Power distribution network measurement data completion method and system, computer equipment and medium

Abstract

The invention provides a power distribution network measurement data completion method and system, computer equipment and a medium, and belongs to the technical field of power distribution system state estimation, and the method comprises the steps: S1, building a standard matrix completion model according to a power distribution network measurement data missing problem; s2, according to power distribution network data feature analysis, linear constraint is added based on the constructed standard matrix completion model, and a complete power distribution network measurement data completion model is constructed; s3, solving the complete power distribution network measurement data completion model by using an alternating minimization method to obtain a power distribution network measurement data matrix after single-moment completion; and S4, performing state estimation on the next moment of the unknown state of the power distribution system by using the complemented measurement data matrix of the power distribution network in combination with a moving average method. The method can well adapt to a novel power distribution system with a high measurement data missing proportion, still has a good completion result under the heavy load condition, and is high in credibility.

Description

Technical Field

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

[0002] Guided by mathematics, control theory and other emerging theories, the state estimation technology of distribution system combined with the characteristics of the power system itself 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 low measurement quality, traditional state estimation technology is difficult to cope with the current low-measurement distribution system.

[0003] In view of the above situation, a study proposed an algorithm for state estimation of distribution system using low-rank matrix completion, which can operate under low measurement conditions with large-scale data missing. This method flexibly combines the measurement value characteristics 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 on a time scale, and in practical applications, it cannot estimate the state of the distribution network with unknown measurements at adjacent moments. Summary of the invention

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

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

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

[0007] Step S2: According to the analysis of the distribution network data characteristics, based on the constructed standard matrix completion model, linear constraints are added to construct a complete distribution network measurement data completion model;

[0008] Step S3, using an alternating minimization method to solve the complete distribution network measurement data completion model, and obtain a distribution network measurement data matrix after completion at a single moment;

[0009] Step S4: using the distribution network measurement data matrix completed at a single moment in combination with a sliding average method to perform state estimation on the next moment of the unknown distribution system state.

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

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

[0012]

[0013] Where X is the completed matrix; (i0, j0) means that the position of a data point in the matrix is ​​the i0th row and j0th column; m means the number of rows of M; n means the number of columns of M; Indicates M Ω The data in row i0 and column j0; Represents the data in row i0 and column j0 in M;

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

[0015]

[0016] Among them, ||X|| * represents the sum of the singular values ​​in X, that is, the nuclear norm in 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] Among them, ||·|| * is the Frobenius norm of the matrix, 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 a multi-phase distribution system;

[0021] The specific operations of constructing a matrix model based on a multi-phase power distribution system are as follows:

[0022] A matrix model based on a multi-phase distribution system is constructed based on the branch index. In the process of constructing a matrix model based on a multi-phase distribution system, M is constructed such that each row represents a power system branch, and each column represents a quantity measurement related to the branch. For each branch The corresponding line in contains:

[0023]

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

[0025] The specific operations of constructing a matrix model based on a multi-phase power distribution system are as follows:

[0026] A matrix model based on a multi-phase distribution system is constructed based on node indexes. In the process of constructing a matrix model based on a multi-phase distribution system based on node indexes, M is constructed such that each row represents a node, and each column represents a quantity measurement related to the node. For each node The corresponding line in contains:

[0027]

[0028] in, 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; Indicates the active power injected by the node; Indicates the reactive power injected by the node;

[0029] make Represents a set of nodes, where node 1 is a balanced node and the rest All nodes are PQ nodes. and are the voltage and injected power phasors at each node, the balanced node voltage and injected power phasors are denoted as v1 and s1, respectively, and the unbalanced node voltage and injected power phasors are denoted as v -1 and -1 ;i ft Indicates branch The current in Represents a collection of lines; through the node admittance matrix Use mathematical form to express the electrical characteristics between different nodes:

[0030]

[0031] Among them, 11 represents the self-admittance of node 1; LL represents the self-admittance of node L; 1L represents the mutual admittance between node 1 and node L; 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] The repetition constraints are as follows:

[0034]

[0035] Where Λ is the set of all repeated measurement pairs in M; represents the measurement value at row i1 and column j1 in X; represents the measurement value at row i1' and column j1' in X;

