A power distribution network topology identification method based on space-time features

Abstract

The application discloses a power distribution network topology identification method based on space-time characteristics, and belongs to the field of power system analysis; firstly, the total problem of topology identification is split into multiple sub-problems of switch state identification, a switch state identification model based on Copula entropy and a hidden Markov chain is constructed through limited node measurement sequences, non-linear correlation characteristics between node voltage amplitude sequences are extracted from time and space dimensions, and thus a mapping relationship from node voltage measurement space-time characteristics to switch states is established; secondly, a model parameter learning algorithm based on maximum likelihood estimation and EM algorithm is established, defects of the EM algorithm, such as sensitivity to initial parameters and influence on global convergence, are overcome; finally, multiple models complete switch state identification in a distributed manner by using the obtained mapping relationship, and combine switch state identification results of each time period to realize quasi-real-time power distribution network topology identification.

Description

Technical Field

[0001] This invention belongs to the field of power system analysis, and in particular relates to a method for topology identification of distribution networks based on spatiotemporal characteristics. Background Technology

[0002] As the hub connecting user terminals and power sources, the distribution network is closely related to industrial production and social life. The topology information of the distribution network is the foundation for distribution network management functions such as power flow calculation, state estimation, voltage and reactive power regulation, and network reconfiguration. However, current distribution network topology identification faces several limitations: First, due to cost constraints, measurement equipment is difficult to install extensively in the distribution network, resulting in limited real-time data for topology identification. Load data and node voltage phase angle data are also difficult to obtain in actual distribution networks. Second, with the rapid development of distributed energy resources, topology identification methods need to consider the impact of the characteristics of distribution network DERs (Distribution Energy Dedicated Lines) on the distribution network. For example, the large-scale grid connection of intermittent DERs such as photovoltaic and wind turbines leads to more variable system operation modes and a significant increase in the number of distribution network topology reconfigurations to ensure safe, reliable, and economical system operation. These common problems at the physical level of the distribution network bring new challenges to topology identification. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention breaks down the overall problem of topology identification into multiple sub-problems of switch state identification, providing a distribution network topology identification method based on spatiotemporal characteristics, comprising the following steps:

[0004] S1. Extract the nonlinear correlation features between node voltage amplitude sequences from the spatial dimension. The spatial features are the direct correlation information (Copula entropy) between the voltage amplitude sequences of adjacent nodes at both ends of the switch.

[0005] S2. Extract the nonlinear correlation features between node voltage amplitude sequences from the time dimension. The time features are the temporal correlation information of the measurement data (state transition distribution in HMM), and establish the mapping relationship from the spatiotemporal features of node voltage measurement to the switching state.

[0006] S3. A parameter learning method based on maximum likelihood estimation and EM algorithm is proposed to approximate the mapping relationship, thereby overcoming the problems of EM algorithm being sensitive to initial parameters and having poor convergence of the global optimal solution.

[0007] S4. A single model uses the learned mapping relationship to complete the identification of the switch state;

[0008] S5. Combine the switching status identification results of multiple models for each time period to achieve distribution network topology identification.

[0009] Furthermore, step S1, which involves extracting the nonlinear correlation features between node voltage amplitude sequences from a spatial dimension, includes:

[0010] 101. The time window is used to collect voltage amplitude measurement sequence data of adjacent nodes at both ends of the switch within a single finite time period:

[0011] w = (V i V j ) T (1)

[0012]

[0013] Among them, for a time period of length T s The node voltage amplitude sequence has T s =n d T w T w Let w be the size of the time window, and n be the size of the time window. d Let w be the total number of w, i and j be the node numbers of the distribution network, and V be the total number of w. i Let v be the voltage magnitude sequence at node i. i (t) represents the voltage magnitude of node i at time t;

[0014] 102. Estimating the node measurement sequence V within the time window w i Empirical Copula density function:

[0015]

[0016] U i =(u i (v i (1)),…,u i (v i (t)),…,u i (v i (T w (4)

[0017] Among them, U i For a set of sample points generated, For v i (t) in V i Let l be the k-th value sorted from smallest to largest, and l be an indicator function, when satisfying When the condition is met, the value is 1; otherwise, the value is 0.

