A prediction algorithm for important nodes and important transmission lines in power systems

Abstract

This invention provides a prediction algorithm for important nodes and transmission lines in a power system, relating to the field of power system technology. The algorithm includes the following steps: S1, improving the mechanism for determining the first initial cluster center and the remaining initial cluster centers; S2, improving the K-means algorithm; S3, using Markov chains as the prediction part of the K-M algorithm; S4, clustering the accumulated historical data on the importance of power system nodes and transmission lines based on the improved K-means algorithm; and S5, analyzing the clustering results. This prediction algorithm for important nodes and transmission lines in a power system provides early warning for power system operation and can further guide the planning of the power system backbone network, thereby improving the robustness of the large power grid and achieving differentiated operation and maintenance efficiency improvement in the power system.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a prediction algorithm for important nodes and important transmission lines of a power system. Background Art

[0002] At present, there are few prediction algorithms for important nodes in power systems. The research on important nodes in power systems is mainly focused on the field of important node evaluation, and is mainly analyzed and studied from the perspective of the topological structure of the power system. A series of evaluation algorithms for important nodes in power systems, such as the electrical betweenness algorithm and the network contraction algorithm, have been proposed. However, this is a common problem that all algorithms have high computational complexity, making it difficult to meet the actual needs of real-time online evaluation, and even more difficult to further realize the prediction of important nodes in power systems. In the field of evaluation of important nodes in power systems, it is currently mainly divided into algorithms based on large-scale simulation represented by the OPA model, and algorithms based on graph theory represented by the line electrical betweenness algorithm. However, both of these two types of algorithms have the disadvantages of high evaluation time complexity, difficulty in real-time evaluation, and difficulty in realizing the prediction of important transmission lines.

[0003] In summary, developing a prediction algorithm for important nodes and important transmission lines in power systems is still a key issue that needs to be urgently addressed in the field of power system technology. Summary of the invention

[0004] The purpose of the invention provided by the present invention is to provide a prediction algorithm for important nodes and important transmission lines in a power system to solve the problems in the above-mentioned background technology.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions: a prediction algorithm for important nodes and important transmission lines in a power system, comprising the following steps:

[0006] S1. Improve the determination mechanism of the first initial cluster center and the determination mechanism of the remaining initial cluster centers;

[0007] S2, improved K-means algorithm;

[0008] S3, using Markov chain as the prediction part of KM algorithm;

[0009] S4, clustering the accumulated historical data of importance of power system nodes and transmission lines according to the improved K-means algorithm;

[0010] S5. Based on the clustering results, use Markov chain to predict the importance of power system nodes and transmission lines in the future.

[0011] Furthermore, in the S1 operation step, the improved determination mechanism selects the first initial cluster center as the data point with the smallest variance in the data set, thereby ensuring that the first initial cluster center is located in a high-density data area. The improved selection process of the first initial cluster center can be described by Formulas 1 to 3:

[0012] Formula 1:

[0013]

[0014] Where x i —data points in the dataset;

[0015] x j —data points in the dataset;

[0016] d(x i , x j )—x i With x j The Euclidean distance between

[0017] Formula 2:

[0018]

[0019] Where n is the number of data points in the dataset;

[0020] E(x i )—x i The average Euclidean distance to other data points;

[0021] Formula 3:

[0022]

[0023] Where Var(x i )—x i The variance of .

[0024] Furthermore, in the S1 operation step, the specific steps of improving the remaining initial cluster center determination mechanism are as follows:

[0025] S101, calculating the variance of each data point in the data set according to formulas 1 to 3, and selecting the data point with the smallest variance as the first initial clustering center;

[0026] S102, calculating the Euclidean distance between the remaining data points in the data set and the first initial cluster center, and selecting the data point with the largest Euclidean cluster as the second initial cluster center;

[0027] S103, calculating the Euclidean distance between each remaining data point in the data set and the determined initial clustering focus, and determining the minimum Euclidean distance corresponding to each data point;

[0028] S104, determining the maximum value among the Euclidean clustering minimum values ​​corresponding to the data points calculated in step 3, and setting the corresponding data point as the next initial clustering center;

[0029] S105 . If the number of determined initial cluster centers meets the requirement, output the initial cluster center points; otherwise, go to step 103 .

[0030] Furthermore, in the S2 operation step, the calculation steps of the improved K-means algorithm include the following steps:

[0031] S201, determine the initial cluster center according to the improved content of the S1 operation step;

[0032] S202, calculating the Euclidean distance between each data point and the cluster center, and classifying the data points according to the size of the Euclidean distance;

[0033] S203, recalculating the cluster center according to the mean value of the data point coordinates in each class;

[0034] S204: If the cluster center calculated this time is consistent with the cluster center calculated last time, clustering is stopped.

