Bad Data Identification in Power System Based on Improved GSA Algorithm

This paper presents a new approach for detection and identification of ultiple bad data --- estimation-identification approach which has been developed in order to improve the performance of static-state estimators of power systems. It describes the important function of detection and identification of bad data which is of crucial importance in designing a static-state estimator as a basic element in power system real-time control; it also discusses tthe basic principle, method of solution and programing technique of so called "Estimation-Identificaition Approach" which is based on the better utilization of the resources of residues and the analysis of the property of its sensitivity matrix; and some test results of simulation on a model system and a practical searching system of doubtful data are given. Test results of identifying bad data is good, it is usually successful especially in the case of the occurence of multi-bad data. At the end of this paper comments concerning the advantages of this approach and its recommendation as a prospective practical approach in real-time applications are given.

Given the complexity of real-life event logs, several trace clustering techniques have been proposed to partition an event log into subsets with a lower degree of variation. In general, these techniques assume that the number of clusters is known in advance. However, this will rarely be the case in practice. Therefore, this paper presents approaches to determine the appropriate number of clusters in a trace clustering context. In order to fulfil the objective of identifying the most appropriate number of trace clusters, two approaches built on similarity are proposed: a stability- and a separation-based method. The stability-based method iteratively calculates the similarity between clustered versions of perturbed and unperturbed event logs. Alternatively, an approach based on between-cluster dissimilarity, or separation, is proposed. Regarding practical validation, both approaches are tested on multiple real-life datasets to investigate the complementarity of the different components. Our results suggest that both methods are successful in identifying an appropriate number of trace clusters.

Averaging amplitudes over consecutive time samples (i.e., time window) is widely used to calculate the peak amplitude of event-related potentials (ERPs). Cluster analysis of the spatio-temporal ERP data is a promising tool to determine the time window of an ERP of interest. However, determining an appropriate number of clusters to optimally represent ERPs is still challenging. Here, we develop a new method to estimate the optimal number of clusters utilizing consensus clustering. Various polarity dependent clustering methods, namely, k-means, hierarchical clustering, fuzzy c-means, self-organizing map, spectral clustering, and Gaussian mixture model, are used to configure consensus clustering after assessing them individually. When a range of clusters is applied many times, the optimal number of clusters should correspond to the expectation, which is the average of the obtained mean inner-similarities of estimated time windows across all conditions and groups converge in the satisfactory thresholds. In order to assess our method, the proposed method has been applied to simulated data and prospective memory experiment ERP data aimed to qualify N2 and P3, and N300 and prospective positivity components, respectively. The results of determining the optimal number of clusters meet at six cluster maps for both ERP data. In addition, our results revealed that the proposed method could be reliably applied to ERP data to determine the appropriate time window for the ERP of interest when the measurement interval is not accurately defined.

Bad-data detection in pre-estimation can help to improve state estimation [Teeuwsen & Erlich, 2006]. Since transient and abnormal conditions may occur in a power system, measurements may be polluted by bad data to cause estimated errors. Hence, it is necessary to accurately detect the bad data. To ensure the reliability of the measured data, a practical state estimator should have an ability to detect and identify the bad data as well as to eliminate their effects on the estimation [Zhang & Lo, 1991]. Generally, bad-date detection is important to guarantee the reliability of the measured data. If one or more errors occur in power system measurements, the states of the estimated system may be biased and the safety of power supply may be potentially dangerous. To avoid this situation, several bad-data detection and identification schemes have been presented. For example, WLS (weighted least squares) was proposed in 1989 [EI-Keib et al., 1989]. The weighted sum of squares of the measurement residuals was chosen as the objective function to be minimized. But, WLS-based state estimators were only developed by using a linearized measurement function [Huang & Lin, 2003] with complicated computations. Then, linear programming (LP) was proposed to improve the identification method [Peterson & Girgis, 1988]. However, the LP estimator may fail to reject the bad data and it can be attributed to the existence of leverage in the power system model [Ali Abur, 1990]. Thus, Ali Abur had proposed hypothesis testing identification (HTI) to extend the case of the LP estimator. Nevertheless, it had caused computational burdens with taking the special properties of the LP estimation equations into account. Huang [Huang & Lin, 2003] proposed a changeable weighting matrix to identify the bad data but it only can apply for static state estimations. Nevertheless, Zhang had proposed recursive measurement error estimation identification (RMEEI) for bad-data identification [Zhang et al., 1992]. State variables, residuals and their parameters can be updated after removing a measurement from the suspected data set to the remaining data set by using a set of linear recursive equations. With splitting the raw measurements into some parts, a set of residual equations used by the traditional methods can only apply to linear systems and it may result the operation of calculation burden and complexity because each part consists of some measurements [Zhang et al., 1992]. Source: Kalman Filter, Book edited by: Vedran Kordic, ISBN 978-953-307-094-0, pp. 390, May 2010, INTECH, Croatia, downloaded from SCIYO.COM

