Recent technological developments have led to significant changes in the power grid. Increasing consumption, widespread adoption of Distributed Energy Resources (DER), installation of smart meters, these are some of the many factors that characterize the changing distribution network. These transformations taking place at the edge of the grid call for improved planning and operation practices. In this context, this thesis aims to improve the grid edge functionality by putting forth a method to address the problem of high demand during peak period by identifying customer groups for participation in demand response programs, which can lead to significant peak shaving for the utility. A possible demand response strategy for peak shaving makes use of Photovoltaic (PV) and Battery energy storage system (BESS). In the process, this work also examines the approach to computation of hosting capacity (HC) for small PV and quantifies the difference obtained in HC when a detailed Low voltage (LV) network is available and included in HC studies. Most PV hosting studies assess the impact on system feeders with aggregated LV loads. However, as more residential customers adopt rooftop solar, the need to include secondary network models in the analysis is studied by performing a comparative study of hosting capacity for a feeder with varying loading information available. / Master of Science / Today, with significant technological advancements, as we proceed towards a modern grid, a mere change in physical infrastructure will not be enough. With the changes in kinds of equipment installed on the grid, a wave of transformation has also begun to flow in the planning and operation practices for a smarter grid. Today, the edge of the grid where the customer is interfaced to the power system has become extremely complex. Customers can use rooftop solar PV to generate their own electricity, they are more informed about their consumption behavior due to installation of smart meters and also have options to integrate other technology like battery energy storage system and electric vehicles. Like with any good technology, adoption of these advancements in the system brings with itself a greater need for reform in operation and planning of the system. For instance, increasing installation of rooftop solar at the customer end calls for review of existing methods that determine the maximum level of PV deployment possible in the network without violating the operating conditions. So, in this work, a comparative study is done to review the PV hosting capacity of a network with varying levels of information available. And the importance of utilities to have secondary network models available is emphasized. With PV deployed in the system, enhanced demand response strategies can be formulated by utilities to tackle high demand during peak period. In a bid to identify customers for participation in such programs, in this work, a computationally efficient strategy is developed to identify customers with high demand during peak period, who can be incentivized to participate in demand response programs. With this, a significant peak shaving can be achieved by the utility, and in turn stress on the distribution network is reduced during peak hours.

The Gaussian mixture model has been used for model-based clustering analysis for decades. Most model-based clustering analyses are based on the Gaussian mixture model. Model averaging approaches for Gaussian mixture models are proposed by Wei and McNicholas, based on a family of 14 Gaussian parsimonious clustering models. In this thesis, we use non-Gaussian mixture models, namely the tEigen family, for our averaging approaches. This paper studies fitting in an averaged model from a set of multivariate t-mixture models instead of fitting a best model. / Thesis / Master of Science (MSc)

A flexible family of mixture models known as cluster-weighted models (CWMs) arise when the joint distribution of a response variable and a set of covariates can be modelled by a weighted combination of several component distributions. We introduce an extension to CWMs where changepoints are present. Similar to the finite mixture of regressions (FMR) with changepoints, CWMs with changepoints are more flexible than standard CWMs if we believe that changepoints are present within the data. We consider changepoints within the linear Gaussian CWM, where both the marginal and conditional densities are assumed to be Gaussian. Furthermore, we consider changepoints within the Poisson and Binomial CWM. Model parameter estimation and performance of some information criteria are investigated through simulation studies and two real-world datasets. / Thesis / Master of Science (MSc)

Målet med denna studie var att undersöka inverkan av brus, normaliseringen av Laplacianen, antalet kluster k och antalet grannar i närhetsgrafen knn på en implementation av spektral klustring. Med hjälp av den framtagna klustringen skulle lämpligheten att använda spektral klustring i en oceanografisk tillämpning utvärderas. Undersökningen utfördes på SMHIs data från två väderstationer under två olika tidpunkter: Vinga (Juli, 2019) och Visby (Juli, 1987). Datan behandlades med hjälp av MATLABs zscore-funktion och användes sedan i den spektrala klustringsalgoritmen. Klustringens kvalitet avgjordes genom att betrakta den spektrala tätheten, beräkna den genomsnittliga variansen mellan kluster och granska egenvärdenas storlek. Resultaten visade att bruset kunde försummas, att den icke-normaliserade Laplacianen var att föredra samt att k = 12 och knn = 15 var ett optimalt parameterval förVinga 2019. Dessutom tycktes vissa oceanografiska fenomen, såsom tidvatten och Ekmaneffekten, återfinnas i klustringen. Slutligen tycks spektral klustring vara en lämplig metod för enklare oceanografiska tillämpningar, även om valet av parametrar måste testas för varje applikation av algoritmen.

The silhouette score is a widely used technique to evaluate the quality of a clustering result. One of the current issues with the silhouette score is its sensitivity to outliers, which can lead to misleading interpretations. This problem is caused by the silhouette score using the arithmetic mean to calculate the average intra and inter-cluster distances. To address this issue, three modified silhouette scores are presented: GenSil, TrimSil, and extended TrimSil, which replace the arithmetic mean with the generalized mean, the trimmed mean and a modified trimmed mean, respectively. Experiments on both simulated and real-world datasets show that GenSil is the most effective method, significantly reducing the impact of outliers and achieving high silhouette scores with negative parameter values. TrimSil also improves silhouette scores but performs worse than GenSil, while the extended TrimSil outperforms TrimSil but is still less effective than GenSil. To further aid in selecting the optimal number of clusters with these modified silhouette scores, a more straightforward visualization technique, the silhouette-parameter plot, is also introduced. / Thesis / Master of Science (MSc)

A non-parametric data clustering technique for achieving efficient data-clustering and improving the number of clusters is presented in this thesis. K-Means and Expectation-Maximization algorithms have been widely deployed in data-clustering applications. Result findings in related works revealed that both these algorithms have been found to be characterized with shortcomings. K-Means was established not to guarantee convergence and the choice of clusters heavily influenced the results. Expectation-Maximization’s premature convergence does not assure the optimality of results and as with K-Means, the choice of clusters influence the results. To overcome the shortcomings, a fast automatic K-EM algorithm is developed that provide optimal number of clusters by employing various internal cluster validity metrics, providing efficient and unbiased results. The algorithm is implemented on a wide array of data sets to ensure the accuracy of the results and efficiency of the algorithm.

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