[0094] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs.

[0095] Embodiment 1

[0096] As Figures 1-3 shown, a method for completing measurement data of a distribution network according to the present invention includes the following steps:

[0097] Step S1, constructing a standard matrix completion model according to the problem of missing measurement data of the distribution network;

[0098] Given an incomplete matrix assumed to be of low rank, the goal of the matrix completion problem is to determine the unknown elements in the matrix. Let be a real-valued data matrix, Ω be the set of known elements in M, represents the data matrix containing the problem of missing measurement data of the distribution network, where, Here, \((i_0, j_0)\in\Omega\) and the rest are 0. Then, the problem of completing the data matrix containing the problem of missing measurement data in the distribution network is expressed as a rank minimization problem:

[0099]

[0100] where \(X\) is the completed matrix; \((i_0, j_0)\) represents the position of a certain data point in the matrix, which is the \(i_0\)-th row and the \(j_0\)-th column; \(m\) represents the number of rows of \(M\); \(n\) represents the number of columns of \(M\); represents \(M\) Ω the data at the \(i_0\)-th row and the \(j_0\)-th column; represents the data at the \(i_0\)-th row and the \(j_0\)-th column of \(M\);

[0101] Since the above rank minimization optimization model is a non-convex NP-hard problem and is difficult to solve, the non-convex NP-hard problem in formula (1) is solved by minimizing the nuclear norm of the matrix through a heuristic algorithm:

[0102]

[0103] where \(\|X\|\) * represents the sum of the singular values in \(X\), that is, the nuclear norm of the matrix;

[0104] Due to the nature of the equality constraint, formula (2) is vulnerable to noise. Modify the equality constraint in formula (2) to obtain the standard matrix completion model:

[0105] \|X Ω -M Ω \| F \leq\delta\ (3);

[0106] where \(\|\cdot\|\) * is the Frobenius norm of the matrix, the parameter \(\delta\geq0\), and it is adjusted according to the degree of measurement noise.

[0107] Step S2. According to the analysis of the distribution network data characteristics, based on the constructed standard matrix completion model, add linear constraints to construct a complete distribution network measurement data completion model;

[0108] When using the standard matrix completion model to solve the problem of missing distribution network data, it is necessary to analyze in combination with the distribution network data characteristics. Therefore, a matrix model based on a polyphase distribution system is constructed;

[0109] Let represent the set of nodes, where node 1 is the slack node and the remaining nodes are all PQ nodes. Let represent the set of lines. The nodal admittance matrix is:

[0110]

[0111] Among them, Υ 11 represents the self-admittance of node 1; Υ LL represents the self-admittance of node L; Υ 1L represents the mutual admittance between node 1 and node L; Υ L1 represents the mutual admittance between node L and node 1;

[0112] Let and be the voltage and the injected power phasor (partially unknown) at each node respectively. The voltage and the injected power phasor of the slack node are represented as v1 and s1 respectively, and the voltage and the injected power phasor of the unslack nodes are represented as v -1 and s -1 ; i ft represents the current in branch . M and X vary according to the specific attributes of the data (such as the type and scale of the measured values), including the following two feasible data matrix forms:

[0113] 1) Branch index: Construct M such that each row represents a power system branch and each column represents the quantity measurements related to that branch. This structure can utilize both branch- and node-related measurements. Specifically, for each branch the corresponding row contains:

[0114]

[0115] where represents the real part, represents the imaginary part; v f | respectively represent the real part, the imaginary part, and the absolute value of the voltage at the f end of the branch; respectively represent the active power and the reactive power injected at the f end of the branch; v t | respectively represent the real part, the imaginary part, and the absolute value of the voltage at the t end of the branch; respectively represent the active power and the reactive power injected at the t end of the branch; respectively represent the real part and the imaginary part of the current flowing through the branch (f, t);

[0116] 2) Node index: Construct M such that each row represents a node and each column represents the quantity measurements related to that node. That is, for each node the corresponding row contains:

[0117]

[0118] where represents the real part of the node voltage; Denotes the imaginary part of the nodal voltage; |v ε Denotes the absolute value of the nodal voltage; Denotes the active power injected at the node; Denotes the reactive power injected at the node.

[0119] Although this structure only uses measurements related to nodes, its advantage is that the resulting small matrix can be used for effective estimation of large-scale problems.