[0018] 103. Extract Copula entropy by statistically analyzing the nearest neighbor information of sample points:

[0019]

[0020] Among them, the time window w exists for 2T.w Given a set of sample points, calculate the distance between the z-th sample point and all other points. The distance between the z-th sample point and its k-th nearest neighbor is... The distance between the τ-th sequence direction and the z-th sample point is strictly less than The number of sample points is denoted as n. τ , Let ψ be the Copula entropy estimator for the time window w, and let ψ be the bigamma function.

[0021] 104. In the process of extracting Copula entropy, the iterative calculation process of ψ(x) is as follows:

[0022]

[0023] Where x is any variable, and γ = 0.5772516 is Euler's constant;

[0024] 105, n d The Copula entropy of each time window w forms a spatial feature sequence D = (d1, ..., d2) according to the temporal relationship. ρ ,…,d nd Assuming the switching state of w remains unchanged, then each w in D has a unique switching state, forming a time sequence of switching states. The switch open state s(1) = 1 and the switch closed state s(2) = 2 constitute the switch state set S = {s(1), s(2)}.

[0025] Furthermore, the step S2, which involves extracting the nonlinear correlation features between node voltage amplitude sequences from the time dimension and establishing a mapping relationship from the spatiotemporal features of node voltage measurements to the switching state, includes:

[0026] 201. Entropy of Copula The boxes are then sorted.

[0027]

[0028] in, The bins are divided into n b A Copula entropy state is used to construct the Copula entropy state register. η is the index of the spatial characteristic state; and These are the maximum and minimum values ​​of the Copula entropy, respectively, and [·] is the floor symbol;

[0029] 202. Hidden Markov chains were used to extract the state transition probability distribution A between the previous time window opening state and the current time window opening state from the time dimension. Its essence is the temporal correlation information of the measurement data.

[0030] A = (a ij ) 2×2 (8)

[0031] Among them, a ij =P(s) ρ+1 =s(j)|s ρ =s(i)),i=1,2,j=1,2,a ij Let w be the probability of the ρth w being in s(i) transitioning to the ρ+1th w being in s(j);

[0032] 203. The probability matrix from the Copula entropy of the current time window to the switching state was established:

[0033] π=(π1,π2) (9)

[0034]

[0035] Where π is the initial probability distribution of the Copula entropy to the switching state, and B is the transition probability distribution of the Copula entropy to the switching state. i Let P(s1 = s(0)) be the probability that w is in s(i) when ρ = 1, and To generate spatial features at the ρth w in s(j) The probability of.

[0036] Furthermore, step S3, which proposes a parameter learning method based on maximum likelihood estimation and the EM algorithm, includes the following steps:

[0037] 301. In the initial stage, the initial parameter values ​​λ of the model are solved using the maximum likelihood estimation method. 0 =(π) 0 A 0 B 0 There exist element-maximum likelihood estimators for π, A, and B.

[0038]

[0039]

[0040]

[0041] Where, α ij For n d The frequency of the ρ-th w in s(i) and the frequency of the (ρ+1)-th w transitioning to s(j), σ i For n d The frequency of initial switching states s(i) among the w, β jη For n d Among the w, those located at s(j) and with spatial characteristics as The frequency of.

[0042] 302. In the x-th iteration, x = 1, 2, ..., the model parameter value λ is updated using the EM algorithm. x =(π) x A x B x ):

[0043]

[0044]

[0045]

[0046] Where l is the indicator function, if If l = 1, then l = 0; otherwise l = 0.

[0047] 303. Convergence terminates, yielding the final model parameters λ. x+1 =(π) x+1 A x+1 B x+1 ).

[0048] Furthermore, the step S4 in which a single model uses the learned mapping relationship to complete the identification of the switch state includes:

[0049] 401. The problem of switch state recognition is to solve for the switch state time sequence S, given the spatial feature sequence D and the mapping relationship λ, so that the probability P(D|S) is maximized.

