Power distribution network state estimation method under extreme communication conditions

Abstract

The application discloses a power distribution network state estimation method under extreme communication conditions. Firstly, a new vector distance measurement method is proposed based on n-dimensional fuzzy sets, and a fuzzy equivalence relation matrix of measurement data is calculated by using the method. On this basis, the historical measurement information collected when the communication system is normal and the small amount of measurement information under extreme communication conditions are mapped to the same low-dimensional common feature space by using shared fuzzy equivalence relations. Finally, the measurement data in the common feature space under extreme communication conditions are labeled by using a deep neural network, and the real-time state of the power distribution network under the condition of a small amount of measurement is obtained. The application can accurately track the voltage amplitude and phase angle of the system under extreme communication conditions, thereby providing effective support for correct decision-making of dispatchers, and has certain engineering practical value.

Description

Technical Field

[0001] This invention relates to a power grid state estimation method, and more particularly to a distribution network state estimation method under extreme communication conditions. Background Technology

[0002] With rapid societal development, the scale of power distribution networks is expanding, and the requirements for power supply reliability are constantly increasing. Currently, real-time monitoring of power distribution networks mainly relies on low-redundancy measurement data and traditional state estimation algorithms to achieve real-time state perception. However, if some measurement data is lost or communication failures occur, it is difficult to guarantee the accuracy and real-time performance of power distribution network state perception. Furthermore, power distribution network automation communication systems are typically installed outdoors, and their measurement and acquisition equipment is inextricably linked to climate and environment. Due to the influence of weather, accidents, human error, or other force majeure factors, power distribution network automation communication systems often experience malfunctions or even power outages, resulting in incomplete collected measurement data and difficulty in accurately calculating real-time status, leading to phenomena such as "blind adjustments" in some distribution lines.

[0003] Distribution network state estimation is a key part of real-time monitoring and coordinated optimization of the distribution network, and observability analysis is a prerequisite and necessary condition for realizing distribution network state estimation. Existing domestic and foreign research on methods for unobservable distribution network state perception include: (1) using pseudo-measurement modeling to achieve basic observability of the distribution network, and then using traditional state estimation algorithms to achieve real-time state perception of the distribution network; (2) using data-driven methods to achieve accurate and fast estimation of the distribution network state under low measurement redundancy; (3) optimizing measurement configuration to achieve high-precision and robust state estimation of the distribution network. In view of the insufficient distribution network measurement, there are now methods using spiking neural networks and artificial neural networks for pseudo-measurement modeling to improve the measurement redundancy of the distribution network and achieve full network observability. There are also data-driven methods to achieve accurate and fast estimation of the distribution network state under low measurement redundancy, including Bayesian inference, deep neural networks (DNN), and supervised learning methods, which learn the mapping relationship between historical section measurement data and historical states, and then realize the distribution network state estimation at the current moment. Regarding the optimization of measurement configuration, some researchers divide distribution networks into two categories: branchless bus series and overlapping bus series. They define a μPMU cost model as a function of the μPMU current path, thereby determining the optimal configuration scheme for μPMUs in the distribution network. Others use customized genetic algorithms and improved adaptive multi-objective binary differential evolution algorithms to solve the objective function for optimal PMU configuration, thus providing PMU configuration schemes based on the optimal solution. In summary, existing research has extensively studied distribution network state awareness under conditions of insufficient measurement redundancy, achieving satisfactory theoretical and practical results. However, research on distribution network state awareness under extreme communication conditions with a very small number of measurements due to factors such as distribution network communication failures is scarce. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to address the problem that a large amount of measurement data is missing under extreme communication failure conditions, resulting in a decrease or even obsolescence in the accuracy of distribution network status perception. This invention provides a method for estimating the status of distribution networks under extreme communication conditions, which can achieve real-time perception of the distribution network status even when the communication system fails.