Bad data in a power system fail to accurately reflect its state of operation. Cleaning bad data is thus necessary for the situational analysis of a data-based power system. Methods for the identification and modification of bad data based on state estimation may fail to converge in iterative calculations, and yield poor results when the errors are significant. State estimation also involves non-linear computation, which incurs a significant computational overhead and makes it difficult to efficiently handle large volumes of data. To solve these problems, this paper proposes a method for the detection and identification of bad data based on constraints on spatial–temporal correlation. In the spatial domain, we fix the equivalent power balance condition through the topology of the network. In sequential distribution, we establish data constraints based on the similarity of data among temporal sections. We then check the data in combination with the spatial–temporal correlation constraints. The proposed method was applied to an IEEE 14-bus system and a provincial grid, and the results show that it can reliably detect and modify bad data to significantly improve their quality. The proposed approach avoids non-linear calculations, is computationally efficient, and can quickly detect and modify bad data.

Clustering is a group of unsupervised statistical techniques commonly used in many disciplines. Considering their applications to fish abundance data, many technical details need to be considered to ensure reasonable interpretation. However, the reliability and stability of the clustering methods have rarely been studied in the contexts of fisheries. This study presents an intensive evaluation of three common clustering methods, including hierarchical clustering (HC), K-means (KM), and expectation-maximization (EM) methods, based on fish community surveys in the coastal waters of Shandong, China. We evaluated the performances of these three methods considering different numbers of clusters, data size, and data transformation approaches, focusing on the consistency validation using the index of average proportion of non-overlap (APN). The results indicate that the three methods tend to be inconsistent in the optimal number of clusters. EM showed relatively better performances to avoid unbalanced classification, whereas HC and KM provided more stable clustering results. Data transformation including scaling, square-root, and log-transformation had substantial influences on the clustering results, especially for KM. Moreover, transformation also influenced clustering stability, wherein scaling tended to provide a stable solution at the same number of clusters. The APN values indicated improved stability with increasing data size, and the effect leveled off over 70 samples in general and most quickly in EM. We conclude that the best clustering method can be chosen depending on the aim of the study and the number of clusters. In general, KM is relatively robust in our tests. We also provide recommendations for future application of clustering analyses. This study is helpful to ensure the credibility of the application and interpretation of clustering methods.

Clustering refers to algorithms to uncover such clusters in unlabeled data. Data points belonging to the same cluster exhibit similar features, whereas data points from different clusters are dissimilar to each other. The identification of such clusters leads to segmentation of data points into a number of distinct groups. In this study it was aimed to classify the 492 Holstein Friesian dairy cattle with determining the optimum number of clusters using the genomic breeding values (GBVs) calculated with 13250 SNPs using GBLUP for milk yield (kg), milk fat (%), milk protein (%), milk lactose (%), and milk dry matter (%). Results showed that the optimum number cluster was determined as two for the genomic breeding values. Determining the most appropriate number of clusters, it provides great convenience in the selection of breeding animals after determining the animals that can provide optimum efficiency in the herd or the animals that need to be eliminated from the existing herd. As a result, it can be said that the k-means method can be used successfully in clustering animals for genomic breeding values, but for this, at first, the optimum number of clusters must be determined.

Phasor measurement units (PMUs) are power system devices placed at various locations in electrical power network that provide the measurement of phasors of voltages and currents from the respective meters or instruments placed at locations. Data provided by the PMUs are used for system analysis and also help to analyze the sequence of events that may have contributed to the failure of the power system. The presence of bad data in PMUs is increasing in today’s power system due to the system complexity and associated issues. This will lead to inaccurate measurement of voltage magnitude and phase angle. Hence, it is important to detect the presence of bad data and identify the PMU which contains the error. In order to identify the bad data, state estimation is carried out to obtain the true state variables by the application of Load Flow Analysis (LFA). The application of Engineering Optimization is called into this work for improving the detection of bad data and its correction. Firefly optimization and particle swarm optimization techniques are developed for the above problem, and later results are compared with respect to the accuracy of results. The system is modeled in MATLAB platform.