[0120] The linear constraints include repetition constraints, noise-adaptive Ohm's law constraints, and linear power flow constraints;

[0121] Among them, the repetition constraint: depending on the different constructions of the data matrix M, some quantities may appear in multiple positions in M.

[0122] In the branch index, if a node is located in multiple branches, the measurements of the quantities related to the given node will appear in multiple rows. Therefore, let Λ be the set containing all pairs of repeated quantity measurements in M, such that That is

[0123]

[0124] Among them, Λ is the set containing all pairs of repeated quantity measurements in M; Denotes the measured value of the quantity located in the i1-th row and j1-th column of X; Denotes the measured value of the quantity located in the i1'-th row and j1'-th column of X;

[0125] The noise-adaptive Ohm's law is as follows:

[0126]

[0127] Among them, ξ r,ft , ξ c,ft Are respectively The error tolerances of the real and imaginary parts of Ohm's law on the branch; Denotes the real part of Ohm's law; Denotes the imaginary part of Ohm's law;

[0128] The linear power flow constraint is as follows:

[0129] Since the exact AC power flow equation is non-linear, the equation is linearly approximated in Cartesian coordinates. The following forms of approximations are used for unbalanced nodal voltages and injected powers:

[0130]

[0131] Among them, Is the real part of the phasor of the unbalanced nodal injected power; Inject the imaginary part of the power phasor into the unbalanced node; the absolute value of the unbalanced node voltage is |v -1 |; the absolute value of the no-load voltage of the unbalanced node is |w|;

[0132] Let be the phasor of the no-load voltage of the unbalanced node, and define When estimating the unbalanced node voltage it is:

[0133]

[0134] where j is the general form of complex number representation;

[0135] Use the exact power flow equation to relate the voltage to the injected power at the balanced node:

[0136]

[0137] Since v1 is known, formula (13) has a linear relationship with the voltage;

[0138] Then formula (9), formula (10), and formula (13) are modified to formula (14), formula (15), and formula (16) respectively:

[0139]

[0140] where τ r , τ c , γ, α r , α c are all error tolerances;

[0141] In formula (9) - formula (10), let Let w (T) , h (T) , B (T) , C (T) represent s -1 , v -1 , w, h, B, C corresponding to time T;

[0142] To simplify subsequent expressions, use formula (17) to express formula (14) and formula (15):

[0143] y≈Ax + b (17);

[0144] where, x = [h (T) ;

[0145] The complete measurement data complementation model of the distribution network is as follows:

[0146]

[0147] Among them, such that μ > 0, ν > 0 are penalty parameters; is a constant;

[0148] z1,..., z 2T , c1,..., c 2T The values of are obtained through the following specific forms of X, y, and x:

[0149]

[0150] Step S3: Use the alternating minimization method to solve the complete distribution network measurement data completion model, and obtain the completed distribution network measurement data matrix at a single moment.

[0151] The solution process of the alternating minimization algorithm that updates variables alternately through the low-rank matrix fitting LMaFit is as follows:

[0152] First, any matrix with rank r is expressed as and in the form of the matrix product, that is, X = UV. Its nuclear norm is expressed in terms of the Frobenius norms of U and V as follows:

[0153]

[0154] For a very small rank r, r << min{m, n}, using the above characterization of the nuclear norm can significantly reduce the scale of the problem; the matrix completion model (18) is reformulated using formula (20) as follows:

[0155]

[0156] such that

[0157] Next, the alternating minimization algorithm alternately solves U and V by setting the number of iterations k = 1,..., N while fixing the rank r of the matrix:

[0158]

[0159] Finally, when the iteration result satisfies stop the iteration, and the residual threshold σ ∈ [0, 1); and it can be adjusted depending on the data situation.

[0160] The solved matrix X = U N V N .

[0161] Step S4: Use the completed distribution network measurement data matrix and the moving average method to perform state estimation on the next moment of the unknown distribution system state.

[0162] The specific operation is as follows:

[0163] For a data sequence of length n, with a window size of l, the formula for calculating the moving average is as follows:

[0164]

[0165] where MA p is the p-th moving average value; x q is the q-th data point in the original data sequence; Substitute the matrix X = U N V N completed at time T into formula (24) to obtain the data matrix at time T + 1 as:

[0166]

[0167] where X q is the single-time-section data matrix.