[0005] Technical solution: A method for estimating the state of a distribution network under extreme communication conditions, comprising:

[0006] Under normal communication system conditions, measurement information T1 is collected. Then, using a distribution network model to simulate the distribution network state under extreme communication conditions, a small amount of measurement information T2 is collected across multiple time sections. The normal communication system conditions refer to the ability to normally acquire measurement information collected by various measurement devices, including active and reactive power injected into each node and voltage amplitude at each node. Extreme communication conditions refer to a significant loss of measurement information, with only active and reactive power measurement information injected by the master station or a very small amount of node active and reactive power measurement information. The distribution network model is a three-phase distribution network power flow calculation model established based on branch parameter information and node information. The extreme communication conditions represent communication system failure scenarios.

[0007] The measurement information T1 under normal communication conditions and the measurement information T2 under extreme communication conditions are transformed into fuzzy sets S1 and S2 respectively using the triangular membership function. The two fuzzy sets S1 and S2 are then mapped to a low-dimensional common feature space using the method of shared fuzzy equivalence relations.

[0008] The data corresponding to the low-dimensional common feature space of the measurement information T1 collected under normal communication system conditions is used as input, and the power distribution network state estimate under normal communication system conditions is used as the expected output for deep neural network training. Then, the data corresponding to the measurement information T2 under extreme communication conditions in the low-dimensional common feature space is input into the trained deep neural network model to obtain the real-time state estimate of the power distribution network under extreme communication conditions.

[0009] Wherein, the membership function μ of the triangle i (x|A i )for:

[0010]

[0011] In the formula: x = (x1, x2, ..., x...) n ), where vector x represents the collected measurement data, x i For the i-th measurement data collected, A i Let a be a vector of some measurement information. ij It is vector Ai The j-th element in the vector A, where n is the vector A. i The number of measurement data, ρ i These are the parameters to be determined.

[0012] The method of using shared fuzzy equivalence relations to map two fuzzy sets S1 and S2 to a low-dimensional common feature space includes: calculating the fuzzy equivalence relation matrix of the measurement data using a vector distance metric method based on n-dimensional fuzzy sets; after obtaining the fuzzy equivalence relation matrix, using the α-cut method to cluster the fuzzy sets; and finally, for fuzzy sets S1 and S2, using the addition operator to add the fuzzy vectors of the same class in each dataset to obtain the common features.

[0013] The method for calculating the fuzzy equivalence relation matrix of measurement data using a vector distance metric based on n-dimensional fuzzy sets includes: assuming the fuzzy set of the measurement data collected under normal conditions of the communication system is... Let S2 be the fuzzy vector corresponding to the measurement data collected under normal communication system conditions after transformation by the triangular membership function. Let S2 be the fuzzy set of the measurement data collected under extreme communication conditions. Let N1 and N2 be the fuzzy vectors corresponding to the measurement data collected under extreme communication conditions after transformation by the triangular membership function, where N1≠N2; let the operator... Operators used to obtain the fuzzy relationships between fuzzy vectors in a dataset The formula is:

[0014]

[0015] In the formula, Representing vectors and Manhattan distance, of which These represent the fuzzy vectors corresponding to the two measurement data, respectively, where n is the fuzzy vector. The number of elements in the middle, ρ i ρ j These are the parameters to be determined;

[0016] Computation Operator for:

[0017]

[0018] In the formula, σ is a set parameter;

[0019] and It has been proven that a fuzzy equivalence relation matrix exists. in Operator The fuzzy relation matrix, where N represents the number of fuzzy vectors corresponding to the measurement information. Called The maximum-minimum transitive closure.

[0020] The method of clustering fuzzy sets using the α-cut method includes: calculating the correlation matrix corresponding to the fuzzy equivalence relation matrix.

[0021]

[0022] In the formula, α is a constant. Indicates the use of operator R T The resulting fuzzy relation matrix;

[0023] Elements that are 1 in each row of the association matrix are considered to be of the same class. For the fuzzy equivalence relation matrices of fuzzy sets S1 and S2, the same parameter α is used for clustering so that the two sets of measurement datasets are clustered with the same number of features.