In this study, clustering based method for activation detection in functional magnetic resonance imaging (fMRI) is employed. Moreover, some features are obtained by fitting two models namely FIR filter and Gamma function, to hemodynamic response function (HRF). After applying clustering methods (that require number of clusters as an input) to feature space, our simulations show that number of clusters can affect activation detection significantly. Therefore a newly proposed clustering algorithm namely evolving neural gas (ENG) that gives optimal number of clusters is exploited. In addition to ENG, the result of four clustering algorithms namely k-means, fuzzy C-means, neural gas, and clara in different number of clusters are evaluated. The results show that the best activation detection is taken place using obtained optimal number of clusters.

The study of good governance over the past two decades has been at the forefront of the world's scientific and international circles, especially in developing countries. The purpose of this study is to evaluate the status of countries based on good governance and determine the ranking of Iran among other countries, using clustering techniques. In order to select an appropriate clustering method and the appropriate number of clusters, the Silhouette coefficient for each K-Means, Two Step and Kohonen method was calculated for the number of different clusters of each. Based on an assessment of these findings, the K-Means 12 cluster method was selected. The research findings show that, among the four countries of the world having common clusters with Iran in terms of the level of human development, Iran ranks among the 'Lowlevel developing countries' and 'Moderate developing countries'. This issue highlights the importance of improving the level of good governance indicators in the country in order to achieve a higher level of development.

Identification of coherent generators (CGs) is necessary for the area-based monitoring and protection system of a wide area power system. Synchrophasor has enabled smarter monitoring and control measures to be devised; hence, measurement-based methodologies can be implemented in online applications to identify the CGs. This paper presents a new framework for coherency identification that is based on the dynamic coupling of generators. A distance matrix that contains the dissimilarity indices between any pair of generators is constructed from the pairwise dynamic coupling of generators after the post-disturbance data are obtained by phasor measurement units (PMUs). The dataset is embedded in Euclidean space to produce a new dataset with a metric distance between the points, and then the support vector clustering (SVC) technique is applied to the embedded dataset to identify the final clusters of generators. Unlike other clustering methods that need a priori knowledge about the number of clusters or the parameters of clustering, this information is set in an automatic search procedure that results in the optimal number of clusters. The algorithm is verified by time-domain simulations of defined scenarios in 39 bus and 118 bus test systems. Finally, the clustering result of 39 bus systems is validated by cluster validity measures, and a comparative study investigates the efficacy of the proposed algorithm to cluster the generators with an optimal number of clusters and also its computational efficiency compared with other clustering methods.

With the development of shale gas reservoirs, various fracture propagation models have been developed to predict hydraulic fracture geometry by considering the stress shadow effects. Also, many researchers have been working on development of various production-simulation approaches to simulate production from the complex fracture geometries. The objective of this study is to combine the fracture propagation modeling and reservoir simulation to optimize production in shale gas reservoirs. First, we have developed a semi-analytical model to simulate shale gas production from the complex non-planar fracture geometry with varying fracture width and fracture permeability along fracture length. The important gas transport mechanisms including gas slippage, gas diffusion, and gas desorption are considered. Second, we integrate the semi-analytical model with a three-dimensional fracture propagation model, which fully couples elastic deformation of the rock and fluid flow to simulate complex hydraulic fracture propagation, to optimize fracture treatment design in Marcellus shale gas reservoirs. Specifically, the fracture propagation model is utilized to predict the more-realistic non-planar fracture geometry with varying fracture width and fracture permeability along fracture length. In this study, the effect of varying number of perforation clusters within a given stage ranging from 2 to 5 on the fracture propagation was investigated. Three values of stage spacing were considered including 100 ft, 200 ft, and 300 ft. After predicting the non-planar fracture geometry, the semi-analytical model is employed to simulate production from such fracture geometries. According to the well productivity, the optimal number of clusters per stage for varying stage spacing is discussed and determined. In addition, we compared the well performance with the optimal number of perforation clusters for the stage spacing of 100 ft, 200 ft, and 300 ft under a given horizontal well length of 2,500 ft. Furthermore, we used the integrated approach to analyze a well performance from Marcellus shale gas reservoirs. Through the field case study, the more-realistic non-planar fracture geometry was quantified. Also, the difference between the non-planar fracture geometry and ideal planar fracture geometry with equal fracture width and fracture half-length was compared. Finally, the optimal fracture treatment design for the field well development was recommended. This work can provide new insights into optimization of number of perforation clusters per stage within a given fracture stage and a better understanding of the non-planar fracture geometry in shale gas reservoirs.

