A new method based on manifold sampling is presented for formulating and solving the optimal well-placement problem in an uncertain reservoir. The method addresses the compounded computational challenge associated with statistical sampling at each iteration of the optimization process. An estimation of the joint probability density function between well locations and production levels is achieved using a small number of expensive function calls to a reservoir simulator. Additional realizations of production levels, conditioned on well locations and required for evaluating the probabilistic objective function, are then obtained by sampling this jpdf without recourse to the reservoir simulator.

A new method is proposed for efficient optimization under uncertainty that addresses the curse of dimensionality as it pertains to the evaluation of probabilistic objectives and constraints. A basis adaptation strategy previously introduced by the authors is integrated into a design optimization framework that construes the optimization cost function as the quantity of interest and computes stochastic adapted bases as functions of design space parameters. With these adapted bases, the stochastic integrations at each design point are evaluated as low-dimensional integrals (mostly one dimensional). The proposed approach is demonstrated on a well-placement problem where the uncertainty is in the form of a stochastic process describing the permeability of the subsurface. An analysis of the method is carried out to better understand the effect of design parameters on the smoothness of the adaptation isometry.

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This short paper investigates distribution-level synchrophasor measurement errors with online and offline tests, and mathematically and systematically identifies the actual distribution of the measurement errors through graphical and numerical analysis. It is observed that the measurement errors in both online and offline case studies follow a non-Gaussian distribution, instead of the traditionally assumed Gaussian distribution. It suggests the use of non-Gaussian models, such as Gaussian mixture models, for representing the measurement errors more accurately and realistically. The presented tests and analysis are helpful for the understanding of distribution-level measurement characteristics, and for the modeling and simulation of distribution system applications, such as state estimation.

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