We address a class of Nash games with nonconvex coupling constraints for which we define a novel notion of local equilibrium, here named local generalized Nash equilibrium (LGNE). Our first technical contribution is to show the stability in the game theoretic sense of these equilibria on a specific local subset of the original feasible set. Remarkably, we show that the proposed notion of local equilibrium can be equivalently formulated as the solution of a quasi-variational inequality with equal Lagrange multipliers. Next, under the additional proximal smoothness assumption of the coupled feasible set, we define conditions for the existence and local uniqueness of a LGNE. To compute such an equilibrium, we propose two discrete-time dynamics, or fixed-point iterations implemented in a centralized fashion. Our third technical contribution is to prove convergence under (strongly) monotone assumptions on the pseudo- gradient mapping of the game and proximal smoothness of the coupled feasible set. Finally, we apply our theoretical results to a noncooperative version of the optimal power flow control problem.

This paper focuses on the control of microgrids where both gas and electricity are provided to the final customer, i.e., multi-carrier microgrids. Hence, these microgrids include thermal and electrical loads, renewable energy sources, energy storage systems, heat pumps, and combined heat and power units. The parameters characterizing the multi-carrier microgrid are subject to several disturbances, such as fluctuations in the provision of renewable energy, variability in the electrical and thermal demand, and uncertainties in the electricity and gas pricing. With the aim of accounting for the data uncertainties in the microgrid, we propose a Robust Model Predictive Control (RMPC) approach whose goal is to minimize the total economical cost, while satisfying comfort and energy requests of the final users. In the related literature various RMPC approaches have been proposed, focusing either on electrical or on thermal microgrids. Only a few contributions have addressed the robust control of multi-carrier microgrids. Consequently, we propose an innovative RMPC algorithm that employs on an uncertainty set-based method and that can provide better performance compared with deterministic model predictive controllers applied to multi-carrier microgrids. With the aim of mitigating the conservativeness of the approach, we define suitable robustness factors and we investigate the effects of such factors on the robustness of the solution against variations of the uncertain parameters. We show the effectiveness of the proposed RMPC approach by applying it to a realistic residential multi-carrier microgrid and comparing the obtained results with the ones of a baseline robust method.

In this article, we propose a distributed demand-side management (DSM) approach for smart grids taking into account uncertainty in wind power forecasting. The smart grid model comprehends traditional users as well as active users (prosumers). Through a rolling-horizon approach, prosumers participate in a DSM program, aiming at minimizing their cost in the presence of uncertain wind power generation by a game theory approach. We assume that each user selfishly formulates its grid optimization problem as a noncooperative game. The core challenge in this article is defining an approach to cope with the uncertainty in wind power availability. We tackle this issue from two different sides: by employing the expected value to define a deterministic counterpart for the problem and by adopting a stochastic approximated framework. In the latter case, we employ the sample average approximation (SAA) technique, whose results are based on a probability density function (PDF) for the wind speed forecasts. We improve the PDF by using historical wind speed data, and by employing a control index that takes into account the weather condition stability. Numerical simulations on a real data set show that the proposed stochastic strategy generates lower individual costs compared to the standard expected value approach.

Railways are a well-recognized sustainable transportation mode that helps to satisfy the continuously growing mobility demand. However, the management of railway traffic in large-scale networks is a challenging task, especially when both a major disruption and various disturbances occur simultaneously. We propose an automatic rescheduling algorithm for real-time control of railway traffic that aims at minimizing the delays induced by the disruption and disturbances, as well as the resulting cancellations of train runs and turn-backs (or short-turns) and shuntings of trains in stations. The real-time control is based on the Model Predictive Control (MPC) scheme where the rescheduling problem is solved by mixed integer linear programming using macroscopic and mesoscopic models. The proposed resolution algorithm combines a distributed optimization method and bi-level heuristics to provide feasible control actions for the whole network in short computation time, without neglecting physical limitations nor operations at disrupted stations. A realistic simulation test is performed on the complete Dutch railway network. The results highlight the effectiveness of the method in properly minimizing the delays and rapidly providing feasible feedback control actions for the whole network.

