Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst-Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.Comment: 21 pages, To appear in Compositio Mathematic

Impact Of Wind Farms With Energy Storage On Transient Stability

Today’s energy infrastructure will need to rapidly expand in terms of reliability and flexibility due to aging infrastructure, changing energy market conditions, projected load increases, and system reliability requirements. Over the few decades, several states in the U.S. are now requiring an increase in wind penetration. These requirements will have impacts on grid reliability given the inherent intermittency of wind generation and much research has been completed on the impact of wind on grid reliability. Energy storage has been proposed as a tool to provide greater levels of reliability; however, little research has occurred in the area of wind with storage and its impact on stability given different possible scenarios. This thesis addresses the impact of wind farm penetration on transient stability when energy storage is added. The results show that battery energy storage located at the wind energy site can improve the stability response of the system