[0035] Otherwise, go to step S202 to continue clustering calculation.

[0036] Furthermore, in the S3 operation step, using the Markov chain to predict important nodes and important transmission lines of the power system includes the following steps:

[0037] S301, calculating the importance value change rate of each node and each transmission line at each time according to the accumulated importance of power system nodes and transmission lines at different times, thereby preprocessing the data set;

[0038] S302, based on the preprocessed data set, construct a probability transfer matrix P as shown in Formula 4;

[0039] Formula 4:

[0040]

[0041] Where n is the number of states in the data set;

[0042] P nn —The probability of transitioning from state n to state n.

[0043] S303. Predicting the importance values ​​of power system nodes and transmission lines in the future based on the probability transfer matrix.

[0044] The present invention provides a prediction algorithm for important nodes and important transmission lines in a power system. It has the following beneficial effects:

[0045] 1. It can provide early warning for the operation of the power system and further guide the planning of the backbone grid of the power system, thereby improving the robustness of the large power grid and realizing differentiated operation and maintenance of the power system to improve quality and efficiency.

[0046] 2. Through the processing of data mining and prediction, a KM (K-means-Markov chain) algorithm is proposed for predicting important nodes and important transmission lines of the power system in the future, filling the algorithm gap in this field. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of the initial cluster center determination mechanism of the present invention;

[0048] Figure 2 This is a clustering flow chart of the improved K-means algorithm of the present invention;

[0049] Figure 3 It is a Markov chain prediction flow chart of the present invention;

[0050] Figure 4 Comparison of the number of correctly predicted node importances by BP neural network, one-shift algorithm, and KM algorithm for IEEE-39 node power system;

[0051] Figure 5 Comparison of average error of node importance prediction using BP neural network, one-shift algorithm, and KM algorithm for IEEE-39 node power system;

[0052] Figure 6 Comparison of the number of transmission line importances accurately predicted by BP neural network, one-shift algorithm, and KM algorithm for IEEE-39 node power system;

[0053] Figure 7 The average error comparison of transmission line importance prediction using BP neural network, one-shift algorithm, and KM algorithm for IEEE-39-node power system is presented. DETAILED DESCRIPTION

[0054] like Figure 1-3 As shown: A prediction algorithm for important nodes and important transmission lines of a power system includes the following steps:

[0055] Step 1: As the power system operates, the data set consisting of the importance values ​​of the power system nodes and transmission lines obtained in each evaluation is an uneven data set consisting of several high-density data areas and multiple low-density data areas. For the original K-means algorithm, once the first initial clustering center is selected in the low-density data area, it will cause a large error between the clustering result and the actual situation. Therefore, the first initial clustering center is selected as the data point with the smallest variance in the data set, thereby ensuring that the first initial clustering center is located in the high-density data area. The improved selection process of the first initial clustering center can be described by formulas (1) to (3):

[0056]

[0057] Where x i —data points in the dataset;

[0058] x j —data points in the dataset;

[0059] d(x i , x j )—x i With x j The Euclidean distance between .

[0060]

[0061] Where n is the number of data points in the dataset;

[0062] E(x i )—x i The average Euclidean distance to other data points.

[0063]

[0064] Where Var(x i )—x i The variance of .

[0065] Other initial cluster center determination mechanisms

[0066] In order to cooperate with the improved mechanism for determining the first initial cluster center, inspired by the concept of maximizing the minimum distance in the field of pattern recognition, data points that are farther away in the data set are more representative than randomly selected data points. At the same time, the initial cluster center selected according to the concept of maximizing the minimum distance can also reduce the phenomenon of overlapping partitions in the clustering process of the K-means algorithm. Assuming that there are data points in the data set and the initial cluster center needs to be determined, the execution steps of the mechanism for determining the initial cluster center outside the initial cluster center are as follows Figure 1 As shown:

[0067] 1) Calculate the variance of each data point in the data set according to formulas (1) to (3), and select the data point with the smallest variance as the first initial clustering center.

[0068] 2) Calculate the Euclidean distance between the remaining data points in the data set and the first initial cluster center, and select the data point with the largest Euclidean cluster as the second initial cluster center.

[0069] 3) Calculate the Euclidean distance between each remaining data point in the data set and the determined initial clustering focus, and determine the minimum Euclidean distance corresponding to each data point.

[0070] 4) Determine the maximum value among the Euclidean clustering minimum values ​​corresponding to each data point calculated in step 3, and set the corresponding data point as the next initial clustering center.

