Power distribution network topology tracking method and device based on finite synchronous phasor measurement

Abstract

The invention provides a power distribution network topology tracking method based on finite synchronous phasor measurement, and the method comprises the following steps: determining a topological structure before the change of the topological structure of a power distribution network, and obtaining the voltage phasor measurement data before and after the change of the topological structure of the power distribution network; determining a linear power flow model of the power distribution network, constructing an underdetermined linear regression model based on the linear power flow model and the voltage phasor measurement data, providing a linear model matching algorithm for solving, and obtaining first matching index values of all the lines by enumerating connection state switching events of all the lines; sorting the first matching index values in an ascending order, and selecting a candidate topological line set according to a sorting result; performing nonlinear state estimation on the candidate topological line set, and determining the most matched topological structure as a final result; according to the method, the topology tracking accuracy is remarkably improved, and the performance of the method is superior to that of an algorithm based on sparse learning.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network, and in particular to a distribution network topology tracking method and device based on finite synchronous phasor measurement. Background Art

[0002] Accurate network topology is crucial for advanced applications such as state estimation (SE), power flow calculation, and safety assessment. In recent years, with the large-scale access of distributed power sources such as photovoltaics and wind power and electric vehicles, the topology of distribution networks has become more flexible and changeable to ensure safe operation and improve the level of new energy consumption. Generally speaking, the status of key circuit breakers in distribution networks is monitored by remote terminals. However, due to communication failures, remote signal jitter, and untimely reporting of on-site switch operations, the switch status information is unreliable; at the same time, due to insufficient measurement, there are a large number of unmonitored switches in the network. If state estimation is performed based on the wrong topology and then dispatch control is implemented, serious consequences may occur. Therefore, it is urgent to carry out research on operating topology tracking under limited measurement information.

[0003] Topology detection problems can be roughly divided into two categories: data-driven methods and model-based methods. Data-driven methods usually require a large number of measuring instruments to be deployed throughout the system, and are often used for offline topology identification of low-voltage distribution networks or medium-voltage distribution networks with infrequent topology changes. Existing topology tracking methods either use a predefined topology library or require a large number of μPMUs (micro-synchronized phasor measurement units). In actual distribution networks, switching operations are generally performed sequentially, so all switching events can be enumerated and SE can be run for each candidate topology. However, solving the nonlinear SE of all candidate topologies is very time-consuming. To this end, this paper proposes a two-stage model matching method for distribution network topology tracking based on finite synchronized phasor measurements. In the first stage, an underdetermined linear regression model is derived based on a linear power flow model and finite voltage phasor measurements, and a linear model matching algorithm is proposed for solving it. By enumerating all line connectivity state switching events and sorting matching indicators, multiple lines whose connectivity states may change are identified; in the second stage, nonlinear state estimation is performed on all candidate topologies, and the best matching topology is selected as the final result. Summary of the invention

[0004] The distribution network topology tracking method based on finite synchronous phasor measurement includes the following steps:

[0005] Determine the topology of the distribution network before the topology changes, and obtain voltage phasor measurement data before and after the topology changes;

[0006] Determine the linear power flow model of the distribution network, and build an underdetermined linear regression model based on the linear power flow model and voltage phasor measurement data, and propose a linear model matching algorithm to solve it. By enumerating all line connectivity state switching events, the first matching index values ​​of all lines are obtained, the first matching index values ​​are sorted in ascending order, and a candidate topology line set is selected according to the sorting results;

[0007] Nonlinear state estimation is performed on the candidate topology line set to determine the best matching topology as the final result.

[0008] Furthermore, the method of performing nonlinear state estimation on the candidate topology line set and determining the most matching topology structure as the final result is as follows:

[0009] The weighted least square method is used to perform state estimation on each candidate topology to obtain the second matching index values ​​of all candidate topologies, and the candidate topology with the lowest second matching index value is determined as the final result.

[0010] Furthermore, when constructing an underdetermined linear regression model based on the linear power flow model and voltage phasor measurement data, it is assumed that there will be no power outage after the distribution network topology changes, so the node load fluctuation can be approximately regarded as Gaussian distribution noise with a mean of zero and a small variance. Under this assumption, the injected power of the node after the topology change is obtained according to the linear power flow model and voltage phasor measurement data, thereby obtaining an underdetermined linear regression model:

[0011]

[0012] Among them, Δε represents Δε after removing the rows and columns of the balancing nodes, Δε=ε′-ε, ε is the deviation vector between the voltage amplitude and the reference value, ε′ is the voltage amplitude deviation vector after the topology change; Δθ represents Δθ after removing the rows and columns of the balancing nodes, Δθ=θ′-θ, θ represents the node phase angle vector, and θ′ represents the phase angle vector after the topology change; are the node conductance matrix and negative node susceptance matrix respectively, H g H after removing the rows and columns of the balance nodes g , H β H after removing the rows and columns of the balance nodes β ; is the node-branch association matrix, consisting of n l n b Dimensional column vector m l Composition, of which M is the M after removing the rows and columns of the balance nodes; is a diagonal matrix, and its l-th diagonal element is the conductance g of branch l. l and susceptance βl ; is the branch state change vector before and after the topology structure changes, where d l Indicates the change state of the lth branch. If the branch is open, it is 1, if it is closed, it is -1, otherwise it is 0; ε′ represents ε′ after removing the rows and columns of balanced nodes; θ′ represents θ′ after removing the rows and columns of balanced nodes; denote the disturbance vectors of active and reactive injected power respectively, η p is η after removing the rows and columns of the balance nodes p , η q is η after removing the rows and columns of the balance nodes q ;

[0013] Extract the configuration voltage phasor measurement n from formula (15): o The rows corresponding to the nodes are:

[0014]

[0015] Where: subscript o represents the row corresponding to the observable node.