[0036] The noise adaptivity Ohm's law constraints are as follows:

[0037]

[0038] Among them, ξ r,ft ,ξ c,ft They are Error tolerance 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 constraints are as follows:

[0040] The following approximations are used for the unbalanced node voltages and injected powers:

[0041]

[0042] in, Inject the real part of the power phasor into the unbalanced node; The imaginary part of the power phasor is injected 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|;

[0043] make is the phasor of the unbalanced node no-load voltage, and is defined as In estimating the unbalanced node voltage When:

[0044]

[0045] Among them, j is a complex number indicating the general form;

[0046] The exact power flow equation is used to relate the voltage to the injected power at the balancing node:

[0047]

[0048] Since v1 is known, formula (13) is linearly related to voltage;

[0049] Then, Formula (9), Formula (10), and Formula (13) are modified into Formula (14), Formula (15), and Formula (16) respectively:

[0050]

[0051] Among them, τ r , τ c ,γ,α r , α c are all error tolerances;

[0052] In formula (9)-formula (10), let make w (T) 、h (T) , B (T) , C (T) represents the s corresponding to time T -1 、v -1 ,w,h,B,C;

[0053] Use formula (17) to express formula (14) and formula (15):

[0054] y≈Ax+b(17);

[0055] in, x=[h (T) ];

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

[0057]

[0058] in, Make μ>0, ν>0 are penalty parameters; is a constant;

[0059] z1,…,z 2T 、c1,…,c 2T The value of is known 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 to obtain the system measurement data matrix after completion at a single moment. The specific operation is as follows:

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

[0063]

[0064] Using formula (20), the matrix completion model (18) is reformulated as follows:

[0065]

[0066] Make

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

[0068]

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

[0070] Solve the matrix X after completion at time T = U N V N .

[0071] Preferably, in step S4, the state of the unknown distribution system state at the next moment is estimated using the completed distribution network measurement data matrix combined with the sliding average method, and the specific operations are:

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

[0073]

[0074] Among them, X q is the data matrix of the qth time section in the original data sequence; X T+1 is the data matrix of the unknown state at time T+1 after calculation.

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

[0076] The standard matrix completion module is used to construct a standard matrix completion model based on the problem of missing measurement data in the distribution network;

[0077] The distribution network measurement data feature adaptive constraint module is used to analyze the distribution network data features, add linear constraints based on the constructed standard matrix completion model, and build a complete distribution network measurement data completion model;

[0078] The distribution network measurement data completion module at a single moment based on alternating minimization is used to solve the complete distribution network measurement data completion model using the alternating minimization method to obtain the distribution network measurement data matrix after completion at a single moment;

[0079] The distribution network measurement data completion module based on the sliding average time series is used to use the distribution network measurement data matrix completed at a single moment combined with the sliding average method to estimate the state of the unknown distribution system at the next moment.

[0080] A computer device comprises: a memory and a processor; the memory stores a computer program, and the processor implements the steps of the above-mentioned distribution network measurement data completion method when executing the computer program.

[0081] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the above-mentioned distribution network measurement data completion method.

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

[0083] (1) In the present invention, the alternating minimization matrix completion algorithm is combined with the sliding average algorithm to realize the state estimation of the next moment of the unknown distribution system state, which makes up for the limitation of the difficulty in analyzing 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 repetition constraints, noise adaptive Ohm's law constraints and linear power flow constraints, it can better adapt to new distribution systems with a high proportion of missing measurement data, and still have good completion results under heavy load conditions, with high credibility;

[0085] (3) The process of the present invention is simpler than that of artificial intelligence algorithms, does not require the division of training sets and test sets, and has high accuracy and credibility, which proves its effectiveness and broad prospects for data analysis of actual power distribution systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 A flow chart of a method for completing distribution network measurement data according to the present invention;

[0087] Figure 2 Schematic diagram of the alternating minimization combined with sliding average matrix completion model;

[0088] Figure 3 The process is run for alternating minimization combined with a sliding average algorithm;

[0089] Figure 4 Complete the results of power flow data for IEEE-33 and IEEE-118 node systems;