[0071] 5) If the number of determined initial cluster centers meets the requirements, the initial cluster center points are output, otherwise go to step 3).

[0072] Step 2: Based on the above improvement of the initial cluster center determination mechanism, the calculation steps of the improved K-means algorithm include the following steps:

[0073] 1) Determine the initial cluster center according to the improved content of S1 operation steps.

[0074] 2) Calculate the Euclidean distance between each data point and the cluster center, and classify the data points according to the size of the Euclidean distance.

[0075] 3) Recalculate the cluster center based on the mean of the data point coordinates in each category.

[0076] 4) If the cluster center calculated this time is consistent with the cluster center calculated last time, stop clustering, otherwise go to step 2) to continue clustering calculation.

[0077] Step 3. Markov chain is widely used in traffic flow forecasting and economic operation situation forecasting due to its advantages of low computational complexity and high accuracy. On the basis of improving the K-means algorithm to mine the accumulated historical data, Markov chain is used as the prediction part of the KM algorithm. At the same time, according to the characteristics of the accumulated power system node and transmission line importance data set, the importance values ​​and importance change rates of nodes and transmission lines in the future are selected to be predicted at the same time. The specific steps of using Markov chain to predict important nodes and important transmission lines in the power system are as follows:

[0078] 1) According to the accumulated importance of power system nodes and transmission lines at different times, the importance value change rate of each node and each transmission line at each time is calculated to pre-process the data set.

[0079] 2) Based on the preprocessed data set, construct the probability transfer matrix P as shown in formula (4).

[0080]

[0081] Where n is the number of states in the data set;

[0082] P nn —The probability of transitioning from state n to state n.

[0083] 3) Predict the importance values ​​of power system nodes and transmission lines in the future based on the probability transfer matrix.

[0084] Step 4: Cluster the accumulated historical data of power system nodes and transmission line importance according to the improved K-means algorithm.

[0085] Step 5: Based on the clustering results, use the Markov chain to predict the importance of power system nodes and transmission lines in the future.

[0086] Even if the computational complexity of the evaluation algorithm for important nodes and important transmission lines in the power system is low, there is still a physically insurmountable time delay between the evaluation results and the actual power system. In addition, with the expansion of the scale of the power system and the increase in the penetration rate of distributed energy, the operation mode of the power system will change more frequently and the magnitude of the change will be more drastic in the future. Therefore, based on the historical data accumulated in the evaluation of important nodes and important transmission lines in the power system, this paper proposes a KM (K-means-Markov chain) algorithm for predicting important nodes and important transmission lines in the power system in the future through the processing of data mining and prediction, filling the algorithm gap in this field.

[0087] Example analysis Figure 4-7 As shown:

[0088] The present invention verifies the rationality and effectiveness of the KM algorithm in the IEEE-39 node power system. Based on the characteristics that the actual power system usually collects key information in the system once every 15 minutes, the present invention uses the OPA model to calculate the power system operation of the IEEE-39 node power system at 672 time points (about the number of power system information collection times in a week) in consideration of the dynamic changes in load demand and power plant output relationship. At the same time, the importance of the IEEE-39 node power system nodes and transmission lines at 672 time points calculated by the EB-SALSA algorithm and the EL-SALSA algorithm constitutes the IEEE-39 node power system historical data set for the analysis and calculation of the prediction algorithm. In addition, the purpose of predicting important nodes and important transmission lines in the power system is not to predict the importance values ​​of nodes and transmission lines with complete accuracy in advance for a period of time, but to predict the change trend in advance to provide early warning for decision makers and guide differentiated operation and maintenance. Therefore, in the present invention, as long as the deviation between the importance prediction value obtained by the prediction algorithm and the actual value does not exceed 2%, the prediction is considered accurate.

[0089] Figure 4 The figure shows the number of nodes with accurate node importance values ​​predicted by BP neural network, one-shift algorithm and KM algorithm at 10 time points (approximately two and a half hours of power system operation) in the IEEE-39 node power system. Figure 4 In the 10 time points, the number of important nodes correctly predicted by the KM algorithm is greater than that of the BP neural network algorithm and the one-shift algorithm. In addition, the performance decay rate of the KM algorithm is also better than that of the BP neural network algorithm and the one-shift algorithm. Figure 4 The figure shows the average error of KM algorithm, BP neural network algorithm and one-shift algorithm at each prediction time point in the prediction of node importance of IEEE-39 node power system. Figure 4 In the results, the average error of KM algorithm at 10 time points is smaller than that of BP neural network algorithm.