[0024] The α-cut method is used to cluster fuzzy sets, where the range of values ​​for α is:

[0025]

[0026] Choose α to be located in the interval with the largest interval; and These are the elements in the fuzzy equivalence relation matrix of fuzzy sets S1 and S2, respectively.

[0027] Elements in the fuzzy equivalence relation matrix of fuzzy sets S1 and S2 and The calculation formula is:

[0028]

[0029]

[0030] in, Represents the measurement fuzzy vector and Manhattan distance, Represents the measurement fuzzy vector and Manhattan distance, of which These represent the fuzzy vectors corresponding to the two types of measurement data under normal conditions of the communication system. Let n represent the fuzzy vectors corresponding to the two measurement data under extreme communication conditions. Number of elements in the middle σ is the parameter to be determined, and σ is the set parameter;

[0031] The parameter vector in the deterministic formula The objective function is determined using gradient descent. and Parameter values:

[0032]

[0033] After determining the parameter vector, the elements of the fuzzy equivalence relation matrix of the fuzzy sets S1 and S2 of the measurement data are calculated. and

[0034] Beneficial effects: Compared with the prior art, the present invention can realize real-time perception of the status of the power distribution network in the event of communication system failure, thereby providing effective support for the correct decision-making of dispatchers and has certain practical engineering value. Attached Figure Description

[0035] Figure 1 This is the overall flowchart of the present invention;

[0036] Figure 2 This is a schematic diagram of an IEEE 13-node distribution network;

[0037] Figure 3 It is the multi-time section tracking curve of the phase voltage amplitude at node 4A;

[0038] Figure 4 It is the multi-time section tracking curve of the phase voltage amplitude at node 4B;

[0039] Figure 5 It is a multi-time section tracking curve of the voltage amplitude of phase 4C at node;

[0040] Figure 6 It is the phase angle tracking curve of phase voltage at node 4A across multiple time sections;

[0041] Figure 7 It is the phase angle tracking curve of phase voltage at node 4B across multiple time sections;

[0042] Figure 8 It is a multi-time section tracking curve of the phase angle of phase voltage at node 4C;

[0043] Figure 9 The absolute error of the voltage amplitude is due to 3% Gaussian noise, which is bad data.

[0044] Figure 10 The voltage phase angle absolute error is due to 3% Gaussian noise in the bad data.

[0045] Figure 11 It is the absolute error of voltage amplitude with negative data;

[0046] Figure 12It is the absolute error of the voltage phase angle with negative data. Detailed Implementation

[0047] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0048] Taking the IEEE 13-node distribution network system as an example, this method is applied for state estimation and a verification experiment is conducted.

[0049] The flowchart of the power distribution network state estimation method under extreme communication conditions described in this invention is as follows: Figure 1 As shown, it includes the following steps:

[0050] (1) Establish a distribution network model. A three-phase distribution network power flow calculation model is established based on branch parameter information and node information;

[0051] (2) Measurement Information Acquisition and Processing. Under normal communication system conditions, the acquired measurement information T1 is used to calculate power flow based on the network parameters of the distribution network and the load curve of a certain area. Random noise is superimposed on the true power flow value to simulate real-time measurement values, obtaining the real-time measurement value and the true load value at each sampling time. The maximum normalized residual method is used to check and remove bad data. Then, the weighted least squares estimation method is used to estimate the state, obtaining the system state variables under continuous time sections. At the same time, a small amount of measurement information T2 under the distribution network scenario of communication failure is collected at multiple time sections.

[0052] Under normal communication conditions, the measurement information collected by the measurement equipment can be transmitted to the master station platform through the communication system. Extreme communication conditions, or communication failures, refer to situations where the measurement information collected by the measurement equipment cannot be transmitted to the master station through the communication equipment. The measurement data only contains the active and reactive power injected by the master station node, or contains the active and reactive power injected by the master station node and a very small number of nodes, as well as the injected active and reactive power and voltage amplitude measurements.