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

[0091] Figure 6 This is the completion status of a heavy-load node in the IEEE-33 node system; Figure 6 (a) shows the node injected active power when 30% of the nodes are missing; Figure 6 (b) shows the node injected reactive power when the loss is 30%; Figure 6 (c) in the figure shows the node injected active power when 60% of the nodes are missing; Figure 6 (d) in the figure shows the node injected reactive power when 60% of the nodes are missing;

[0092] Figure 7 The figure is a structural schematic diagram of a distribution network measurement data completion device. DETAILED DESCRIPTION

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

[0094] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0095] Embodiment 1

[0096] like Figure 1-Figure 3 As shown, the present invention provides a method for completing distribution network measurement data, comprising the following steps:

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

[0098] Given an incomplete matrix assumed to be low rank, the goal of the matrix completion problem is to determine the unknown elements in the matrix. is a real-valued data matrix, 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 Here (i0, j0)∈Ω, and the rest are 0, then the data matrix completion problem including the missing distribution network measurement data problem is expressed as a rank minimization problem:

[0099]

[0100] Where X is the completed matrix; (i0, j0) means that the position of a data point in the matrix is ​​the i0th row and j0th column; m means the number of rows of M; n means the number of columns of M; Indicates M Ω The data in row i0 and column j0; Represents the data in row i0 and column j0 in M;

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

[0102]

[0103] Among them, ||X|| * represents the sum of the singular values ​​in X, that is, the nuclear norm in the matrix;

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

[0105] ||X Ω -M Ω || F ≤δ (3);

[0106] Among them, ||·|| * is the Frobenius norm of the matrix, the parameter δ ≥ 0, and 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, linear constraints are added to construct a complete distribution network measurement data completion model;

[0108] The standard matrix completion model is used to solve the problem of missing distribution network data. It is necessary to analyze the characteristics of distribution network data, so a matrix model based on multi-phase distribution system is constructed.

[0109] make Represents a set of nodes, where node 1 is a balanced node and the rest All nodes are PQ nodes, let Represents the set of lines, node admittance matrix for:

[0110]

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

[0112] make and The voltage and injected power phasor at each node are respectively (partially unknown), and the balanced node voltage and injected power phasor are represented as v1 and s1, respectively, and the unbalanced node voltage and injected power phasor are represented as v -1 and -1 ;i ft Indicates branch The current in; M and X vary according to the specific attributes of the data (such as the type and scale of the measurements), including the following two possible data matrix forms:

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

[0114]

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

[0116] 2) Node index: construct M so that each row represents a node and each column represents a quantity measurement related to the node. That is, for each node The corresponding line in contains:

[0117]

[0118] in, 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; Indicates the active power injected by the node; Indicates the reactive power injected by the node.

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

[0120] Linear constraints include repetitive constraints, noise adaptive Ohm's law constraints, and linear power flow constraints;

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

[0122] In the branch index, the measurements associated with a given node appear in multiple rows if the node is in multiple branches. Therefore, let Λ be the set of all pairs of repeated measurements in M ​​such that Right now

[0123]

[0124] Where Λ is the set of all repeated measurement pairs in M; represents the measurement value at row i1 and column j1 in X; represents the measurement value at row i1' and column j1' in X;

[0125] Noise adaptivity Ohm's law is as follows:

[0126]

[0127] Among them, ξ r,ft ,ξ c,ft They are Error tolerance 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;

[0128] The linear power flow constraints are as follows:

[0129] Since the exact AC power flow equation is nonlinear, the equation is Cartesian linearized. The following approximations are used for the unbalanced node voltage and injected power:

[0130]

[0131] in, Inject the real part of the power phasor into the unbalanced node; The imaginary part of the power phasor is injected 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] make is the phasor of the unbalanced node no-load voltage, and is defined as In estimating the unbalanced node voltage When:

[0133]

[0134] Among them, j is a complex number indicating the general form;

[0135] The exact power flow equation is used to relate the voltage to the injected power at the balancing node:

[0136]

[0137] Since v1 is known, formula (13) is linearly related to voltage;

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

[0139]

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

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

[0142] In order to simplify the subsequent expressions, formula (17) is used to express formula (14) and formula (15):

[0143] y≈Ax+b(17);

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

[0145] The complete distribution network measurement data completion model is as follows:

[0146]

[0147] in, Make μ>0, ν>0 are penalty parameters; is a constant;

[0148] z1,...,z 2T 、c1,...,c 2T The value of is known from the following specific forms of X, y, and x:

[0149]

[0150] Step S3: using an alternating minimization method to solve the complete distribution network measurement data completion model, and obtaining a distribution network measurement data matrix after completion at a single moment.

