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In this paper, we study how to utilize forecasts to design online electrical vehicle (EV) charging algorithms that can attain strong performance guarantees. We consider the scenario of an aggregator serving a large number of EVs together with its background load, using both its own renewable energy (for free) and the energy procured from the external grid. The goal of the aggregator is to minimize its peak procurement from the grid, subject to the constraint that each EV has to be fully charged before its deadline. Further, the aggregator can predict the future demand and the renewable energy supply with some levels of uncertainty. We show that such prediction can be very effective in reducing the competitive ratios of online control algorithms, and even allow online algorithms to achieve close-to-offline-optimal peak. Specifically, we first propose a 2-level increasing precision model (2-IPM), to model forecasts with different levels of accuracy. We then develop a powerful computational approach that can compute the optimal competitive ratio under 2-IPM over any online algorithm, and also online algorithms that can achieve the optimal competitive ratio. Simulation results show that, even with up to 20% day-ahead prediction errors, our online algorithms still achieve competitive ratios fairly close to 1, which are much better than the classic results in the literature with a competitive ratio of $e$ . The second contribution of this paper is that we solve a dilemma for online algorithm design, e.g., an online algorithm with good competitive ratio may exhibit poor average-case performance. We propose a new Algorithm-Robustification procedure that can convert an online algorithm with good average-case performance to one with both the optimal competitive ratio and good average-case performance. We demonstrate via trace-based simulations the superior performance of the robustified version of a well-known heuristic algorithm based on model predictive control. [ABSTRACT FROM PUBLISHER]

Purpose – This paper proposes an improved algorithm to compute selective harmonics elimination pulse width modulation (SHEPWM) angles, based on the Newton-Raphson (NR) iteration for cascaded multilevel inverter (CMI). Design/methodology/approach – Newton Raphson (NR) is a very popular numerical method for transcendental equations that lack analytical solutions. It has been successfully used to compute the angles for selective harmonics elimination pulse width modulation (SHEPWM) schemes. Despite its effectiveness, NR has not been used for SHEPWM with cascaded multilevel inverter (CMI) structure with equal and non-equal DC voltage sources. It is known that for CMI, inappropriate selection of initial angles causes long-iteration time and possibly non-convergence takes place. The computational difficulty is compounded by the fact that the SHEPWM switching angles need to be correctly sequenced, i.e. each angle must be assigned to the correct output voltage level of the CMI. In this work, an attempt is made to reduce the iteration time and to resolve the non-convergence problem. The main idea is to relax the switching angle constraint by placing the switching angle sequencing outside the main loop of NR iteration. This allows for the program to run more freely and able to generate more possible solutions for the switching angles. Then these angles are selected to fulfill the requirements of multilevel sequencing. The performance of the proposed technique will be compared with the standard NR for CMI with equal and non-equal DC sources. The latter case is quite common for CMI with renewable energy applications because the sources normally have different voltage levels. Findings – Using MATLAB simulation, it will be shown that using this scheme, accurate SHEPWM angles can be achieved for a wide range of fundamental components. Furthermore, significant reduction in iteration time to compute the SHEPWM switching angles is achieved. Originality/value – This paper proposes an improved algorithm to compute SHEPWM angles based on NR iteration. [ABSTRACT FROM AUTHOR]