[0016] Furthermore, by performing compact singular value decomposition on the underdetermined linear regression model, whitening preprocessing of the relevant noise variables is achieved, and the processed underdetermined linear regression model is obtained:

[0017]

[0018] After whitening the noise, the noise vector The mean of becomes zero, and the covariance matrix becomes U o 、V o is an orthogonal matrix, Σ o is a sparse diagonal matrix containing all nonzero singular values.

[0019] Furthermore, by enumerating all line connectivity state switching events, the method for obtaining the first matching index values ​​of all lines is:

[0020] By enumerating all possible d and solving s1 and s2 for each specific vector d according to formula (18), the first matching index value, i.e., the least squares (LS) target value, is obtained;

[0021] For the topology tracking problem, when a vector d is given, there is only one non-zero element d l , so formula (18) can be rewritten as:

[0022]

[0023] Then formula (23) is simplified to a linear regression model containing only two variables:

[0024]

[0025] For a specific vector d, the first matching index value is calculated as follows:

[0026]

[0027] Among them, the least squares solution Solve by the following formula:

[0028]

[0029] Furthermore, nonlinear state estimation is performed on the candidate topology line set to determine the best matching topology as the final result:

[0030] For a network topology T with m measurements, its measurement model is:

[0031] z=h(x)+e (21)

[0032] Where: is the state variable vector, which contains the voltage magnitudes and phase angles of all nodes except the reference node phase angle; The measured variable vector includes active and reactive power injection measurements (power injection before topology change is used as pseudo measurement) and voltage phasor measurements; is the measurement error vector; h(·) is the nonlinear measurement function vector under a given candidate topology;

[0033] The second matching index value of the candidate topology is defined as the state estimation objective function value, that is:

[0034]

[0035] Where: The norm is defined as is the error covariance matrix;

[0036] Let the first-order derivative of the objective function be 0, and use Taylor expansion to linearize it at the initial point x0, and we get:

[0037] -2H T (x)R -1 [zh(x)]=0 (23)

[0038] -H T (x0)R -1 [zh(x0)-H(x0)·Δx]=0 (24)

[0039] Starting from the initial point x0, the Newton-Gaussian method is used to solve the nonlinear state estimation, and the equation for each iteration is:

[0040] Δx (k) =[H T (x (k) )R -1 H(x (k) )] -1 H T (x (k) )R -1 [zh(x (k) )] (25)

[0041] Calculate the second matching index values ​​of all candidate topologies, and determine the candidate topology with the lowest second matching index value as the final result:

[0042]

[0043] Furthermore, when the first matching index values ​​are sorted in ascending order and the candidate topology line set is selected according to the sorting result, the first k candidate topology line sets in ascending order need to be selected according to the measurement error level and the number of synchronous phasor measurement devices through offline simulation test.

[0044] A distribution network topology tracking device based on finite synchronous phasor measurement includes:

[0045] A data acquisition module is used to determine the topology of the distribution network before the topology structure changes, and to obtain voltage phasor measurement data before and after the topology structure of the distribution network changes;

[0046] The candidate topology line set determination module is used to determine the linear power flow model of the distribution network, and to construct an underdetermined linear regression model based on the linear power flow model and voltage phasor measurement data, and to propose a linear model matching algorithm for solving it. By enumerating all line connectivity state switching events, the first matching index values ​​of all lines are obtained, the first matching index values ​​are sorted in ascending order, and the candidate topology line set is selected according to the sorting result;

[0047] The best matching topology structure determination module is used to perform nonlinear state estimation on the candidate topology line set and determine the best matching topology structure as the final result.

[0048] A computing device comprising:

[0049] one or more processing units;

[0050] A storage unit for storing one or more programs,

[0051] Wherein, when the one or more programs are executed by the one or more processing units, the one or more processing units execute the distribution network topology tracking method based on finite synchronous phasor measurement as described above.

[0052] A computer-readable storage medium having a non-volatile program code executable by a processor, wherein when the computer program is executed by the processor, the steps of the distribution network topology tracking method based on limited synchronized phasor measurement as described above are implemented.

[0053] The advantages and positive effects of the present invention are:

[0054] (1) The two-stage topology tracking method for distribution network of the present invention, in the first stage, uses the linearized power flow model and limited voltage phasor measurement to derive an underdetermined linear regression model to identify the lines whose connectivity may change and uses the linear model matching algorithm to solve it. In the second stage, nonlinear SE is performed on the first k candidate topologies, and the best matching topology is selected as the final result. The accuracy of topology tracking is significantly improved, the search space of SE matching in the second stage is greatly reduced, and the performance is better than the algorithm based on sparse learning.