[0053] (3) Fuzzy relations are a method for measuring the similarity between fuzzy sets, among which fuzzy equivalence relations are a special case of fuzzy relations. In this embodiment, triangular membership functions are selected to construct fuzzy sets. The two sets of measurement information obtained in step (2) are respectively written into fuzzy set form using triangular membership functions. The two sets of measurement information collected here are used to transform each measurement into a fuzzy set form using triangular membership functions. The specific formula is as follows:

[0054]

[0055] In the formula: x = (x1, x2, ..., x...) n ), a ij It is a set The j-th element. N is the number of elements in the set. ρ i These are the parameters to be determined.

[0056] (4) Using the method of shared fuzzy equivalence relations, the two sets of fuzzy sets are mapped to a low-dimensional common feature space. As described in step (3), for a normal communication system, the fuzzy set of the measurement data collected by the measurement equipment is set as follows: In the event of a communication system failure, the fuzzy set of the collected measurement data is: Where N1≠N2. Here, we propose an operator. The fuzzy relationships between the fuzzy vectors in the dataset are obtained by the following formula:

[0057]

[0058] In the formula: d(A) i A j ) represents A i A j The minimum Manhattan distance between all elements in ρ. i ρ j These are the unknown parameters to be determined. To ensure that the obtained values ​​are all within the range [0, 1], we introduce an exponential function with base e, i.e., the operator R. D for:

[0059]

[0060] definition It is an operator The maximum-min transitive closure. Because yes The fuzzy relation matrix has It is a fuzzy equivalence relation matrix and In the formula, σ is a pre-set parameter.

[0061] After obtaining the fuzzy equivalence relation matrix, the α-cut method is used to cluster the fuzzy sets:

[0062]

[0063] In the formula, α is a constant. The above formula yields an incidence matrix corresponding to a fuzzy equivalence relation matrix. When an element in the fuzzy equivalence relation matrix is ​​greater than α, the corresponding element in the incidence matrix is ​​marked as 1; when it is less than α, the corresponding element in the incidence matrix is ​​marked as 0. Finally, elements in each row of the incidence matrix that are 1 are considered to belong to the same class. Therefore, for the collected fuzzy measurement datasets S1 and S2, by sharing fuzzy equivalence relations, the fuzzy equivalence relation matrices of the two sets of measurement information fuzzy sets can be clustered using the same parameter α, so that the two sets of measurement datasets are clustered with the same number of features.

[0064] To select a suitable α, the elements r in the two sets of fuzzy equivalence relation matrices corresponding to fuzzy sets S1 and S2 are... i (i = 1, 2, ..., M = min(N1, N2)) need to be as equal as possible. Based on the above, the fuzzy equivalence relation matrix of two fuzzy sets can be obtained using operators. Therefore, the elements in the matrix can be represented as:

[0065]

[0066]

[0067] The parameter vector in the deterministic formula Solve the objective function using gradient descent:

[0068]

[0069] In the formula: These are elements in two sets of fuzzy equivalence relation matrices. The learning rate is set to η, and the number of iterations is IterM. and After obtaining the parameter values, the elements of the fuzzy equivalence relation matrix of the fuzzy sets S1 and S2 of the measurement data can be obtained. and

[0070] After obtaining the specific elements of the two sets of fuzzy equivalence relation matrices, the value of α is first determined, and then clustering is performed. The value of α needs to be within a specific interval, which can be expressed by the general formula:

[0071]

[0072] In the formula: i0 = 0, 1, ..., M-1. When and At that time, the following intervals can be obtained: When α falls within these intervals, S1 and S2 can be clustered into the same number of low-dimensional features. When α lies within the interval with the largest margin, the two datasets can share most of the information. After determining the value of α, clustering is performed using the "α-cut" method. For datasets S1 and S2, the common features are obtained by adding the fuzzy vectors of the same class in each dataset using the addition operator:

[0073]

[0074]

[0075] Finally, the low-dimensional measurement dataset in the common feature space is normalized for each feature, using the following formula:

[0076]

[0077] (5) The data corresponding to the multi-time section measurement data T1 collected under normal communication system conditions in the low-dimensional common feature space is used as input and the state estimate corresponding to the measurement data T1 is used as output to train the DNN. Then, the part corresponding to the measurement data under extreme communication conditions in the low-dimensional common feature space is brought into the DNN to obtain the state quantity of the distribution network system under extreme communication conditions.