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

[0152] First, any matrix of rank r All expressed as and The matrix product form of X = UV, that is, its nuclear norm is expressed as the Frobenius norm of U and V as follows:

[0153]

[0154] For extremely small rank r, r<<min{m,n}, the above representation using the nuclear norm can significantly reduce the size of the problem; using formula (20) to reformulate the matrix completion model (18) as follows:

[0155]

[0156] Make

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

[0158]

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

[0160] Solve the matrix X after completion at time T = U N V N .

[0161] Step S4: Use the completed distribution network measurement data matrix combined with the sliding average method to estimate the state of the unknown distribution system at the next moment.

[0162] The specific operations are:

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

[0164]

[0165] Among them, MA p is the pth sliding average; x q is the qth data point in the original data sequence; the matrix X after completion at time T = U N V N Substituting into formula (24), the data matrix at time T+1 is:

[0166]

[0167] Among them, X q A single time section data matrix.

[0168] The selection of window size depends on the actual data situation. When the historical data changes relatively steadily over a period of time, a smaller sliding window can be selected. On the contrary, when the fluctuation is drastic, the sliding window should be appropriately increased to prevent overfitting noise from causing a decrease in the accuracy of the results.

[0169] In order 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 and reactive power, and node output active power and reactive power.

[0170]

[0171] in, Represents the estimated value of the qth data point.

[0172] The distribution system power flow data matrix after sliding average processing (taking node index as an example) is constructed as follows:

[0173]

[0174] Among them, T n Indicates the sampling time of the measuring device.

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

[0176] 1) Processing of data sets of different sizes. The test results of the alternating minimization matrix completion algorithm on the IEEE-33 node and IEEE-118 node systems are shown in the figure. Figure 4 As shown, the alternating minimization matrix completion method on two systems is compared with the classical weighted least squares (WLS) state estimation algorithm.

[0177] The power flow data sets of the two examples are randomly deleted by 10%-70% and complemented using the alternating minimization matrix completion algorithm. When the number of known measurement values ​​is greater than 70%, the MAPE of the power flow data completion result is less than 1%. At this time, the MAPE of the WLS completion result is about 1%, which shows that the result has good accuracy. When the number of known measurement values ​​is less than 70%, WLS cannot run in this state. Therefore, under the measurement data conditions where WLS can run, the estimated value of the method proposed in the present invention is similar to the estimated value of WLS in terms of error. When WLS cannot run, the method proposed in the present invention can still run with high error accuracy, and has good completion accuracy in systems that process data of different scales. Figure 5 The completion results of the voltage amplitude when the IEEE-118 bus system power flow data is missing 30%-40% are compared with the standard data.

[0178] Figure 6 The completion results of the injected active and reactive power of a heavy-load node in the IEEE-33 node system when 30% and 60% are missing are compared with the standard data of the example. It can be seen that when more than half of the data is missing, the method proposed in the present invention can still generate relatively accurate completion data, and the method is still applicable when the node is under heavy load.

[0179] 2) Time series data set processing. 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, it cannot run when there is a lot of missing data, this embodiment combines the alternating minimization matrix completion algorithm (MC) with the moving average algorithm (MA) to process the flow data completion in time series.

[0180] Table 1 Results of completing the flow data in time series

[0181]

[0182]

[0183] From the results in the above table, we can see that when the missing proportion of measured data is greater than 30%, the error of the alternating minimization algorithm is about 1%, and when the data is completely missing at the next moment, it can be combined with the classic sliding average algorithm to predict all types of flow data at that moment, and the relative accuracy is about 1.4%, with high accuracy and reliability. This calculation process does not require the known measurement data set to be divided into training sets and test sets. The algorithm execution efficiency is high, the process is simple and clear, and it is suitable for state estimation analysis scenarios in large-scale distribution system data missing conditions.