[0055] (2) The method of the present invention can still obtain a high accuracy rate by using limited phasor measurement when all lines are equipped with switches, and the performance is further improved when the number of switches is reduced;

[0056] (3) The two-stage topology tracking method proposed in the present invention runs very fast. Since the variable dimension of each matching index calculation is only two, the CPU time increases approximately linearly with the system scale; therefore, the proposed method is very suitable for online use. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments, but it should be understood that these drawings are designed only for explanation purposes and are not intended to limit the scope of the present invention. In addition, unless otherwise specified, these drawings are intended only to conceptually illustrate the structural configurations described herein and are not necessarily drawn to scale.

[0058] Figure 1 A schematic flow chart of a distribution network topology tracking method based on finite synchronous phasor measurement provided in an embodiment of the present invention;

[0059] Figure 2 A 33-node distribution network provided in Embodiment 2 of the present invention;

[0060] Figure 3 The topology tracking success rate of the 33-node system provided in Example 2 of the present invention (Scheme 1);

[0061] Figure 4 The topology tracking success rate of the 33-node system provided in Example 2 of the present invention (Solution 2);

[0062] Figure 5 The topology tracking success rate under different measurement noise levels of the 33-node system provided in Example 2 of the present invention (Scheme 1);

[0063] Figure 6 The topology tracking success rate under different measurement noise levels of the 33-node system provided in Example 2 of the present invention (Scheme 2);

[0064] Figure 7 A 69-node distribution network provided in Embodiment 2 of the present invention;

[0065] Figure 8 The topology tracking success rate of the 69-node system provided in Example 2 of the present invention (Solution 1);

[0066] Fig. 9 The topology tracking success rate of the 69-node system provided in Example 2 of the present invention (Solution 2). DETAILED DESCRIPTION

[0067] In order to make the purpose, technical scheme and advantages of the implementation of the present invention clearer, the technical scheme in the embodiment of the present invention will be described in more detail below in conjunction with the drawings in the embodiment of the present invention. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of the present invention, not all of the embodiments. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limitations on the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0068] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0069] Example 1

[0070] The distribution network topology tracking method based on finite synchronous phasor measurement includes the following steps:

[0071] Determine the topology of the distribution network before the topology changes, and obtain voltage phasor measurement data before and after the topology changes;

[0072] Determine the linear power flow model of the distribution network, and build an underdetermined linear regression model based on the linear power flow model and voltage phasor measurement data, and propose a linear model matching algorithm to solve it. By enumerating all line connectivity state switching events, the first matching index values ​​of all lines are obtained, the first matching index values ​​are sorted in ascending order, and a candidate topology line set is selected according to the sorting results;

[0073] Nonlinear state estimation is performed on the candidate topology line set to determine the best matching topology as the final result.

[0074] Specifically, the method for determining the linear power flow model of the distribution network is:

[0075] For a b nodes and n l For a distribution network with branches, the node voltage is close to 1.0pu, and the phase angle difference of each branch is close to 0; at this time, the active and reactive power injection equations of the nodes are as follows:

[0076]

[0077] Where: P i , Q i are the active and reactive injected power of node i respectively; V i ,θ i are the voltage amplitude and phase angle of node i, ε i =V i -1 is the deviation between the voltage amplitude and the reference value; g ij , b ij are the conductance and susceptance of branch ij, β ij =-b ij ;Ω b ,Ω l They are node sets and branch sets respectively;

[0078] Rewrite the linear power flow model (1) into matrix-vector form:

[0079] p≈H g ε+H β θ

[0080] q≈H β ε-H g θ(28)

[0081] Where: are the active and reactive power injection vectors of the nodes respectively; are the node conductance matrix and the negative node susceptance matrix respectively; where H g , H β is the weighted Laplace matrix of the network, which can be expressed as the sum of the weighted outer products of the columns of the node-branch association matrix:

[0082]

[0083] in: is the node-branch association matrix, consisting of n l n b Dimensional column vector m l composition;

[0084] is a diagonal matrix, and its l-th diagonal element is the conductance g of branch l. l and susceptance β l .

[0085] When constructing an underdetermined linear regression model based on the linear power flow model and voltage phasor measurement data, it is assumed that there will be no power outage after the distribution network topology changes. Therefore, the node load fluctuation can be approximately regarded as Gaussian distribution noise with zero mean and small variance. Under this assumption, the injected power of the node before and after the topology change can be expressed as:

[0086] p′=p+η p , q′=q+η q (30)

[0087] Where: represent the active and reactive injection power vectors after the topology change, respectively;

[0088] denote the disturbance vectors of active and reactive injected power respectively.

[0089] Substituting formula (2) into formula (4), we can get:

[0090] H g ′ε′+H′ β θ′=H g V+H β θ+η p

[0091] H′ β ε′-H g 'θ'=H β VH g θ+η q (31)

[0092] Where: They represent the voltage amplitude deviation vector and phase angle vector after the topology change respectively; H g ′、H′ β They represent the node conductance matrix and negative node susceptance matrix after the topology change respectively; θ is the voltage phase angle vector, ε is the deviation vector between the voltage amplitude and the reference value, and V is the voltage amplitude vector.

