Optimal Charging of Electric Vehicles in Smart Grid: Characterization and Valley-Filling Algorithms

Electric vehicles (EVs) offer an attractive long-term solution to reduce the dependence on fossil fuel and greenhouse gas emission. However, a fleet of EVs with different EV battery charging rate constraints, that is distributed across a smart power grid network requires a coordinated charging schedule to minimize the power generation and EV charging costs. In this paper, we study a joint optimal power flow (OPF) and EV charging problem that augments the OPF problem with charging EVs over time. While the OPF problem is generally nonconvex and nonsmooth, it is shown recently that the OPF problem can be solved optimally for most practical power networks using its convex dual problem. Building on this zero duality gap result, we study a nested optimization approach to decompose the joint OPF and EV charging problem. We characterize the optimal offline EV charging schedule to be a valley-filling profile, which allows us to develop an optimal offline algorithm with computational complexity that is significantly lower than centralized interior point solvers. Furthermore, we propose a decentralized online algorithm that dynamically tracks the valley-filling profile. Our algorithms are evaluated on the IEEE 14 bus system, and the simulations show that the online algorithm performs almost near optimality ($<1$ relative difference from the offline optimal solution) under different settings.Comment: This paper is temporarily withdrawn in preparation for journal submissio

Guarantees of Riemannian Optimization for Low Rank Matrix Completion

We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from its partial entries. Assume $m$ entries of an $n\times n$ rank $r$ matrix are sampled independently and uniformly with replacement. We first prove that with high probability the Riemannian gradient descent and conjugate gradient descent algorithms initialized by one step hard thresholding are guaranteed to converge linearly to the measured matrix provided \begin{align*} m\geq C_\kappa n^{1.5}r\log^{1.5}(n), \end{align*} where $C_\kappa$ is a numerical constant depending on the condition number of the underlying matrix. The sampling complexity has been further improved to \begin{align*} m\geq C_\kappa nr^2\log^{2}(n) \end{align*} via the resampled Riemannian gradient descent initialization. The analysis of the new initialization procedure relies on an asymmetric restricted isometry property of the sampling operator and the curvature of the low rank matrix manifold. Numerical simulation shows that the algorithms are able to recover a low rank matrix from nearly the minimum number of measurements

Comparative approaches for assessing access to alcohol outlets: exploring the utility of a gravity potential approach.

BackgroundA growing body of research recommends controlling alcohol availability to reduce harm. Various common approaches, however, provide dramatically different pictures of the physical availability of alcohol. This limits our understanding of the distribution of alcohol access, the causes and consequences of this distribution, and how best to reduce harm. The aim of this study is to introduce both a gravity potential measure of access to alcohol outlets, comparing its strengths and weaknesses to other popular approaches, and an empirically-derived taxonomy of neighborhoods based on the type of alcohol access they exhibit.MethodsWe obtained geospatial data on Seattle, including the location of 2402 alcohol outlets, United States Census Bureau estimates on 567 block groups, and a comprehensive street network. We used exploratory spatial data analysis and employed a measure of inter-rater agreement to capture differences in our taxonomy of alcohol availability measures.ResultsSignificant statistical and spatial variability exists between measures of alcohol access, and these differences have meaningful practical implications. In particular, standard measures of outlet density (e.g., spatial, per capita, roadway miles) can lead to biased estimates of physical availability that over-emphasize the influence of the control variables. Employing a gravity potential approach provides a more balanced, geographically-sensitive measure of access to alcohol outlets.ConclusionsAccurately measuring the physical availability of alcohol is critical for understanding the causes and consequences of its distribution and for developing effective evidence-based policy to manage the alcohol outlet licensing process. A gravity potential model provides a superior measure of alcohol access, and the alcohol access-based taxonomy a helpful evidence-based heuristic for scholars and local policymakers