[0184] Embodiment 2

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

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

[0187] The distribution network measurement data feature adaptive constraint module is used to analyze the distribution network data features, add linear constraints based on the constructed standard matrix completion model, and build a complete distribution network measurement data completion model;

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

[0189] The distribution network measurement data completion module based on the sliding average time series is used to use the distribution network measurement data matrix completed at a single moment combined with the sliding average method to estimate the state of the unknown distribution system at the next moment.

[0190] If the above functions are implemented in the form of software functional 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, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

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

[0192] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0193] Therefore, the present invention adopts the above-mentioned distribution network measurement data completion method, system, computer equipment and medium. This method can better adapt to new distribution systems with a high proportion of missing measurement data, and still has good completion results under heavy load conditions, with high credibility.

[0194] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for completing distribution network measurement data, characterized in that: The following steps are involved: Step S1, constructing a standard matrix completion model according to the problem of missing distribution network measurement data; Step S2: According to the analysis of the distribution network data characteristics, based on the constructed standard matrix completion model, linear constraints are added to construct a complete distribution network measurement data completion model; Step S3, using an alternating minimization method to solve the complete distribution network measurement data completion model, and obtain a distribution network measurement data matrix after completion at a single moment; Step S4: using the distribution network measurement data matrix completed at a single moment in combination with a sliding average method to perform state estimation on the next moment of the unknown distribution system state.

2. A method for completing distribution network measurement data according to claim 1, characterized in that: In step S1, a standard matrix completion model is constructed according to the problem of missing distribution network measurement data. The specific operations are as follows: make is a real-valued data matrix, Ω is the set of known elements in M, represents the data matrix containing the missing measurement data of the distribution network, where Here (i0, j0)∈Ω, and the rest are 0, then the data matrix completion problem including the missing distribution network measurement data is expressed as: Where X is the completed matrix; (i0, j0) means that the position of a data point in the matrix is ​​the i0th row and j0th column; m means the number of rows of M; n means the number of columns of M; Indicates M Ω The data in row i0 and column j0; Represents the data in row i0 and column j0 in M; The non-convex NP-hard problem in formula (1) is solved by minimizing the nuclear norm of the matrix through a heuristic algorithm: Among them, ||X|| * represents the sum of the singular values ​​in X, that is, the nuclear norm in the matrix; Modify the equality constraint in formula (2) to obtain the standard matrix completion model: ||X Ω -M Ω || F ≤δ (3); Among them, ||·|| * is the Frobenius norm of the matrix, parameter δ ≥ 0.

3. A method for completing distribution network measurement data 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 a multi-phase distribution system; The specific operations of constructing a matrix model based on a multi-phase power distribution system are as follows: A matrix model based on a multi-phase distribution system is constructed based on the branch index. In the process of constructing a matrix model based on a multi-phase distribution system, M is constructed such that each row represents a power system branch, and each column represents a quantity measurement related to the branch. For each branch The corresponding line in contains: In the formula, represents the real part, represents the imaginary part; v f | respectively represent the real part, imaginary part and absolute value of the voltage at the branch end point f; They represent the active power and reactive power injected at the branch endpoint f respectively; v t | respectively represent the real part, imaginary part and absolute value of the voltage at the branch endpoint t; They represent the active power and reactive power injected at the branch endpoint t respectively; They represent the real and imaginary parts of the current flowing through the branch (f, t); The specific operations of constructing a matrix model based on a multi-phase power distribution system are as follows: A matrix model based on a multi-phase distribution system is constructed based on node indexes. In the process of constructing a matrix model based on a multi-phase distribution system based on node indexes, M is constructed such that each row represents a node, and each column represents a quantity measurement related to the node. For each node The corresponding line in contains: in, represents the real part of the node voltage; represents the imaginary part of the node voltage; |v ε | represents the absolute value of node voltage; Indicates the active power injected by the node; Indicates the reactive power injected by the node; make Represents a set of nodes, where node 1 is a balanced node and the rest All nodes are PQ nodes. and are the voltage and injected power phasors at each node, the balanced node voltage and injected power phasors are denoted as v1 and s1, respectively, and the unbalanced node voltage and injected power phasors are denoted as v -1 and -1 ;i ft Indicates branch The current in Represents a collection of lines; through the node admittance matrix Use mathematical form to express the electrical characteristics between different nodes: Among them, 11 represents the self-admittance of node 1; LL represents the self-admittance of node L; 1L represents the mutual admittance between node 1 and node L; L1 represents the mutual admittance between node L and node 1.