[0168] The selection of the window l size depends on the actual data situation. When the historical data changes relatively smoothly within a period of time, a smaller moving window can be selected. Conversely, when the fluctuations are severe, the moving window should be appropriately increased to prevent overfitting noise from causing a decrease in the result accuracy.

[0169] To test the performance of the alternating minimization matrix completion algorithm, the mean absolute percentage error (MAPE) is used to show the relative standard value error after completing the missing power flow data of each node, including the node voltage amplitude, voltage phase angle, node injected active power, reactive power, node output active power, and reactive power.

[0170]

[0171] where represents the estimated value of the q-th data point.

[0172] Construct the power flow data matrix of the distribution system after moving average processing (taking the node index as an example) as follows:

[0173]

[0174] where T n represents the sampling moment of the measurement device.

[0175] The present invention will be further described below through two different calculation examples.

[0176] 1) Processing of datasets of different scales. The test results of the alternating minimization matrix completion algorithm on the IEEE-33 bus and IEEE-118 bus systems are as follows Figure 4 shown. The alternating minimization matrix completion method on the two systems was compared with the classical weighted least squares (WLS) state estimation algorithm.

[0177] 10%-70% of the power flow datasets of the two cases were randomly deleted and completed using the alternating minimization matrix completion algorithm. When the number of known measurements is greater than 70%, the MAPE of the power flow data completion result is less than 1%. At this time, the MAPE of the completion result of WLS is about 1%, indicating that the result has good accuracy. When the number of known measurements is less than 70%, WLS cannot run in this state. Therefore, under the measurement data conditions where WLS can run, the estimated values of the method proposed in the present invention are similar to those of WLS in terms of error. In the case where WLS cannot run, the method proposed in the present invention can still run and has high error accuracy, and has good completion accuracy in systems with different scales of data volumes. Figure 5 Shows the comparison of the voltage magnitude completion results with the standard data when 30%-40% of the power flow data of the IEEE-118 bus system is missing.

[0178] Figure 6 Shows the comparison of the completion results of the injected active and reactive powers of a heavily loaded bus in the IEEE-33 bus system when 30% and 60% of the data is missing with the standard data of the case. It can be seen that in the case where more than half of the data is missing, the method proposed in the present invention can still generate relatively accurate completed data, and the method is still applicable when the bus is in a heavily loaded state.

[0179] 2) Processing of time series datasets. Since the alternating minimization matrix completion algorithm is difficult to process measurement data in time series, and although WLS can process time series data to a certain extent but cannot run in the state of a large amount of missing data, in this embodiment, the alternating minimization matrix completion algorithm (MC) is combined with the moving average algorithm (MA) to process the completion of power flow data in time series.

[0180] Table 1 Completion results of power flow data in time series

[0181]

[0182]

[0183] As can be seen from the results in the above table, when the missing ratio of measurement data is greater than 30%, the error of the result completed by the alternating minimization algorithm is about 1%. And under the condition that the data of the next moment is completely missing, it can be combined with the classical moving average algorithm to predict all types of power flow data at this moment, and the relative accuracy is about 1.4%, with high accuracy and credibility. This calculation process does not need to divide the known measurement data set into training set and test set, and the algorithm execution efficiency is high, and the process is simple and clear, which is suitable for the state estimation analysis scenario in the case of large-scale distribution system data missing.

[0184] Embodiment 2

[0185] As Figure 7 shown, the present invention also provides a device for completing distribution network measurement data, including a standard matrix completion module, a characteristic adaptability constraint module for distribution network measurement data, a module for completing distribution network measurement data at a single moment based on alternating minimization, and a module for completing distribution network measurement data based on moving average time series;

[0186] Among them, the standard matrix completion module is used to construct a standard matrix completion model according to the problem of missing distribution network measurement data;

[0187] The characteristic adaptability constraint module for distribution network measurement data is used to analyze according to the characteristics of distribution network data, and based on the constructed standard matrix completion model, add linear constraints to construct a complete distribution network measurement data completion model;

[0188] The module for completing distribution network measurement data at a single moment based on alternating minimization is used to solve the complete distribution network measurement data completion model by using the alternating minimization method to obtain the completed distribution network measurement data matrix at a single moment;

[0189] The module for completing distribution network measurement data based on moving average time series is used to estimate the state of the next moment of the unknown distribution system state by combining the completed distribution network measurement data matrix at a single moment with the moving average method.

