Abstract-This paper presents a probabilistic approach for statistical modeling of the loads in distribution networks. In a distribution network, the probability density functions (pdfs) of loads at different buses show a number of variations and cannot be represented by any specific distribution. The approach presented in this paper represents all the load pdfs through Gaussian mixture model (GMM). The expectation maximization (EM) algorithm is used to obtain the parameters of the mixture components. The performance of the method is demonstrated on a 95-bus generic distribution network model.
Index Terms-Expectation maximization (EM) algorithm,Gaussian mixture model, load profile.
Abstract-This paper introduces a technique for meter placement for the purpose of improving the quality of voltage and angle estimates across a network. The proposed technique is based on the sequential improvement of a bivariate probability index governing relative errors in voltage and angle at each bus. The meter placement problem is simplified by transforming it into a probability bound reduction problem, with the help of the two sided-Chebyshev inequality. A straightforward solution technique is proposed for the latter problem, based on the consideration of 2-error ellipses. The benefits of the proposed technique are revealed by Monte Carlo simulations on a 95-bus UKGDS network model. Index Terms-Bivariate Chebyshev bound, distribution management system, distribution system state estimation, error ellipse, measurement placement.
Power system dynamic state estimation (DSE) remains an active research area. This is driven by the absence of accurate models, the increasing availability of fast-sampled, timesynchronized measurements, and the advances in the capability, scalability, and affordability of computing and communications. This paper discusses the advantages of DSE as compared to static state estimation, and the implementation differences between the two, including the measurement configuration, modeling framework and support software features. The important roles of DSE are discussed from modeling, monitoring and operation aspects for today's synchronous machine dominated systems and the future power electronics-interfaced generation systems. Several examples are presented to demonstrate the benefits of DSE on enhancing the operational robustness and resilience of 21st century power system through time critical applications. Future research directions are identified and discussed, paving This work was partially supported by US Department of Energy under Advanced Grid Modernization Program.
Experimental methods, characterization data and 1 H NMR and 13 C NMR spectra of monomers for all polymers are described below.Materials. Fluorene, 3-bromothiophene, 3-thiophenecarboxaldehyde and malononitrile were obtained from Aldrich Chemical Co. 9,9-Dihexylfluorene. 1 To a solution of 5.0 gm (30.1 mmol) of fluorene in THF (60 ml) at -78 o C was added dropwise, 25 ml (62.5 mmol) of n-butyllithium (2.5 M in hexane).The mixture was stirred at -78 o C for 1 h, and 11.5 gm (70 mmol) of 1-bromohexane in THF (15 ml) was added dropwise to the mixture. The solution was allowed to warm to room temperature and was stirred for overnight. The mixture was poured into water and extracted with ether (3 X 30 ml). The organic layer was washed with brine solution and dried over anhydrous MgSO 4 . The solvent was removed by reduced
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