A new method is presented to denoise 1-D experimental signals using wavelet transforms. Although the state-of-the-art wavelet denoising methods perform better than other denoising methods, they are not very effective for experimental signals. Unlike images and other signals, experimental signals in chemical and biophysical applications, for example, are less tolerant to signal distortion and under-denoising caused by the standard wavelet denoising methods. The new method: 1) provides a method to select the number of decomposition levels to denoise; 2) uses a new formula to calculate noise thresholds that does not require noise estimation; 3) uses separate noise thresholds for positive and negative wavelet coefficients; 4) applies denoising to the approximation component; and 5) allows the flexibility to adjust the noise thresholds. The new method is applied to continuous wave electron spin resonance spectra and it is found that it increases the signal-to-noise ratio (SNR) by more than 32 dB without distorting the signal, whereas standard denoising methods improve the SNR by less than 10 dB and with some distortion. In addition, its computation time is more than six times faster.

This work presents a stochastic optimization framework for operations and planning of an electricity network as managed by an Independent System Operator. The objective is to maximize the total expected net benefits over the planning horizon, incorporating the costs and benefits of electricity consumption, generation, ancillary services, load-shedding, storage and load-shifting. The overall framework could be characterized as a secure, stochastic, combined unit commitment and AC optimal power flow problem, solving for an optimal state-dependent schedule over a pre-specified time horizon. Uncertainty is modeled to expose the scenarios that are critical for maintaining system security, while properly representing the stochastic cost. The optimal amount of locational reserves needed to cover a credible set of contingencies in each time period is determined, as well as load-following reserves required for ramping between time periods. The models for centrally-dispatched storage and time-flexible demands allow for optimal tradeoffs between arbitraging across time, mitigating uncertainty and covering contingencies. This paper details the proposed problem formulation and outlines potential approaches to solving it. An implementation based on a DC power flow model solves systems of modest size and can be used to demonstrate the value of the proposed stochastic framework.

The primary goal of a power system is to provide consumers with reliable access to power at the most economical cost. Under the declining costs of renewable energy sources, the increasing cost of natural gas, and growing emissions control policies, investment in variable renewable energy (VRE) sources including wind and solar is accelerating. As a fundamental optimization tool in the operation and planning of electric power systems, the optimal power flow (OPF) is critical for setting the optimal state of control variables by minimizing desired objective while satisfying all related constraints. However, a comprehensive review of the generic OPF framework that includes all categories of objectives, control variables, and constraints will provide a valuable background to many of the integration studies that are necessary to facilitate the transition of energy systems. A comprehensive OPF framework is essential for researchers to identify the most critical challenges to their applications to develop new solution methods to improve computational efficiency and to take advantage of the increasing computing power to reduce the number of approximations in OPF models. In this work, we aim to provide a comprehensive survey and a generic OPF formulation, along with a detailed explanation of the major formulations for conventional OPF objective functions, control variables, and network constraints, in particular those related to the handling of VREs. This article also highlights the modeling and challenges in the distribution system, and potential formulations to incorporate with the significant variability and intermittency of VRE sources. In addition to a discussion of various formulations and foci for the OPF problem, we compare the implications of these decisions on a small case study to highlight differences.