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Solution approaches to chance constrained programming (CCP) have been recently developed and applied in many areas for optimization under uncertainty. Due to the nonlinear model with multiple uncertain variables as well as multiple output constraints, CCP has not been directly applied to optimal power flow (OPF) under uncertainty. The objective of this paper is twofold. First, we introduce the CCP approach to OPF under uncertainty and analyze the computational complexity of the chance constrained OPF. Second, the effectiveness of implementing a back-mapping approach and a linear approximation of the nonlinear model equations to solve the formulated CCP problem is investigated. Load power uncertainties are considered as multivariate random variables with correlated normal distribution. Based on both the nonlinear and the linearized model, results of a five-bus system and the IEEE 30-bus test system are presented to demonstrate the scope of chance constrained OPF. [ABSTRACT FROM PUBLISHER]

Microwave lenses such as the Bootlace/Rotman lenses are designed by placing physical ports of lens input on the theoretical phase centers. These phase center positions are calculated using geometrical optic method under the assumptions of perfect cylindrical waves and true time delay. A real physical lens does not satisfy these conditions due to different port implementation approaches and mutual coupling effects. Full wave investigations and measurements have indicated strong variation at both phase and amplitude couplings between the input and output ports. Efficient theoretical models predicting both phase and amplitude performances are still in great demand to perform advanced lens optimization. The full wave simulation demonstrates accurate results. However, it is not convenient in optimization iterations due to its high computational cost and sophisticated programming process. Based on a ray tracing concept recently explored by the authors, this paper extends its design and formulate a suitable approach for general lens simulation. A microwave lens is systematically treated by hybrid of a flexible tapered port model and multiple-ray-path coupling approach. This method leads to designing the minimum return loss tapered port and fast lens simulation of reasonable accuracy. The predicted results of amplitude, phase couplings, array factors are validated by both full wave simulation and measurement. The comparison shows that the proposed method is fast, accurate and sufficient to predict various microwave lens parameters. This concept can be extended to designing stripline and waveguide lenses as well. [ABSTRACT FROM AUTHOR]

This paper provides a methodology to assist a strategic producer in making informed decisions on generation investment. A single target year is considered with demand variations modeled through blocks. The strategic behavior of the producer is represented through a bilevel model: the upper-level considers both investment decisions and strategic production actions and the lower-level corresponds to market clearing. Prices are obtained as dual variables of power balance equations. Rival uncertainties (on offering and investment) are characterized through scenarios. The resulting model is a large-scale mixed-integer LP problem solvable using currently available branch-and-cut techniques. Results pertaining to an illustrative example and a case study are reported and discussed. [ABSTRACT FROM PUBLISHER]