[0190] When the above functions are implemented in the form of software function units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or part of this technical solution can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0191] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a definite sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch instructions from the instruction execution system, apparatus, or device and execute the instructions), or in conjunction with these instruction execution systems, apparatuses, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0192] It should be noted that the content not elaborated in detail in the present invention is all prior art and well-known to those skilled in the art.

[0193] Therefore, the present invention adopts the above-mentioned method, system, computer device, and medium for complementing distribution network measurement data. This method can better adapt to a new type of distribution system with a relatively high proportion of missing measurement data, and still has a good complementation result and high credibility under heavy load conditions.

[0194] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent substitutions, and these modifications or equivalent substitutions do not make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for complementing measurement data of a distribution network, characterized in that, It includes the following steps: Step S1: Construct a standard matrix completion model according to the problem of missing measurement data in the distribution network; Step S2: Based on the analysis of the data characteristics of the distribution network, add linear constraints to the constructed standard matrix completion model to construct a complete distribution network measurement data completion model; Step S3: Use the alternating minimization method to solve the complete distribution network measurement data completion model to obtain the completed distribution network measurement data matrix at a single moment; Step S4: Use the completed distribution network measurement data matrix at a single moment in combination with the moving average method to estimate the state of the next moment of the unknown distribution system; In Step S2, the linear constraints include repeated constraints, noise-adaptive Ohm's law constraints, and linear power flow constraints; Among them, the repeated constraint is as follows: （1）； Among them, is the set containing all pairs of repeated measurements in denotes X the measurement value in the th row and denotes X the measurement value in the th row and The noise-adaptive Ohm's law constraint is as follows: （2）； Among them, , are respectively the error tolerances of the real and imaginary parts of Ohm's law on the branch; represents the real part of Ohm's law; represents the imaginary part of Ohm's law; The linear power flow constraint is as follows: For unbalanced node voltages and injection powers, the following forms of approximations are used: （3）； （4）； Among them, is the real part of the power phasor injected into the unbalanced node; is the imaginary part of the power phasor injected into the unbalanced node; the absolute value of the unbalanced node voltage is ; the absolute value of the no-load voltage of the unbalanced node is ; Let be the phasor of the no-load voltage of the unbalanced node, and define When estimating the voltage of the unbalanced node it is: （5）； （6）； Among them, is in the general form of a complex number representation; represents the self-admittance of node L; represents the mutual admittance between node L and node 1; represents the balanced node voltage; Use the exact power flow equation to relate the voltage to the injection power at the balanced node: （7）； Since is known, formula (7) has a linear relationship with voltage; Then, formula (3), formula (4), and formula (7) are respectively modified to formula (8), formula (9), and formula (10): （8）； （9）； （10）； Among them, , , , , are all error tolerances; In Formulas (3) - (4), let and let , , , , , represent those corresponding to time T , , , , , ; Use formula (11) to express formula (8) and formula (9): （11）； Among them, ; ; ; .

2. The method for complementing measurement data of a distribution network according to claim 1, wherein In Step S1, to construct a standard matrix completion model according to the problem of missing measurement data in the distribution network, the specific operations are as follows: Let be a real-valued data matrix, and be a set of known elements in ; denote a data matrix containing the problem of missing measurement data in the distribution network, where , here , and the rest are 0, then the problem of completing the data matrix containing the problem of missing measurement data in the distribution network is expressed as: （12）； Among them, X is the completed matrix; indicates that the position of a certain data point in the matrix is the -th row and the -th column; represents the number of rows of; represents the number of columns of; represents the data at the -th row and the -th column in; represents the data at the -th row and the -th column in; Solve the non-convex NP-hard problem in formula (12) by minimizing the nuclear norm of the matrix through a heuristic algorithm: （13）； Among them, denotes X the sum of singular values, that is, the nuclear norm in the matrix; Modify the equality constraint in formula (13) to obtain the standard matrix completion model: （14）； Among them, is the Frobenius norm of the matrix, and the parameter .

