Formal asymptotic analysis of online scheduling algorithms for plug-in electric vehicles' charging

A large-scale integration of plug-in electric vehicles (PEVs) into the power grid system has necessitated the design of online scheduling algorithms to accommodate the after-effects of this new type of load, i.e., PEVs, on the overall efficiency of the power system. In online settings, the low computational complexity of the corresponding scheduling algorithms is of paramount importance for the reliable, secure, and efficient operation of the grid system.Generally, the computational complexity of an algorithm is computed using asymptotic analysis. Traditionally, the analysis is performed using the paper-pencil proof method, which is error-prone and thus not suitable for analyzing the mission-critical online scheduling algorithms for PEVcharging. To overcome these issues, this paper presents a formal asymptotic analysis approach for online scheduling algorithms for PEV charging using higher-order-logic theorem proving, which is a sound computer-based verification approach. For illustration purposes, we present the complexity analysis of two state-of-the-art online algorithms: the Online cooRdinated CHARging Decision (ORCHARD) algorithm and online Expected Load Flattening (ELF) algorithm. C 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).