[0093] ΔH g , ΔH β Defined as H g ′、H′ β and H g , H β The difference is calculated and formula (5) is rewritten as:

[0094] (H g -ΔH g )ε′+(H β -ΔH β )θ′=H g ε+H β θ+η p

[0095] (H β -ΔH β )ε′-(H g -ΔH g )θ′=H β ε-H g θ+η q (32)

[0096] in:

[0097]

[0098] Where: is the branch state change vector before and after the topology change, where d l Indicates the change state of the lth branch. If the branch is open, it is 1, if it is closed, it is -1, and if the branch state does not change, it is 0; It is the set of branches whose states change before and after the topology transformation;

[0099] Define Δε=ε′-ε, Δθ=θ′-θ, and formula (6) becomes:

[0100] H g Δε+H β Δθ=MD g diag{d}M T ε′+MD β diag{d}M T θ′+η p

[0101] H β Δε-H g Δθ=MD β diag{d}M T ε′-MD g diag{d}M T θ′+η q (34)

[0102] Further rewrite equation (8) into matrix vector form:

[0103]

[0104] Since the rank of the coefficient matrix on the left side of equation (9) is 2(n b -1), so the inverse operation cannot be performed. g , H β , the rows and columns corresponding to the balanced nodes and unbalanced nodes in M ​​are separated, so that formula (9) can be rewritten as:

[0105]

[0106] Where: The underlined matrix / vector represents the matrix / vector after removing the rows and columns of the balanced nodes.

[0107] After removing the equations related to the equilibrium node, equation (8) can be rewritten as:

[0108] H g Δε+H β Δθ=MD g diag{d}M T ε′+MD β diag{d}M T θ′+η p

[0109] H β Δ ε - H g Δ θ = M D β diag{d} M T ε ′- M D g diag{d} M T θ ′+ η q (37)

[0110] Further rewrite equation (11) into matrix vector form:

[0111]

[0112] At this point, the coefficient matrix on the left becomes a reversible matrix; define Then formula (12) is simplified to:

[0113]

[0114] Since H is a reversible matrix, it seems intuitive that a linear regression model can be established based on the limited voltage phasor measurement to solve the sparse vector d. However, ε′ and θ′ in Eq. (13) are the voltage vectors of all nodes after the topology change except the balanced node, so the definition is Formula (13) becomes:

[0115]

[0116] Where: s contains the voltage amplitude difference and phase angle difference at both ends of all branches after the topology change.

[0117] Multiply both sides of the equation by H -1 , we obtain the observation model that relates the unknown vectors s1, s2 and d to the measured changes in the voltage phasor:

[0118]

[0119] Wherein, Δε represents Δε after removing the rows and columns of the balancing nodes, Δε=ε′-ε, ε is the deviation vector between the voltage amplitude and the reference value, ε′ is the voltage amplitude deviation vector after the topology change; Δθ represents Δθ after removing the rows and columns of the balancing nodes, Δθ=θ′-θ, θ represents the node voltage phase angle vector, θ′ represents the phase angle vector after the topology change; are the node conductance matrix and negative node susceptance matrix respectively, H g H after removing the rows and columns of the balance nodes g , H β H after removing the rows and columns of the balance nodes β ; is the node-branch association matrix, consisting of n l n b Dimensional column vector m l Composition, of which M is the M after removing the rows and columns of the balance nodes; is a diagonal matrix, and its l-th diagonal element is the conductance g of branch l. l and susceptance β l ; is the branch state change vector before and after the topology structure changes, where d l Indicates the change state of the lth branch. If the branch is open, it is 1, if it is closed, it is -1, otherwise it is 0; ε′ represents ε′ after removing the rows and columns of balanced nodes; θ′ represents θ′ after removing the rows and columns of balanced nodes; denote the disturbance vectors of active and reactive injected power respectively, η p is η after removing the rows and columns of the balance nodes p , η q is η after removing the rows and columns of the balance nodes q ;

[0120] Extract the configuration voltage phasor measurement n o The rows corresponding to the nodes are:

[0121]

[0122] Where: subscript o represents the row corresponding to the observable node.

[0123] In actual distribution networks, the number of branches whose connectivity status changes before and after the topology change is small, that is, d is very sparse, [(diag{d}s1) T (diag{d}s2) T ] T is also very sparse. Therefore, based on the linear regression model shown in formula (16), the topology tracking problem can be transformed into a sparse vector recovery problem, namely the Least Absolute Shrinkage And Selection Operator (Lasso) problem, and solved using the existing sparse learning algorithm. Since the dense matrix [H -1 ] o The multiplication of will introduce correlation between noise vectors, so directly solving the linear observation model will introduce errors. -1 ] o The compact singular value decomposition (SVD) is performed to achieve the whitening preprocessing of the related noise variables, that is, Among them U o 、V o is an orthogonal matrix, Σ o is a sparse diagonal matrix containing all non-zero singular values; by [H -1 ] o After SVD, equation (16) can be rewritten as:

[0124]

[0125] Multiply both sides of equation (17) by and Get the transformed linear observation model:

[0126]

[0127] After whitening the noise, the noise vector The mean of becomes zero, and the covariance matrix becomes

[0128] Considering that for any branch l, the corresponding s in s l and It should be 0 or non-0 at the same time, so the following Group Lasso model can be established:

[0129]

[0130] Where: yes The submatrix of the columns associated with branch l in ; Force each branch's s l and At the same time, it is exactly 0, and the sparsity of the solution can be changed by adjusting the parameter λ.

