Linear and Nonlinear Programming Methods for Dispatching Power in an Integrated AC-DC System

As the number of dc systems increases, it is natural to ask what other roles, aside that of bulk power transfer, that these systems could play in the operation of modern power systems. The objective of this research is to develop formulations and methods of solution to coordinate the dispatch of powers in an integrated ac-dc power system for purposes of minimizing transmission losses and production costs. In Section I we present an LP formulation and method of solution to minimize the ac and dc network transmission losses by coordinating the traditional reactive sources with the dispatch of the dc power transfers, taking into consideration the usual constraints on equipment ratings, line flows and bus voltage magnitudes. Results on sample test systems indicate that substantial reduction in network losses can be achieved by a coordinated dispatch involving the dc power transfers. Section II describes the mathematical formulation and method of solution for the optimal power flow problem of an integrated ac-dc power system. The method is capable of handling the network, converter tap, and control constraints of more than one multiterminal dc systems. The method uses a sequence of quadratic programming subproblems to determine the search directions. Also discussed are ways for determining the initial estimates of the Lagrange multiplier. Tests performed on modified IEEE 30 and 118 bus systems gave reasonable solution time and rate of convergence. The results obtained on the sample systems also indicate that there could be further economic advantage when the dispatch of dc powers is coordinated with the conventional controllable sources using the optimal power flow program. Section III reports on the findings from a comparative study of three methods to screen and rank severe contingencies for preventive dispatch

Microarray background correction: maximum likelihood estimation for the normal–exponential convolution

Background correction is an important preprocessing step for microarray data that attempts to adjust the data for the ambient intensity surrounding each feature. The “normexp” method models the observed pixel intensities as the sum of 2 random variables, one normally distributed and the other exponentially distributed, representing background noise and signal, respectively. Using a saddle-point approximation, Ritchie and others (2007) found normexp to be the best background correction method for 2-color microarray data. This article develops the normexp method further by improving the estimation of the parameters. A complete mathematical development is given of the normexp model and the associated saddle-point approximation. Some subtle numerical programming issues are solved which caused the original normexp method to fail occasionally when applied to unusual data sets. A practical and reliable algorithm is developed for exact maximum likelihood estimation (MLE) using high-quality optimization software and using the saddle-point estimates as starting values. “MLE” is shown to outperform heuristic estimators proposed by other authors, both in terms of estimation accuracy and in terms of performance on real data. The saddle-point approximation is an adequate replacement in most practical situations. The performance of normexp for assessing differential expression is improved by adding a small offset to the corrected intensities