[0050] 402. Find the optimal path that maximizes the probability P(D|S) through dynamic programming. This path is the switching state time sequence S.

[0051] 403. Introduce two definitions, δ ρ (i) represents the maximum probability among all single paths when the ρ-th w is in s(i), ψ ρ (i) is the (ρ-1)th node in the path with the highest probability of w for the ρth node.

[0052] 404. Initialize δ ρ (i) and ψ ρ (i):

[0053]

[0054] 405. For ρ = 2, 3, ..., n d Recursively solve δ ρ (i) and ψ ρ (i):

[0055]

[0056] 406. Convergence Termination:

[0057]

[0058] 407. For ρ = n d -1,n d -2,n d -3,…,1, backtracking to solve the switch state timing sequence:

[0059] s ρ =ψ ρ+1 (s ρ+1 (19)

[0060] Furthermore, step S5, which combines the switching state identification results of multiple models for each time period, to achieve distribution network topology identification, includes the following steps:

[0061] 501. The switching state recognition result of a single model is as follows:

[0062] s(k)=λ(V i V j (20)

[0063] Here, s(k) represents the state of the k-th switch, which is essentially the connectivity of the nodes at both ends of the switch.

[0064] 502. The switching state identification results of multiple models are the final topology identification results:

[0065] ε=(s(1),…,s(k),…,s(m)) (21)

[0066] Where ε represents an m-bit one-hot code.

[0067] Beneficial effects

[0068] Compared with the prior art, the beneficial effects of the present invention are:

[0069] For distribution networks with a high proportion of connected DERs, the strength of the correlation between system node voltage sequences is not only directly related to the topology but also to other complex influencing factors such as the type and output of the DER. The proposed method can analyze the nonlinear correlation between node voltage sequences within a short data collection time, thus accurately deriving the connectivity between nodes. Furthermore, updating massive amounts of data in medium- and low-voltage distribution networks can incur significant communication costs; the proposed method employs distributed processing to significantly reduce the computational burden on the distribution network. The proposed parameter learning method improves the model's convergence efficiency and goodness of fit. Attached Figure Description

[0070] Figure 1This is a schematic diagram of the power distribution network topology identification method of the present invention.

[0071] Figure 2 This is a schematic diagram of spatial features in the power distribution network topology identification method of the present invention.

[0072] Figure 3 This is the switch state identification model in the power distribution network topology identification method of the present invention.

[0073] Figure 4 This is a typical daily load curve for the IEEE 33-node distribution system.

[0074] Figure 5 Initial topology and node measurement configuration of the IEEE 33-node power distribution system.

[0075] Figure 6 Copula entropy distribution of all switches in different states.

[0076] Figure 7 Parameter learning process. Detailed Implementation

[0077] The following is in conjunction with the appendix Figure 1-7 The technical solution of the present invention will be further described in detail with specific implementation examples.

[0078] The scene configuration is as follows:

[0079] The experiment was conducted on a computer equipped with an Intel Core i7-10700 CPU, with a main frequency of 1.6GHz and 8GB of memory. The code was written in Python 3.6 and MATLAB R2018b. The switch identification model was deployed in multiple Python processes to simulate the distributed processing of a real power distribution network at multiple terminals.

[0080] To make the simulation data more closely resemble the actual operation of the distribution network, this section uses the Houseload App to generate a 120-day household load curve at a 1-minute sampling rate. Typical daily load data is shown below. Figure 1 As shown. Five to 300 household loads are allocated to each node in the distribution network based on the node's load capacity. The reactive power injected into the node can be calculated using equation (22). The voltage amplitude measurement data of the node is obtained through power flow calculation simulation using Matpower software. Based on this power data, measurement data from μPMU devices can be simulated.

[0081] ε=(s(1),…,s(k),…,s(m)) (21)

[0082] Where ε represents an m-bit one-hot code.