[0131] By enumerating all line connectivity state switching events, the method for obtaining the first matching index values ​​of all lines is as follows:

[0132] If only the connectivity of the lth branch changes each time the topology changes, then there is only one non-zero element in the vector d at a time, that is, when the lth branch is disconnected, d l =1, when the lth branch is closed d l =-1; The exhaustive search method enumerates all possible d and solves s1 and s2 for each specific vector d according to formula (18) to obtain the matching index value, that is, the least squares (LS) target value. Specifically, for a specific vector d, the matching index value is calculated by the following formula:

[0133]

[0134] Among them, the solution of LS Solve by the following formula:

[0135]

[0136] Sort all first matching index values ​​in ascending order, and the vector d with the smallest first matching index value is the final solution:

[0137]

[0138] For the topology tracking problem, when a vector d is given, there is only one non-zero element d l , so formula (18) can be rewritten as:

[0139]

[0140] Then formula (23) is simplified to a linear regression model containing only two variables:

[0141]

[0142] For a specific vector d, the first matching index value is calculated as follows:

[0143]

[0144] Among them, the solution of LS Solve by the following formula:

[0145]

[0146] The d with the smallest first matching index value is determined as the final solution. And from formula (26), since there are only two unknown variables in the linear LS model, the algorithm based on linear model matching is very fast.

[0147] It should be noted that when the first matching index values ​​are sorted in ascending order and the candidate topology line sets are selected according to the sorting results, the first k candidate topology line sets in ascending order need to be selected. According to experience, each system is different, and k can be determined by offline simulation testing based on the measurement error level and the number of PMUs.

[0148] The method of performing nonlinear state estimation on the candidate topology line set and determining the most matching topology structure as the final result is: using the weighted least square method to perform state estimation on each candidate topology to obtain the second matching index value of all candidate topologies, and determining the candidate topology with the lowest second matching index value as the final result; specifically, as shown below:

[0149] Linear approximation errors and insufficient measurement information will lead to low topology tracking accuracy. Therefore, nonlinear SE is performed on the first k candidate topologies, and the best matching topology is selected as the final result. The weighted least squares (WLS) method is used to perform SE on each candidate topology to obtain the corresponding matching index value. The SE principle based on WLS is briefly described as follows:

[0150] For a network topology T with m measurements, its measurement model is:

[0151] z=h(x)+e (53)

[0152] Where: is the state variable vector, which contains the voltage magnitude and phase angle of all nodes except the reference node phase angle; The measured variable vector includes active and reactive power injection measurements (power injection before topology change is used as pseudo measurement) and voltage phasor measurements; is the measurement error vector; h(·) is the nonlinear measurement function vector under a given candidate topology;

[0153] The second matching index value of the candidate topology is defined as the state estimation objective function value, that is:

[0154]

[0155] Where: The norm is defined as is the error covariance matrix;

[0156] Let the first-order derivative of the objective function be 0, and use Taylor expansion to linearize it at the initial point x0, and we get:

[0157] -2H T (x)R -1 [zh(x)]=0 (55)

[0158] -H T (x0)R -1 [zh(x0)-H(x0)·Δx]=0 (56)

[0159] Starting from the initial point x0, the Newton-Gaussian method is used to solve the nonlinear state estimation, and the equation for each iteration is:

[0160] Δx (k) =[H T (x (k) )R -1 H(x (k) )] -1 H T (x (k) )R -1 [zh(x (k) )] (57)

[0161] Calculate the second matching index values ​​of all candidate topologies, and determine the candidate topology with the lowest second matching index value as the final result:

[0162]

[0163] Example 2

[0164] In order to verify the effectiveness of the topology tracking method proposed in this application, 33-node and 69-node distribution systems are used for testing respectively; the block sparse Bayesian learning (BSBL) algorithm, which is widely used in sparse recovery problems such as distribution network fault location, is used to solve equation (21) for comparison;

[0165] First, preprocess the data:

[0166] The true values ​​of all measured values ​​are simulated by using MATPOWER to calculate the power flow. For voltage amplitude measurement, the relative measurement error is superimposed on the true value according to the following formula:

[0167] V i =V i,true [1+randn(0,1 2 ) V / 3] (59)

[0168] Where: V i 、V i,true is the measured value and true value of the voltage amplitude of the i-th node; randn(0,1 2 ) is the standard Gaussian distribution; e V is the relative measurement error percentage of all voltage amplitude measurements;

[0169] For voltage phase angle measurement, the absolute measurement error is superimposed on its true value according to the following formula:

[0170] θ i =θ i,true +randn(0,1 2 ) θ (60)

[0171] Where: θ i ,θ i,true is the measured value and true value of the voltage phase angle of the ith node; e θ is the standard deviation of the measurement error of all voltage phase angles;

[0172] By adding relative measurement errors to the load, the changes in network load can be simulated:

[0173]

[0174] Where: are the active power injection of node i before and after the topology change, respectively; are the reactive power injection of node i before and after the topology change; e η is the relative measurement error percentage of network load change;

[0175] When testing a 33-node power distribution system, the proposed topology tracking method is verified and evaluated by setting two switch deployment schemes:

[0176] Solution 1: Assume that all 37 lines are equipped with switches (including tie lines), but the bridge lines (in an undirected connected graph, if removing an edge will disconnect the graph, then the edge is a bridge line) need to be excluded. Therefore, in addition to bridge lines 1-2, the remaining 36 lines are tested;

[0177] Solution 2: Assume that 20 lines are equipped with switches (including tie lines). The specific switch locations are as follows: Figure 2 shown.

