Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

A Multiple Criteria Utility-based Approa h for the Unit Commitment with Wind Power and Pumped Storage Hydro

The integration of wind power in eletricity generation brings new challenges to unit commitment due to the random nature of wind speed. For this particular optimisation problem, wind uncertainty has been handled in practice by means of conservative stochastic scenario-based optimisation models, or through additional operating reserve settings. However, generation companies may have different attitudes towards operating costs, load curtailment, or waste of wind energy, when considering the risk caused by wind power variability. Therefore, alternative and possibly more adequate approaches should be explored. This work is divided in two main parts. Firstly we survey the main formulations presented in the literature for the integration of wind power in the unit commitment problem (UCP) and present an alternative model for the wind-thermal unit commitment. We make use of the utility theory concepts to develop a multi-criteria stochastic model. The objectives considered are the minimisation of costs, load curtailment and waste of wind energy. Those are represented by individual utility functions and aggregated in a single additive utility function. This last function is adequately linearised leading to a mixed-integer linear program (MILP) model that can be tackled by general-purpose solvers in order to find the most preferred solution. In the second part we discuss the integration of pumped-storage hydro (PSH) units in the UCP with large wind penetration. Those units can provide extra flexibility by using wind energy to pump and store water in the form of potential energy that can be generated after during peak load periods. PSH units are added to the first model, yielding a MILP model with wind-hydro-thermal coordination. Results showed that the proposed methodology is able to reflect the risk profiles of decision makers for both models. By including PSH units, the results are significantly improved.