[0083] The effectiveness of the proposed method was verified using an IEEE 33-bus distribution system. The system has a rated voltage of 12.66 kV, contains 28 branches, and 9 line switches (S1-S9). The node measurement configuration is {V2, V3, V6, V8, V9, V...}. 12 V 13 V 15 V 18 V 19 V 21 V 22 V 23 V 25 V 26 V 29 V 33 The initial topology and node measurement configuration are as follows: Figure 2 As shown in the diagram, two wind turbines and two photovoltaic cells are connected to this system.

[0084] Closing one switch while opening others generates numerous topologies to form a topology library. A topology is removed from the topology library if it exhibits any of the following three conditions:

[0085] ① The node connectivity requirements are not met, resulting in islanding in the distribution network;

[0086] ② If power flow constraints are not met during simulation, and node voltages or line power flow exceed limits, it is assumed that the topology will not...

[0087] This occurs during actual operation;

[0088] ③ The topology is a weak loop and does not satisfy the radial topological constraint.

[0089] Based on the above principles, the topologies were screened, and 24 topologies were ultimately retained.

[0090] During normal system operation, it is assumed that the output prediction errors of photovoltaic and wind turbines follow a Gaussian distribution, with the mean being the actual output at each moment and the variance being 10% of the actual output. Nodes connected to photovoltaics are designated as PQ nodes, and nodes connected to wind turbines are designated as PV nodes.

[0091] Five topologies were randomly selected as known topologies, and the remaining 19 were considered unknown topologies. The first 60 days of simulation data were used as the training set, and the next 60 days as the test set. The training set included random topology variations, with the variations drawn from all known topologies and some unknown topologies. The test set contained topology variations from the remaining topology types, i.e., topologies not present in the training set. In the test set, 300 random topology variations were introduced, ensuring that the selected topology differed from the previous one in each variation.

[0092] Since each topological change does not necessarily cause changes in all switch states, and most switches are in the open state most of the time, the number of samples in the closed state is far less than the number of samples in the open state, thus forming an imbalanced sample set. To reasonably evaluate the effectiveness and adaptability of the proposed method, the average F1 score of 10 experiments is introduced as the evaluation index. In the F1 score, positive samples are samples in the closed state, and negative samples are samples in the open state.

[0093] Step 1: Extract the nonlinear correlation features between node voltage amplitude sequences from the spatiotemporal dimension.

[0094] Copula theory was used to perform spatial correlation analysis on the node voltage amplitude measurement sequence. Verification showed that a value of k of 5 and a time window size T were suitable. w The value is 10. For example... Figure 6 As shown in (a), the horizontal axis represents the absolute value of the Copula entropy, and the vertical axis represents the two states of the switch, indicated by the variables "1" and "0," where "1" represents the switch being closed and "0" represents the switch being open. The figure shows that different actual switch states result in different Copula entropy distributions within different ranges. When the Copula entropy ranges from [-1.31, -0.77] to [-0.61, 0], the switch state can be preliminarily determined by observing the Copula entropy distribution over different time windows.

[0095] like Figure 6 As shown in (b), the horizontal axis represents switch numbers S1-S9, and the vertical axis represents the statistical number of samples where the Copula entropy is in a non-intersecting state at different time windows. The figure shows that most of the statistical samples are from switches in the off-state. This may be because: firstly, Copula entropy correlation analysis from a statistical independence perspective is more favorable for samples in the off-state; secondly, samples in the off-state account for a high proportion of the imbalanced sample set, leading to a higher probability of Copula entropy being in a non-intersecting state. For some switches far from the photovoltaic or wind turbine nodes, such as switches S1, S4, and S6, the number of statistical samples is larger than for other switches, indicating that DER also has an impact on the spatial correlation analysis process based on Copula theory. Figure 6 This demonstrates the effectiveness of Copula entropy in the preliminary analysis of the nonlinear correlation of node voltage amplitude measurement sequences.

[0096] Step 2: A parameter learning method based on maximum likelihood estimation and the EM algorithm is proposed to approximate the mapping relationship.