[0178] According to Kirchhoff's matrix tree theorem, in Scheme 1, there are 50,751 possible spanning trees for a 33-node system. By randomly selecting relevant spanning trees from the 50,751 spanning trees, each switch performs 20 closing and opening operations to generate different network topologies before and after the topology change. Schemes 1 and 2 simulate 1,440 and 800 network topology changes, respectively.

[0179] First, test the number of PMUs with different synchronized phasor measurement devices:

[0180] The proposed topology tracking method is tested with different numbers of μPMUs (micro-synchronized phasor measurement units). The configuration of μPMUs is obtained by the built-in genetic algorithm (GA) in MATLAB. Each μPMU only measures the voltage phasor of the node where it is installed. The number of tests that successfully identify topology changes in 1440 tests is used as the fitness function. V ,e θ ,e η They are set to 0.016%, 0.0033%, and 5% respectively. The optimal μPMU configurations obtained under different μPMU number and NPMU constraints are shown in Table 1.

[0181] Table 1 PMU configuration of 33-bus system

[0182] NPMU Optimal PMU Configuration 1 12 2 7，9 3 7,9,22 4 6,9,21,23 5 6,9,21,25,32 6 6,9,11,18,21,25 7 7,9,13,18,21,24,31 8 5,9,11,17,21,23,27,33

[0183] Figure 3 The topology tracking success rate curve of scheme 1 under different NPMUs; it can be seen from the figure that the success rate of topology tracking increases with the increase of the number of μPMUs. However, if the network topology with the smallest first matching index MI is selected as the final result in each test, that is, the first row is selected from the ascending MI vector, then even if 8 μPMUs are configured, the success rate is only 70%, which is due to the linear approximation error of the linearized power flow model and insufficient measurement information. If the selection criteria are relaxed and the top-5 of the MI vector is selected in each test, then when only 5 μPMUs are configured, the success rate can reach 100%, that is, the real switching line always falls in the top-5 of the ascending sorting vector MI, thereby reducing the search space of the second stage from 36 to 5, greatly reducing the calculation amount of SE matching, and thus proving the effectiveness of the proposed method. In addition, the use of SVD and noise whitening can further improve the accuracy of topology tracking. And it can be seen from the figure that when all non-bridged lines can be switched, the BSBL algorithm is less effective.

[0184] The accuracy of the proposed method is tested under Scheme 2. The topology tracking success rate curves under different NPMUs are shown in Figure 2. Figure 4 As shown. Figure 3 By comparison, it can be seen that the success rate curve improves, indicating that the proposed method performs better when the number of switches is small. For example, when configuring switches for 20 lines, the top-5 of MI are selected in each test, then the success rate can reach 100% when only 4 μPMUs are configured. Similarly, the use of SVD and noise whitening further improves the accuracy of topology tracking. It can be seen from the figure that the BSBL algorithm is only equivalent to the proposed method when the top-1 of MI is selected. Moreover, selecting the top-k from the BSBL algorithm results does not help to improve the success rate. This is because this type of algorithm will make most of the elements of the solution vector zero, thus invalidating the sorting.

[0185] Secondly, different noise levels were tested:

[0186] In order to verify the robustness of the proposed method to measurement noise, 10 measurement noise levels are set for voltage phasor measurement as shown in Table 2. At the same time, 5 load change levels ranging from 10% to 50% are set for testing.

[0187] Table 2 Voltage phasor measurement noise level

[0188] plan <![CDATA[e V / and θ ]]> plan <![CDATA[e V / and θ ]]> 1 0.01％ / 0.001° 6 0.06％ / 0.006° 2 0.02％ / 0.002° 7 0.07％ / 0.007° 3 0.03％ / 0.003° 8 0.08％ / 0.008° 4 0.04％ / 0.004° 9 0.09％ / 0.009° 5 0.05％ / 0.005° 10 0.010％ / 0.0010°

[0189] For scheme 1, the topology tracking success rate curve of the 33-node distribution network under different measurement noise levels is shown in the figure below: Figure 5 It can be seen that the success rate decreases slowly as the measurement noise and load change levels increase before and after the topology change.

[0190] Under Scheme 2, the topology tracking success rate curve of the 33-node distribution network under different measurement noise levels is shown in the figure below: Figure 6 As shown in the figure, as the measurement noise and load fluctuation levels increase, the success rate also has a similar downward trend. However, when the maximum measurement noise is 0.10%, 0.010° ​​and the load change is 50%, the success rate remains at around 95%, which shows that the two-stage topology tracking method proposed in this application has high robustness to both measurement noise and load fluctuation.

[0191] In the second stage, as long as the line whose actual state has changed is included in the top k lines screened out in the first stage (based on experience, each system is different and can be determined based on the measurement error level and the number of PMUs through offline simulation tests), the SE matching method based on precise μPMU voltage phasor measurement and power injection pseudo-measurement before the topology change can accurately identify the line.

[0192] When the 69 nodes (such as Figure 7 When testing the power distribution system (as shown in Figure 1), the switch deployment scheme is designed as follows:

[0193] Solution 1: Assume that except for 16 bridged lines such as 8-51 and 51-52, the remaining 57 lines are all configured with switches;

[0194] Solution 2: Assume that 21 lines are equipped with switches (including tie lines). The specific switch locations are as follows: Figure 7 As shown;

[0195] According to Kirchhoff's matrix tree theorem, there are a total of 407,924 possible spanning trees for a 69-node system. By randomly selecting relevant spanning trees from the 407,924 spanning trees, each switch performs 20 closing and opening operations to generate different network topologies before and after the operation. Schemes 1 and 2 simulated 2,280 and 840 network topology changes, respectively. V ,e θ ,e η They are set to 0.016%, 0.0033%, and 5% respectively. The best μPMU configurations under different μPMU number and NPMU constraints are shown in Table 3.