[0090] Figure 6 The figure shows the number of transmission lines with accurate values ​​of importance of transmission lines in the IEEE-39 node power system at 10 time points (approximately two and a half hours of power system operation) predicted by BP neural network, one-shift algorithm and KM algorithm respectively. Figure 6 In the 10 time points, the KM algorithm showed obvious advantages over the BP neural network algorithm and the one-shift algorithm. Figure 7 The figure shows the average error of KM algorithm, BP neural network algorithm and one-shift algorithm in the prediction of transmission line importance of IEEE-39 node power system at each prediction time point. Figure 7The KM algorithm also shows obvious advantages over the BP neural network and the one-shift algorithm in terms of the error of prediction of important transmission lines in the IEEE-39 node power system.

[0091] With the development of information perception technology and communication technology, the current power system can already collect important information of nodes and transmission lines in the power system at regular intervals. Based on the collected information, the important nodes and important transmission lines in the power system can be evaluated using the important node algorithm and the important transmission line algorithm. However, even if the computational complexity of the algorithm is lower, the evaluation results of the important nodes and important transmission lines of the power system still lag behind the real-time dynamic changes of the power system. Therefore, based on the data accumulated by the evaluation algorithm of important nodes and important transmission lines in the power system, the present invention proposes an algorithm that combines data mining and prediction for the prediction of important nodes and important transmission lines in the power system. In addition, it is compared with the one-time translation algorithm and the BP neural network algorithm in the IEEE-39 node power system to verify the rationality and effectiveness of the algorithm proposed in the present invention.

[0092] The above are only preferred embodiments of the present invention. It should be pointed out that a person skilled in the art can make several modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A prediction algorithm for important nodes and important transmission lines in a power system, characterized in that: The following steps are involved: S1. Improve the determination mechanism of the first initial cluster center and the determination mechanism of the remaining initial cluster centers; S2, improved K-means algorithm; S3, using Markov chain as the prediction part of KM algorithm; S4, clustering the accumulated historical data of importance of power system nodes and transmission lines according to the improved K-means algorithm; S5. Based on the clustering results, use the Markov chain to predict the importance of power system nodes and transmission lines in the future; In the S1 operation step, the improved determination mechanism selects the first initial cluster center as the data point with the smallest variance in the data set, thereby ensuring that the first initial cluster center is located in the high-density data area. The improved selection process of the first initial cluster center is described by Formulas 1 to 3: Formula 1: Where x i —data points in the dataset; x j —data points in the dataset; d(x i ,x j )—x i With x j The Euclidean distance between Formula 2: Where n is the number of data points in the dataset; E(x i )—x i The average Euclidean distance to other data points; Formula 3: Where Var(x i )—x i The variance of In the S1 operation step, the specific steps of improving the remaining initial cluster center determination mechanism are as follows: S101, calculating the variance of each data point in the data set according to formulas 1 to 3, and selecting the data point with the smallest variance as the first initial clustering center; S102, calculating the Euclidean distance between the remaining data points in the data set and the first initial cluster center, and selecting the data point with the largest Euclidean cluster as the second initial cluster center; S103, calculating the Euclidean distance between each remaining data point in the data set and the determined initial clustering focus, and determining the minimum Euclidean distance corresponding to each data point; S104, determining the maximum value among the Euclidean clustering minimum values ​​corresponding to the data points calculated in step 3, and setting the corresponding data point as the next initial clustering center; S105, if the number of determined initial cluster centers meets the requirement, output the initial cluster center points, otherwise go to step S103; In the S2 operation step, the calculation steps of the improved K-means algorithm include the following steps: S201, determine the initial cluster center according to the improved content of the S1 operation step; S202, calculating the Euclidean distance between each data point and the cluster center, and classifying the data points according to the size of the Euclidean distance; S203, recalculating the cluster center according to the mean value of the data point coordinates in each class; S204, if the cluster center calculated this time is consistent with the cluster center calculated last time, stop clustering, otherwise go to step S202 to continue clustering calculation; In the S3 operation steps, the use of Markov chain to predict important nodes and important transmission lines of the power system includes the following steps: S301, calculating the importance value change rate of each node and each transmission line at each time according to the accumulated importance of power system nodes and transmission lines at different times, thereby preprocessing the data set; S302, based on the preprocessed data set, construct a probability transfer matrix P as shown in Formula 4; Formula 4: Where n is the number of states in the data set; P nn —The probability of transitioning from state n to state n; S303. Predicting the importance values ​​of power system nodes and transmission lines in the future based on the probability transfer matrix.

Images