[0078] This invention constructs two separate deep learning networks for voltage amplitude and phase angle, respectively. A multi-layer feedforward DNN is employed, with the first layer being the input layer, the last layer the output layer, and hidden layers in between, all connected in a fully connected manner. The input data consists of low-dimensional data in a common feature space, and the output layer outputs the node voltage amplitude or phase angle. Through extensive offline training and parameter tuning, a DNN model with strong fitting ability is obtained, meaning the state-aware accuracy of the training samples meets certain requirements.

[0079] In the real-time perception phase, the low-dimensional data corresponding to communication failures in the common feature space are input into the trained DNN to obtain the corresponding state variables. For real-time issues, in extreme communication failure situations, when new measurement information is received, the new measurement information is placed at the top of the historical information while the bottom measurement information is deleted, thereby maintaining a stable measurement dataset size.

[0080] Verification experiment: Verification was conducted using the IEEE 13-bus system. A schematic diagram of the IEEE 13-bus distribution network is shown below. Figure 2As shown. First, the actual load data obtained from a certain region is normalized, and 3000 continuous time segments are selected, each lasting 15 minutes. Based on this, load curves extracted from the actual distribution network are used for power flow calculation to obtain the true state values ​​under multiple time segments. Based on the power flow calculation values, the true values ​​of node-injected active power, reactive power, and branch current are obtained. Gaussian noise with a mean of 0 and a variance of 1% is added to the true values ​​of node-injected active and reactive power, Gaussian noise with a mean of 0 and a variance of 0.5% is added to the true values ​​of node voltage amplitude, and Gaussian noise with a mean of 0 and a variance of 0.5% is added to the branch current, simulating the noise-injected measurement data collected by the measurement equipment.

[0081] For the IEEE 13-node system under normal communication conditions, 87 measurements were taken, including active power, reactive power, and voltage amplitude at each node. For extreme communication conditions, three extreme scenarios were tested: 1) only active and reactive power measurement data from the master station node were available; 2) master station measurement data and active and reactive power measurement data from node 2 were available in scenario 1; 3) master station measurement data and active and reactive power measurement data from nodes 2 and 4 were available in scenario 1. The estimated values ​​of distribution network voltage amplitude and phase angle under these three extreme scenarios were calculated using the methods described in this invention.

[0082] Estimation accuracy test: To verify the accuracy of the method proposed in this invention, the mean absolute error across multiple time sections is used as an indicator to measure the accuracy of state estimation. The specific formula is as follows:

[0083]

[0084]

[0085] In the formula: T is the total number of time sections, and N is the number of state variables. These are the estimated values ​​of voltage amplitude and voltage phase angle output by the DNN at a certain moment, respectively. The true values ​​of voltage amplitude and voltage phase angle at the corresponding moment (i.e., power flow calculation values).

[0086] Table 1. Mean Absolute Error of IEEE 13-Node System State Estimation under Three Extreme Communication Scenarios

[0087]

[0088] Table 1 shows the mean absolute error (MAE) of the state estimation method proposed in this invention when different amounts of measurement information are collected under three extreme communication conditions. As can be seen from Table 1, the estimation error of the node voltage amplitude gradually decreases and the accuracy gradually improves with the increase of real-time measurement data under extreme communication conditions. It is worth noting that with the increase of the number of measurements under extreme communication conditions, the estimation error of the node voltage phase angle generally decreases, occasionally increasing slightly, but the overall phase angle estimation error remains within an acceptable range.