[0097] The proposed semi-supervised learning method is used to learn the parameters of the switch recognition model, with a maximum of 50 iterations and n observed states. b Set it to 20. For example... Figure 7As shown in Table 1, taking switch S1 as an example, the horizontal axis represents the number of iterations, and the vertical axis represents the log-likelihood value -logP(D|S,λ), aiming to evaluate the goodness of fit between the sample data and the model. A larger value indicates a higher goodness of fit. It can be seen that compared to the EM algorithm, the proposed method has a higher initial goodness of fit, reaches the convergence inflection point faster, and ultimately achieves a higher goodness of fit. This is because the EM algorithm is very sensitive to the selection of initial values; the quality of the initial values ​​directly determines the convergence efficiency and whether the global optimum can be reached. However, the EM algorithm relies on random initialization. The proposed method, based on some prior knowledge, initializes the model parameters through maximum likelihood estimation, improving the efficiency and goodness of fit during offline model training.

[0098] Table 1

[0099]

[0100] Step 3: A single model uses the learned mapping relationship to complete the identification of the switch state.

[0101] Table 2 shows the specific performance of the proposed method on the test set. Considering that each topology change is actually a switching action of a small number of switches, the effect of topology identification (identifying the state of all switches) cannot specifically reflect the situation of each switch, and it is still necessary to record the state of each switch. It can be observed that for a single switch, the performance of each switch state identification model is different, with a difference of 1% to 2.9% compared with the topology identification. This is because the poor performance of the switch identification model affects the final result during the topology identification process. Online running time refers to the time for a single sample in the test set to be applied online by the switch identification model. Since the online time of different models varies, the online running time of all switches here is taken as the maximum parallel prediction time of all models. It can be observed that multiple models can identify the switch state in a short time, while the online running time is negligible in actual distribution network applications. This means that the online efficiency of the model depends only on the size of the time window and the sampling rate of the measurement data.

[0102] Table 2

[0103]

Claims

1. A method for topology identification of distribution networks based on spatiotemporal characteristics, characterized in that, The method includes the following steps: S1. Spatial features are established from the direct correlation information between voltage amplitude sequences of adjacent nodes at both ends of the distribution network switch using the Copula entropy algorithm; the spatial features are nonlinear correlation features between node voltage amplitude sequences extracted from the spatial dimension. S2. Establish time features by determining the temporal correlation information of node measurement data through the state transition distribution of the Hidden Markov Chain method. The spatiotemporal features are extracted from the time dimension to show the nonlinear correlation characteristics between node voltage amplitude sequences; including:

201. Entropy of Copula The boxes are then sorted. (7) in, Sorted into boxes A Copula entropy state is used to construct the Copula entropy state register. , An index for spatial feature states; and These are the maximum and minimum values ​​of the Copula entropy, respectively, and [•] is the floor symbol; 202. Hidden Markov chains were used to extract the state transition probability distribution between the previous time window switching state and the current time window switching state from the time dimension. Establish time-series correlation information for measurement data: (8) in, , i =1,2, j =1,2, a ij For the first indivual w In s( i ) transferred to the indivual w In s( j The probability of ).

203. The probability matrix from the Copula entropy of the current time window to the switching state was established: (9) (10) in, Let be the initial probability distribution of Copula entropy to the switching state. Let Copula entropy be the probability distribution of the transition from the switching state to the switching state. for hour w In s( i The probability of ) P ( s 1=s(0)), and ; In the first indivual w In s( j Generate spatial features The probability of; S3. Construct a distribution network switch state model based on the mapping relationship between spatial characteristic sequences, temporal characteristic sequences, and switch states: S4. Update the parameters of the distribution network switch state model through maximum likelihood estimation and EM algorithm; S5. Extract the updated distribution network switch status mapping relationship to obtain the distribution network switch status identification result; including:

401. The switch state recognition problem is processed as follows: given a spatial feature sequence D and mapping relationship Solve the switching state timing sequence S , making the probability maximum; 402. Find a path using dynamic programming that satisfies the probability The largest optimal path is the switching state timing sequence. S； S6. By using the switch state identification results of each time period from multiple switch state models established in the distribution network, the topology identification of the distribution network is realized.