[0196] Table 3 PMU configuration of 69-node system

[0197]

[0198] Figure 8 The topology tracking success rate curves of different NPMUs are shown in the scheme; similar to the test results of the 33-node system, the success rate of topology tracking is also increasing with the increase of the number of μPMUs. If the top-2 of MI is selected in each test, the success rate is less than 80% even if 10 μPMUs are configured. However, if the top-10 of MI is selected in each test, the success rate can reach 100% when only 5 μPMUs are configured, which significantly reduces the search space of the second-stage SE matching and proves the effectiveness of the proposed method. Unlike the 33-node system, in this system, the use of SVD does not have a significant impact on the topology tracking performance; similarly, the BSBL algorithm performs poorly when all non-bridged lines can be switched.

[0199] The proposed method is tested under Scheme 2. The topology tracking success rate curves under different NPMUs are shown in the figure below. Fig. 9 As shown. Figure 8Compared with the proposed method, the success rate of topology tracking has been improved. For example, when configuring switches for 21 lines, the top-5 of MI is selected in each test, and the success rate can reach 100% when only 4 μPMUs are configured. Similarly, the BSBL algorithm is only equivalent to the proposed method when the top-1 of MI is selected, and it cannot significantly improve the success rate when more lines are selected, which verifies the superiority of the proposed method.

[0200] Finally, perform the CPU runtime test:

[0201] Table 4 shows the average CPU time required for each test. It can be seen from the table that the method proposed in this application runs very fast, and the CPU running time increases approximately linearly with the increase in system scale. This is because each matching index calculation only needs to solve a linear least squares problem with two variables. Therefore, the two-stage topology tracking algorithm proposed in this application has extremely high efficiency and speed, and is very suitable for online applications.

[0202] Table 4 CPU time of the proposed topology tracking method

[0203] Power distribution system 33 nodes 69 nodes time 2.3ms 5.1ms

[0204] Example 3

[0205] This embodiment provides a distribution network topology tracking device based on finite synchronous phasor measurement, including:

[0206] A data acquisition module is used to determine the topology of the distribution network before the topology structure changes, and to obtain voltage phasor measurement data before and after the topology structure of the distribution network changes;

[0207] The candidate topology line set determination module is used to determine the linear power flow model of the distribution network, and build an underdetermined linear regression model based on the linear power flow model and voltage phasor measurement data, and propose a linear model matching algorithm for solving it. By enumerating all line connectivity state switching events, the first matching index values ​​of all lines are obtained, the first matching index values ​​are sorted in ascending order, and the candidate topology line set is selected according to the sorting result;

[0208] The best matching topology structure determination module is used to perform nonlinear state estimation on the candidate topology line set and determine the best matching topology structure as the final result.

[0209] A computing device is also provided, comprising:

[0210] one or more processing units;

[0211] A storage unit for storing one or more programs,

[0212] Among them, when the one or more programs are executed by the one or more processing units, the one or more processing units execute the distribution network topology tracking method based on finite synchronous phasor measurement in this embodiment; it should be noted that the computing device may include but is not limited to a processing unit and a storage unit; those skilled in the art can understand that the computing device including a processing unit and a storage unit does not constitute a limitation on the computing device, and may include more components, or a combination of certain components, or different components. For example, the computing device may also include input and output devices, network access devices, buses, etc.

[0213] A computer-readable storage medium having a non-volatile program code executable by a processor, wherein when the computer program is executed by the processor, the steps of the distribution network topology tracking method based on limited synchronous phasor measurement in this embodiment are implemented; it should be noted that the readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above; the program contained on the readable medium can be transmitted using any appropriate medium, including, but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the above. For example, the program code for performing the operation of the present invention can be written in any combination of one or more programming languages, and the programming language includes an object-oriented programming language, such as Java, C++, etc., and also includes a conventional procedural programming language, such as C language or similar programming language. The program code can be executed entirely on a user computing device, partially on a user device, as an independent software package, or entirely on a remote computing device or server. In cases involving a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0214] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. Although the present invention has been described in detail with reference to the above embodiments, a person skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A distribution network topology tracking method based on finite synchronized phasor measurement, characterized in that: The steps include: Determine the topology of the distribution network before the topology changes, and obtain voltage phasor measurement data before and after the topology changes; Determine the linear power flow model of the distribution network, and build an underdetermined linear regression model based on the linear power flow model and voltage phasor measurement data, and propose a linear model matching algorithm to solve it. By enumerating all line connectivity state switching events, the first matching index values ​​of all lines are obtained, the first matching index values ​​are sorted in ascending order, and a candidate topology line set is selected according to the sorting results; Nonlinear state estimation is performed on the candidate topology line set to determine the best matching topology as the final result.

2. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: The method of performing nonlinear state estimation on the candidate topology line set and determining the most matching topology structure as the final result is: The weighted least square method is used to perform state estimation on each candidate topology to obtain the second matching index values ​​of all candidate topologies, and the candidate topology with the lowest second matching index value is determined as the final result.

3. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: When constructing an underdetermined linear regression model based on the linear power flow model and voltage phasor measurement data, it is assumed that there will be no power outage after the distribution network topology changes, so the node load fluctuation can be approximately regarded as Gaussian distribution noise with zero mean and small variance. Under this assumption, the injected power of the node after the topology change is obtained according to the linear power flow model and voltage phasor measurement data, thereby obtaining the underdetermined linear regression model: Among them, Δ ε represents Δε after removing the rows and columns of the balancing nodes, Δε=ε′-ε, ε is the deviation vector between the voltage amplitude and the reference value, ε′ is the voltage amplitude deviation vector after the topology change; Δ θ represents Δθ after removing the rows and columns of the equilibrium nodes, Δθ=θ′-θ, θ represents the node phase angle vector, and θ′ represents the phase angle vector after the topology change; are the node conductance matrix and negative node susceptance matrix respectively, H g H after removing the rows and columns of the balance nodes g , H β H after removing the rows and columns of the balance nodes β ; is the node-branch association matrix, consisting of n l n b Dimensional column vector m l Composition, of which M M is the M after removing the rows and columns of the balance nodes; is a diagonal matrix, and its l-th diagonal element is the conductance g of branch l. l and susceptance β l ; is the branch state change vector before and after the topology structure changes, where d l Indicates the change state of the lth branch. If the branch is open, it is 1, if it is closed, it is -1, otherwise it is 0; ε ′ represents ε′ after removing the rows and columns of the balance nodes; θ ′ represents θ′ after removing the rows and columns of equilibrium nodes; denote the disturbance vectors of active and reactive injected power respectively, η p is η after removing the rows and columns of the balance nodes p , η q is η after removing the rows and columns of the balance nodes q ; Extract the configuration voltage phasor measurement n from formula (15): o The rows corresponding to the nodes are: Where: subscript o represents the row corresponding to the observable node.

4. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 3 is characterized in that: By performing compact singular value decomposition on the underdetermined linear regression model, whitening preprocessing of the relevant noise variables is achieved, and the processed underdetermined linear regression model is obtained: After whitening the noise, the noise vector V o T The mean of η becomes zero and the covariance matrix becomes U o 、V o is an orthogonal matrix, Σ o is a sparse diagonal matrix containing all nonzero singular values.

5. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 4 is characterized in that: By enumerating all line connectivity state switching events, the method for obtaining the first matching index values ​​of all lines is as follows: By enumerating all possible d and solving s1 and s2 for each specific vector d according to formula (18), the first matching index value, i.e., the least squares target value, is obtained; For the topology tracking problem, when a vector d is given, there is only one non-zero element d l , so formula (18) can be rewritten as: Then formula (23) is simplified to a linear regression model containing only two variables: For a specific vector d, the first matching index value is calculated as follows: Among them, the least squares solution Solve by the following formula:

6. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: When performing nonlinear state estimation on the candidate topology line set and determining the best matching topology as the final result: For a network topology T with m measurements, its measurement model is: z=h(x)+e (8) Where: is the state variable vector, which contains the voltage magnitudes and phase angles of all nodes except the reference node phase angle; It is a vector measurement variable, including active and reactive power injection measurement and voltage phasor measurement; is the measurement error vector; h(·) is the nonlinear measurement function vector under a given candidate topology; The second matching index value of the candidate topology is defined as the state estimation objective function value, that is: Where: The norm is defined as is the error covariance matrix; Let the first-order derivative of the objective function be 0, and use Taylor expansion to linearize it at the initial point x0, and we get: -2H T (x)R -1 [z-h(x)]=0 (10) -H T (x0)R -1 [zh(x0)-H(x0)·Δx]=0 (11) Starting from the initial point x0, the Newton-Gaussian method is used to solve the nonlinear state estimation, and the equation for each iteration is: Δx (k) =[H T (x (k) )R -1 H(x (k) )] -1 H T (x (k) )R -1 [z-h(x (k) )] (12) Calculate the second matching index values ​​of all candidate topologies, and determine the candidate topology with the lowest second matching index value as the final result:

7. The distribution network topology tracking method based on finite synchronized phasor measurement according to claim 1 is characterized in that: When the first matching index values ​​are sorted in ascending order and the candidate topology line set is selected according to the sorting result, the first k candidate topology line sets in ascending order need to be selected according to the measurement error level and the number of synchronized phasor measurement devices through offline simulation tests.

8. A distribution network topology tracking device based on finite synchronized phasor measurement, characterized in that: include: A data acquisition module is used to determine the topology of the distribution network before the topology structure changes, and to obtain voltage phasor measurement data before and after the topology structure of the distribution network changes; The candidate topology line set determination module is used to determine the linear power flow model of the distribution network, and build an underdetermined linear regression model based on the linear power flow model and voltage phasor measurement data, and propose a linear model matching algorithm for solving it. By enumerating all line connectivity state switching events, the first matching index values ​​of all lines are obtained, the first matching index values ​​are sorted in ascending order, and the candidate topology line set is selected according to the sorting result; The best matching topology structure determination module is used to perform nonlinear state estimation on the candidate topology line set and determine the best matching topology structure as the final result.

9. A computing device, characterized in that: include: one or more processing units; A storage unit for storing one or more programs, Wherein, when the one or more programs are executed by the one or more processing units, the one or more processing units execute the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a processor-executable non-volatile program code, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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