[0089] The following verifies the multi-time-section tracking effect:

[0090] To verify the stability and state tracking performance of the algorithm proposed in this invention, this section demonstrates the state tracking of the distribution network under extreme communication conditions, namely when only the master station injects active and reactive power measurements. Figures 3-8 Taking node 4 as an example, the real-time tracking curves of node voltage amplitude and phase angle under 500 time sections are shown.

[0091] Since the phase angle values ​​of the three phases of the distribution network are around 0, -2 / 3π, and 2 / 3π respectively, in order to more clearly demonstrate the node phase angle tracking effect, the phase angles of phase B and phase C are shifted by 2 / 3π and 4 / 3π respectively. Figures 3-5 The multi-time section tracking curves of the voltage amplitude of phases A, B, and C at node 4 are provided. Figures 6-8 The multi-time-section tracking curves of the phase angle of phase voltages at node 4A / B / C are shown. Figures 3-8 It can be seen that under extreme communication conditions (with only master station measurements), the method proposed in this invention can generally accurately track the real-time changes in node voltage amplitude and phase angle, but its tracking performance is slightly worse for minor fluctuations in the state of some nodes. In summary, when the distribution network is unobservable under extreme communication conditions, traditional WLS estimators cannot perform real-time estimation (cannot converge), while the method proposed in this paper can track real-time state changes well and meet engineering requirements.

[0092] Robustness Testing: To test the robustness of the proposed method, this section tests the estimation performance under extreme communication conditions (i.e., measurement information is available at the master station, node 2, and node 4) and two different bad data scenarios. The bad data scenarios are: 1) the noise of the active and reactive power measurements at node 2 increases to Gaussian noise with a mean of 0 and a variance of 3%; 2) the active and reactive power measurements at node 4 are negative. Figure 9 and Figure 10 These represent the estimation errors of the voltage amplitude and phase angle at distribution network nodes when noise increases. Figure 11 and Figure 12 These represent the estimation errors of the voltage amplitude and phase angle at the distribution network nodes when the measurements become the opposite values.

[0093] The simulation results above verify the effectiveness and practicality of the model constructed in this invention. This demonstrates that, under extreme communication failure conditions, the distribution network state estimation calculation method based on shared fuzzy equivalence relations can achieve real-time perception of the distribution network state even in the event of communication system failure, thereby providing effective support for dispatchers' correct decision-making and possessing certain engineering practical value.

Claims

1. A method for estimating the state of a distribution network under extreme communication conditions, characterized in that, include: Under normal communication system conditions, measurement information T1 is collected, and the distribution network state under extreme communication conditions is simulated through a distribution network model to collect a small amount of measurement information T2 at multiple time sections. The normal communication system conditions refer to the ability to normally acquire the measurement information collected by each measurement device, including the active power and reactive power injected by each node and the voltage amplitude of each node. The extreme communication conditions refer to the loss of a large amount of measurement information, with only the main station injecting active and reactive power measurement information or a very small amount of node active and reactive power measurement information. The measurement information T1 under normal communication conditions and the measurement information T2 under extreme communication conditions are transformed into fuzzy sets S1 and S2 respectively using the triangular membership function. The two fuzzy sets S1 and S2 are mapped to a low-dimensional common feature space by using the method of shared fuzzy equivalence relation. The data corresponding to the low-dimensional common feature space of the measurement information T1 collected under normal communication system conditions is used as input, and the power distribution network state estimate under normal communication system conditions is used as the expected output for deep neural network training. Then, the data corresponding to the measurement information T2 under extreme communication conditions in the low-dimensional common feature space is input into the trained deep neural network model to obtain the real-time state estimate of the power distribution network under extreme communication conditions.

2. The distribution network state estimation method under extreme communication conditions as described in claim 1, characterized in that: The power distribution network model is a three-phase power flow calculation model established based on branch parameter information and node information; the extreme communication conditions are communication system failure scenarios.