Clustering is one of the relevant data mining tasks, which aims to process data sets in an effective way. This paper introduces a new clustering heuristic combining the E-transitive heuristic adapted to quantitative data and the k-means algorithm with the goal of ensuring the optimal number of clusters and the suitable initial cluster centres for k-means. The suggested heuris-tic, called PFK-means, is a parameter-free clustering algorithm since it does not require the prior initialization of the number of clusters. Thus, it generates progressively the initial cluster centres until the appropriate number of clusters is automatically detected. Moreover, this paper exposes a thorough comparison between the PFK-means heuristic, its diverse variants, the E-Transitive heuristic for clustering quantitative data and the traditional k-means in terms of the sum of squared errors and accuracy using different data sets. The experiments results reveal that, in general, the proposed heuristic and its variants provide the appropriate number of clusters for different real-world data sets and give good clusters quality related to the traditional k-means. Furthermore, the experiments conducted on synthetic data sets report the performance of this heuristic in terms of processing time.

Network equivalence is a technique useful for many areas including power systems. In many power system analyses, generation shift factor (GSF)-based bus clustering methods have been widely used to reduce the complexity of the equivalencing problem. GSF captures power flow on a line when power is injected at a node using bus to bus electrical distance. A more appropriate measure is the one which captures what may be called the electrical line distance with respect to a bus termed as relative bus to line distance. With increase in power transactions across different regions, the use of relative bus to line distance becomes appropriate for many analyses. Inspired by the recent trends in network science on the study of network dynamics based on the topological characteristics of a network, in this paper, we present a bus clustering method based on average electrical distance (AED). AED is independent of changes in location of slack bus and is based on the concept of electrical distance introduced in the context of molecular chemistry and pursued later for applications in social and complex networks. AED represents the AED from a bus to buses of the transmission line of interest. We first propose an AED-based method to group the buses into clusters for power systems network equivalence using k-means clustering algorithm integrated with silhouette analysis. One limitation of this method is that despite its speed, sometimes it may yield clusters of inferior quality compared to the optimal solution. To overcome this limitation, we next present our improved clustering method which incorporates a seeding technique that initializes centroids probabilistically. We also incorporate a technique in our method to find the number of clusters, k, to be given as input to our clustering algorithm. The resulting algorithm called AED-based k-means++ clustering method yields a clustering that is O(logk) competitive. Our network equivalence technique is next described. Finally, the efficacy of our new equivalencing technique is demonstrated by evaluating its performance on the IEEE 300-bus system and comparing that to the performance of our AED-based method (Sharma et al. in Power network equivalents: a network science-based k-means clustering method integrated with silhouette analysis. In: Complex networks and their application VI, Lyon, France. p. 78–89, 2017) and the existing GSF-based method.

To find an optimal cluster size and number of clusters for a reasonable estimate of the prevalence of cataract blindness in people aged > or = 50 years in 19 rural districts of a state in India. Cluster sampling methodology was used in 19 rural districts of Karnataka State, India. In each district, 15 clusters were randomly selected and 90 people aged > or = 50 years were examined in each cluster. As a result the visual acuity and lens status of a total of 22,218 people were assessed. For each district, the design effect for cluster size ranging from 20 to 90 was calculated and the optimal cluster size and the required number of clusters to achieve an accuracy of 1% errors and 80% confidence was assessed. The age and gender adjusted prevalence of cataract blindness varied from 1.58% to 7.24%, which justifies district level surveys. The design effect is nearly 1.5 for clusters of sizes 30 and 40. With an average prevalence of 4.93% with 1% error and 80% confidence level, the optimal number of clusters is 37 and 28 for a cluster size of 30 and 40 respectively and the average sample size for a district around 1100. Rapid assessments for cataract blindness in those aged > or = 50 years can be conducted at district level in India with existing resources and at affordable costs. These provide reliable data, essential for effective monitoring and planning. Other parameters, for instance, surgical coverage can also be assessed. The availability of standardized software for data entry and analysis and strict adherence to survey procedures is essential.