3. A method for completing measurement data of a distribution network according to claim 2, characterized in that, In Step S2, before constructing the complete distribution network measurement data completion model, it also includes constructing a matrix model based on the polyphase distribution system; Among them, the specific operations for constructing a matrix model based on the polyphase distribution system are as follows: Construct a matrix model based on a multi-phase distribution system using branch indices. During the process of constructing the matrix model based on the multi-phase distribution system using branch indices, it is constructed such that each row represents a power system branch and each column represents the measurements related to that branch. For each branch , the corresponding row in （15）； In the formula, represents the real part, represents the imaginary part; , , respectively represent the real part, imaginary part and absolute value of the voltage at the branch end ; respectively represent the active power and reactive power injected at the branch end ; , , respectively represent the real part, imaginary part and absolute value of the voltage at the branch end ; , respectively represent the active power and reactive power injected at the branch end ; , respectively represent the real part and imaginary part of the current flowing through the branch . Among them, the specific operations for constructing a matrix model based on the polyphase distribution system are as follows: Construct a matrix model based on a polyphase distribution system based on node indices. During the process of constructing the matrix model based on a polyphase distribution system based on node indices, it is constructed such that each row represents a node and each column represents the measurements related to that node. For each node , the corresponding row in （16）； Among them, represents the real part of the node voltage; represents the imaginary part of the node voltage; represents the absolute value of the node voltage; represents the active power injected into the node; represents the reactive power injected into the node; Let represent the set of nodes, where node 1 is the slack node and the remaining nodes are all PQ nodes, and be the voltage and the injected power phasor at each node respectively. The slack node voltage and the injected power phasor are represented as and respectively, while the non-slack node voltages and the injected power phasors are represented as and respectively; represents the current in branch ; represents the set of lines; the electrical characteristics between different nodes are expressed in mathematical form through the nodal admittance matrix : （17）； Among them, represents the self-admittance of Node 1; represents the self-admittance of Node L; represents the mutual admittance between Node 1 and Node L; represents the mutual admittance between Node L and Node 1.

4. A method for completing measurement data of a distribution network according to claim 3, characterized in that, In Step S2, the complete distribution network measurement data completion model is as follows: （18）； Among them, and and such that , ; and are penalty parameters; and are constants; , The value is obtained through the following , , specific forms: ， ， （19）。 5. A method for complementing measurement data of a distribution network according to claim 4, characterized in that In Step S3, use the alternating minimization method to solve the complete distribution network measurement data completion model to obtain the completed system measurement data matrix at a single moment. The specific operations are as follows: Any matrix of rank can be expressed as the matrix product of and , that is . Its nuclear norm is expressed in terms of the Frobenius norms of and as follows: ​ （20）； Use formula (20) to re-express the matrix completion model (18) as follows: （21）； Cause , ; The alternating minimization algorithm sets the number of iterations in the case of a fixed matrix rank and alternately solves and : （22）； （23）； When the iteration result satisfies , stop the iteration, and the residual threshold ; The matrix after completion at time T is solved .

6. A method for completing measurement data of a distribution network according to claim 5, characterized in that In Step S4, use the completed distribution network measurement data matrix in combination with the moving average method to estimate the state of the next moment of the unknown distribution system. The specific operations are: For a data sequence of length , with a window size of , substitute the matrix after completing the time T into Equation (24) to calculate the moving average: （24）； Among them, is the data matrix of the th time section in the original data sequence; is the data matrix at the moment obtained after calculation for the unknown state.

7. A device for completing measurement data of a distribution network, characterized in that, For implementing the distribution network measurement data completion method according to any one of claims 1-6, it includes: A standard matrix completion module for constructing a standard matrix completion model according to the problem of missing measurement data in the distribution network; A distribution network measurement data characteristic adaptability constraint module for adding linear constraints to the constructed standard matrix completion model based on the analysis of the data characteristics of the distribution network to construct a complete distribution network measurement data completion model; A single-moment distribution network measurement data completion module based on alternating minimization for using the alternating minimization method to solve the complete distribution network measurement data completion model to obtain the completed distribution network measurement data matrix at a single moment; The sliding average time series-based distribution network measurement data completion module is used to perform state estimation on the next moment of the unknown distribution system state by combining the completed distribution network measurement data matrix at a single moment with the sliding average method.

8. A computer device, comprising: A memory and a processor; the memory stores a computer program, characterized in that when the processor executes the computer program, the steps of the distribution network measurement data completion method according to any one of claims 1 to 6 are implemented.

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

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