2. The distribution network topology identification method based on spatiotemporal characteristics according to claim 1, characterized in that, Step S1, which extracts the nonlinear correlation features between node voltage amplitude sequences from the spatial dimension, includes:

101. The time window is used to collect voltage amplitude measurement sequence data of adjacent nodes at both ends of the switch within a single finite time period: (1) (2) Among them, for a time period of length of The node voltage amplitude sequence exists , For time windows w Size, for w Total number i and j For the node number of the distribution network, V i For nodes voltage amplitude sequence, Represents a node exist Voltage amplitude at any given moment; 102. Estimating the time window w Mid-node measurement sequence V i Empirical Copula density function: (3) (4) in, U i For a set of sample points generated, for v i ( t )exist V i Sorted from smallest to largest k One value, For an indicator function, when it satisfies When the condition is met, the value is 1; otherwise, the value is 0.

103. Extract Copula entropy by statistically analyzing the nearest neighbor information of sample points: (5) Among them, time window w There are 2 T w For the nth sample point, calculate the nth... z The distance between the nth sample point and other points, the i-th z The sample point and its i.e. k The distance to the nearest neighbor is It will be in the first The direction of the sequence is related to the first... z The distance between each sample point is strictly less than The number of sample points is denoted as , For time windows w Copula entropy estimator, It is a double gamma function; 104. In the process of extracting Copula entropy, The iterative calculation process is as follows: (6) in, For any variable, Here is Euler's constant; 105. a time window w Copula entropy constitutes a spatial feature sequence based on temporal relationships. D =( d 1,…, ,…, d nd ), assuming w If the switch state remains unchanged, then D Each w Each state has a unique switching state, forming a switching state timing sequence. S =( s 1,…, ,…, s nd Switch off state and switch closed state Constitutes the set of switch states .

3. The distribution network topology identification method based on spatiotemporal characteristics according to claim 1, characterized in that, The step S4, which involves updating the parameters of the distribution network switch state model, includes:

301. In the initial stage, the initial parameter values ​​of the model are solved using the maximum likelihood estimation method. ,exist , A , B Element maximum likelihood estimator , , : (10) (11) (12) in, for n d indivual w The Middle indivual w In s( i ), in the indivual w Transfer to s( j The frequency of ) for n d indivual w The initial switch state is s( i The frequency of ) β jη for n d indivual w In the middle of s( j And the spatial characteristics are The frequency of; 302, in the x In the next iteration Update model parameter values ​​using the EM algorithm : (13) (14) (15) in, l Let be an indicator function, if d ρ = ,but l =1, otherwise l =0; 303. Convergence terminates, and the final parameters of the model are obtained. .

4. The distribution network topology-constrained identification method according to claim 1, characterized in that, The step of identifying the switch status through the distribution network switch status model mapping relationship in step S5 includes:

403. Two definitions are introduced. For the first indivual w In s( i The maximum probability among all individual paths when ) ψ ρ ( i ) is the first indivual w The path with the highest probability is the 1st One node; 404, Initialization and ψ ρ ( i ): (16) 405. Regarding Solve recursively and ψ ρ ( i ): (17) 406. Convergence Termination: (18) 407. Regarding Backtracking to solve the switching state timing sequence: (19)。 5. The distribution network topology identification method based on spatiotemporal characteristics according to claim 1, characterized in that, Step S6, which combines the switch state identification results of multiple distribution network switch state models for each time period, to achieve distribution network topology identification, includes the following steps:

501. The switching state recognition result of a single model is as follows: (20) in, Indicates the first k The state of a switch is essentially the connectivity of the nodes at both ends of the switch; 502. The switching state identification results of multiple models are the final topology identification results: (21) in, Represented as m A unique hot code for a given position.

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