In this paper, we consider a smart grid where users behave selfishly, aiming at minimizing cost in the presence of uncertain wind power availability. We adopt a demand side management (DSM) model, where active users (so-called prosumers) have both private generation and local storage availability. These prosumers participate to the DSM strategy by updating their energy schedule, seeking to minimize their local cost, given their local preferences and the global grid constraints. The energy price is defined as a function of the aggregate load and the wind power availability. We model the resulting problem as a non-cooperative Nash game and propose a semi-decentralized algorithm to compute an equilibrium. To cope with the uncertainty in the wind power, we adopt a rolling-horizon approach, and in addition we use a stochastic optimization technique. We generate several wind power production scenarios from a defined probability density function (PDF), determining an approximate stochastic cost function. Simulations results on a real dataset show that the proposed approach generates lower individual costs compared to a standard expected value approach.

We present a Robust Model Predictive Control (RMPC) approach for multi-carrier microgrids, i.e., microgrids based on gas and electricity. The microgrid that we consider includes thermal loads, electrical loads, renewable energy sources, energy storage systems, heat pumps, and combined heat and power plants. Moreover, the system under control is affected by several external disturbances, e.g., uncertainty in renewable energy generation, electrical and thermal demand. The goal of the controller is to minimize the overall economical cost and the energy exchange with the main grid, while guaranteeing comfort. Whereas several RMPC methods have been developed for electrical or thermal microgrids, little or no attention has been devoted to robust control of multi-carrier microgrids. Therefore, we consider a novel RMPC algorithm that can improve the performance with respect to classical deterministic Model Predictive Control (Det-MPC) controllers in the context of multi-carrier microgrids. The RMPC method relies on the box-uncertainty-set robust optimization, where uncertain parameters are assumed to take their values from different intervals independently. The RMPC approach is able to successfully satisfy the constraints even in the presence of the mentioned disturbances. Simulations of a realistic residential case study show the benefits of the proposed approach with respect to Det-MPC controllers.

The railway sector is currently experiencing a rapid evolution from fully manual towards automatic rail traffic control systems, due to the growth of transport demand and networks complexity. One of the main issues is to automatically and effectively reschedule the railway traffic in case of unexpected events, thus avoiding dramatic drops in the system performance. In the literature, the majority of contributions aims at automatically minimizing the train delays or optimizing the railway system performance (e.g., energy consumption). However, such strategies are not always able to ensure satisfaction of passengers that in many cases experience the side-effects of the rescheduling actions (e.g., cancellation of train runs, cancellation of coincidences, rerouting of trains, etc.). In this paper, we propose a demandoriented train rescheduling automatic technique that minimizes simultaneously the train delays and the discomfort perceived by passengers. When an unexpected event occurs, the rescheduling problem is set, based on the current state and nominal timetable of the system and its passengers flows. Hence, the problem is solved providing the control actions necessary to minimize both the delays and number of passengers subject to severe side-effects. The rescheduling is here formulated as a mixed integer linear programming problem, where the operating rules of the railway network are represented by linear equality and inequality constraints, while the objective is a linear function to be minimized. The possible control actions consist in re-timing the rail traffic and modifying the connections among lines. The proposed technique is preliminarily evaluated on a test case and a discussion is provided on the outcomes.

The real-time rescheduling of railway traffic in case of unexpected events is a challenging task. This is mainly due to the complexity of the railway service, which has to ensure safety, punctuality, and efficiency to customers by respecting timetable, framework, and resources constraints. Most of the available researches focus on short delays (i.e., disturbances). Approaches typically rely on simplified macroscopic models for large-scale systems or detailed microscopic models for one or a few lines, due to the long computation time required for solving the rescheduling problem. Only a small number of works consider rescheduling in case of long delays (i.e., disruptions) and all of them are also based on either a macroscopic or a microscopic model. This research focuses on disruptions and aims at filling the gap between macroscopic and microscopic modelling by proposing an innovative bi-level rescheduling algorithm based on a mesoscopic Mixed Integer Linear Programming (MILP) model. The technique allows obtaining a feasible rescheduled timetable in a short computation time respecting not only timetable and safety constraints (typical of macroscopic models) but also capacity and ordering constraints for the disrupted stations (typical of microscopic models). The bi-level algorithm first solves the macroscopic MILP rescheduling problem and then, considering the cancellation and non-admissible platform assignments results, it solves a mesoscopic MILP rescheduling problem. This allows to significantly reduce the search space and consequently the computation time. The method is tested for the rescheduling of the Dutch railway traffic in case of a full blockade between two consecutive stations.