4. A method for completing distribution network measurement data according to claim 3, characterized in that: In step S2, the linear constraints include repetition constraints, noise adaptive Ohm's law constraints and linear power flow constraints; The repetition constraints are as follows: Where Λ is the set of all repeated measurement pairs in M; represents the measurement value at row i1 and column j1 in X; represents the measurement value at row i1' and column j1' in X; The noise adaptivity Ohm's law constraints are as follows: Among them, ξ r,ft ,ξ c,ft They are Error tolerance 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 constraints are as follows: The following approximations are used for the unbalanced node voltages and injected powers: in, Inject the real part of the power phasor into the unbalanced node; The imaginary part of the power phasor is injected 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|; make is the phasor of the unbalanced node no-load voltage, and is defined as In estimating the unbalanced node voltage When: Among them, j is a complex number indicating the general form; The exact power flow equation is used to relate the voltage to the injected power at the balancing node: Since v1 is known, formula (13) is linearly related to voltage; Then, Formula (9), Formula (10), and Formula (13) are modified into Formula (14), Formula (15), and Formula (16) respectively: Among them, τ r , τ c ,γ,α r , α c are error tolerances; In formula (9)-formula (10), let make w (T) 、h (T) , B (T) , C (T) represents the s corresponding to time T -1 、v -1 ,w,h,B,C; Use formula (17) to express formula (14) and formula (15): y≈Ax+b(17); in, x=[h (T) ]; 5. A method for completing distribution network measurement data according to claim 4, characterized in that: In step S2, the distribution network measurement data completion model is as follows: in, Make μ>0, ν>0 are penalty parameters; is a constant; z1,...,z 2T 、c1,...,c 2T The value of is known from the following specific forms of X, y, and x:

6. A method for completing distribution network measurement data according to claim 5, characterized in that: In step S3, the alternating minimization method is used to solve the complete distribution network measurement data completion model to obtain the system measurement data matrix after completion at a single moment. The specific operation is as follows: Any matrix of rank r All expressed as and The matrix product form of X = UV, that is, its nuclear norm is expressed as the Frobenius norm of U and V as follows: Using formula (20), the matrix completion model (18) is reformulated as follows: Make The alternating minimization algorithm fixes the matrix rank r, sets the number of iterations k = 1,...,N, and alternately solves U and V: When the iteration result satisfies When , stop the iteration, the residual threshold σ∈[0,1); Solve the matrix X after completion at time T = U N V N .

7. A method for completing distribution network measurement data according to claim 6, characterized in that: In step S4, the state of the unknown distribution system at the next moment is estimated using the completed distribution network measurement data matrix combined with the sliding average method. The specific operations are: For a data sequence of length n, with a window size of l, the matrix X after completion at time T = U N V N Substitute into formula (24) to calculate the sliding average: Among them, X q is the data matrix of the qth time section in the original data sequence; X T+1 is the data matrix of the unknown state at time T+1 after calculation.

8. A distribution network measurement data completion device, characterized in that: include: The standard matrix completion module is used to construct a standard matrix completion model based on the problem of missing measurement data in the distribution network; The distribution network measurement data feature adaptive constraint module is used to analyze the distribution network data features, add linear constraints based on the constructed standard matrix completion model, and build a complete distribution network measurement data completion model; The distribution network measurement data completion module at a single moment based on alternating minimization is used to solve the complete distribution network measurement data completion model using the alternating minimization method to obtain the distribution network measurement data matrix after completion at a single moment; The distribution network measurement data completion module based on the sliding average time series is used to use the distribution network measurement data matrix completed at a single moment combined with the sliding average method to estimate the state of the unknown distribution system at the next moment.

9. A computer device comprising: A memory and a processor; the memory stores a computer program, wherein the processor implements the steps of the distribution network measurement data completion method described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for completing distribution network measurement data according to any one of claims 1 to 7 are implemented.

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