3. The distribution network state estimation method under extreme communication conditions as described in claim 1, characterized in that, The membership function μ of the triangle i (x|A i )for: In the formula: x = (x1, x2, ..., x...) n ), where vector x represents the collected measurement data, x i For the i-th measurement data collected, A i Let a be a vector of some measurement information. ij It is vector A i The j-th element in the vector A, where n is the vector A. i The number of measurement data, ρ i These are the parameters to be determined.

4. The distribution network state estimation method under extreme communication conditions as described in claim 1, characterized in that, The method of using shared fuzzy equivalence relations to map two fuzzy sets S1 and S2 to a low-dimensional common feature space includes: calculating the fuzzy equivalence relation matrix of the measurement data using a vector distance metric method based on n-dimensional fuzzy sets; after obtaining the fuzzy equivalence relation matrix, using the α-cut method to cluster the fuzzy sets; and finally, for fuzzy sets S1 and S2, using the addition operator to add the fuzzy vectors of the same class in each dataset to obtain the common features.

5. The distribution network state estimation method under extreme communication conditions as described in claim 4, characterized in that, The method for calculating the fuzzy equivalence relation matrix of measurement data using a vector distance metric based on n-dimensional fuzzy sets includes: assuming the fuzzy set of the measurement data collected under normal conditions of the communication system is... Let be the fuzzy vectors corresponding to the measurement data collected under normal communication system conditions after transformation by the triangular membership function, and let be the fuzzy set of the measurement data collected under extreme communication conditions. Let N1 and N2 be the fuzzy vectors corresponding to the measurement data collected under extreme communication conditions after transformation by the triangular membership function, where N1≠N2; let the operator... Operators used to obtain the fuzzy relationships between fuzzy vectors in a dataset The formula is: In the formula, Representing vectors and Manhattan distance, of which These represent the fuzzy vectors corresponding to the two measurement data, respectively, where n is the fuzzy vector. The number of elements in the middle, ρ i ρ j These are the parameters to be determined; Computation Operator for: In the formula, σ is a set parameter; and It has been proven that a fuzzy equivalence relation matrix exists. in Operator The fuzzy relation matrix, where N represents the number of fuzzy vectors corresponding to the measurement information. Called The maximum-minimum transitive closure.

6. The distribution network state estimation method under extreme communication conditions as described in claim 4, characterized in that, The method of clustering fuzzy sets using the α-cut method includes: calculating the correlation matrix corresponding to the fuzzy equivalence relation matrix. In the formula, α is a constant. Indicates the use of operator R T The resulting fuzzy relation matrix; Elements that are 1 in each row of the association matrix are considered to be of the same class. For the fuzzy equivalence relation matrices of fuzzy sets S1 and S2, the same parameter α is used for clustering so that the two sets of measurement datasets are clustered with the same number of features.

7. The distribution network state estimation method under extreme communication conditions as described in claim 4, characterized in that, The α-cut method is used to cluster fuzzy sets, where the range of values ​​for α is: Choose α to be located in the interval with the largest interval; and These are the elements in the fuzzy equivalence relation matrix of fuzzy sets S1 and S2, respectively.

8. The distribution network state estimation method under extreme communication conditions as described in claim 4, characterized in that, Elements in the fuzzy equivalence relation matrix of fuzzy sets S1 and S2 and The calculation formula is: in, Represents the measurement fuzzy vector and Manhattan distance, Represents the measurement fuzzy vector and Manhattan distance, of which These represent the fuzzy vectors corresponding to the two types of measurement data under normal conditions of the communication system. Let n represent the fuzzy vectors corresponding to the two measurement data under extreme communication conditions. Number of elements in the middle σ is the parameter to be determined, and σ is the set parameter; The parameter vector in the deterministic formula The objective function is determined using gradient descent. and Parameter values: After determining the parameter vector, the elements of the fuzzy equivalence relation matrix of the fuzzy sets S1 and S2 of the measurement data are calculated. and

Images