Andres Cortés

Self-Triggered Best-Response Dynamics for Continuous Games

Motivated by the development of novel and practically implementable coordination algorithms for multi-agent systems, here we investigate the adaptation of classical best-response dynamics by means of self-triggered communications. First, we show that, if the best response dynamics is defined for a continuous-action-space potential game, convergence towards the Nash Equilibria set is guaranteed under continuity on utilities and component-wise pseudo-concavity of the potential function. Then, we modify the best-response dynamics to account for more economic self-triggered communication strategies while ensuring convergence to the equilibrium set. The proposed algorithm is then analyzed in the framework of hybrid systems theory.

A hierarchical algorithm for optimal plug-in electric vehicle charging with usage constraints

We present a hierarchical offline coordination algorithm for charging of Plug-in Electric Vehicles (PEVs), in which PEVs aim to optimally charge their batteries, subject to usage constraints along the day. With this algorithm, each PEV adjusts its charging strategy according to the price information, which is provided by an aggregator, while usage schedule constraints are respected at every iteration. A non-anonymous version of the algorithm is able to operate under communication failures. Both versions of the algorithm are proven to converge to the set of optimal solutions of the charging problem. This solution is optimal in the sense that it minimizes the cost of the consumed energy by both PEV and non-PEV loads. The solution has a valley-filling profile, since it leads to a configuration where PEVs aim to charge at low demand hours, minimizing, if possible, load peaks that are known to degrade the performance of power systems. In order to show convergence, we present an invariance result for difference inclusions, which works under a set of assumptions where LaSalle invariance principle does not apply. The algorithm performance is demonstrated throughout simulations.

Integration of PV generation and storage on power distribution systems using MPC

This paper presents the implementation of a Model Predictive Control (MPC) strategy for integration of solar PV generation with batteries on an active power distribution system, i.e. micro-grid. Here, the discrete-time finite-horizon optimal control problem associated to the MPC is presented as a non- convex optimization problem. Then, this control problem is solved by utilization of a convexification approach in an efficient approach. To test the performance of the proposed algorithm, a testbed is designed by endowing the IEEE37 test feeder with PV generation and storage capacities. Performance evaluation is carried out for different optimization horizons, different PV penetration, and solar forecasting error.

Optimal plug-in electric vehicle charging with schedule constraints

This paper proposes a decentralized algorithm that allows a group of Plug-in Electric Vehicles (PEVs) to arrive at an optimal strategy to charge their batteries during the day. By communicating repeatedly with an energy coordinator, the PEVs adjust their battery-charging plans by means of a price-feedback signal that accounts for the aggregated demand. The algorithm allows PEVs to adjust their plan simultaneously while respecting schedule constraints at every iteration. The collective strategy is optimal in that it minimizes the overall price of the supplied energy and leads to an off-peak utilization of the grid. The algorithm is proven to converge to a solution by means of nonlinear analysis tools of discrete-time systems. In order to show convergence, we present a refinement of the LaSalle invariance principle for discrete-time systems. Simulations demonstrate the proficiency of the algorithm in two particular scenarios.

Self-triggered best-response dynamics for mobile sensor deployment

The coordination of large numbers of autonomous agents has lead to the development of novel theoretical tools for the analysis and design of practical control algorithms with performance guarantees. Aligned with this research, this paper investigates the adaptation of classical best-response dynamics to achieve coverage control by a mobile sensor network subject to communication constraints. To do this, we first formulate a 1-D deployment scenario as a continuous-time-space potential game with a componentwise concave potential function. Making use of the stability theory for non-smooth dynamical systems, we characterize how the set-valued, best-response dynamics can converge to the set of Nash equilibria under some general conditions. This allows us to guarantee that sensor trajectories converge toward positions that maximize the covered area. We then modify the best-response dynamics to account for a self-triggered communication strategy that decreases the multi-agent communication effort while ensuring convergence to the equilibrium set. Finally, we present some simulations that demonstrate the performance of the proposed strategy.

A hierarchical demand-response algorithm for optimal vehicle-to-grid coordination

We propose an algorithm to deal with the problem of decentralized coordination of charging/discharging of a large population of plug-in electric vehicles (PEVs). We introduce a framework in which the power grid is modeled as an undirected rooted tree. The root of the tree represents the generation/transmission side of the system and the leaves represent PEVs. Intermediate nodes represent congestible elements on the distribution side (e.g., transformers), which have a bound on the demand they can attend. In the proposed algorithm, the root generates a control signal based on the price per unit of power according to the demand for each time. Intermediate nodes modify the control signal according to the difference between the demand they take care of, and its capacity upper bound. PEVs update their charging/discharging strategies according to this pricing signal. Simulations demonstrate the algorithm performance for a particular example.

A Projection-Based Decomposition Algorithm for Distributed Fast Computation of Control in Microgrids

We present a novel algorithm for the computation of optimal predictive storage and reactive power control in microgrids operating in grid-tied mode. This algorithm is based on the dual decomposition method, but local constraints are handled by means of primal projections. The use of projections significantly increases the speed of convergence of the approach with respect to the dual decomposition algorithm, which uses dual variables for the local constraints of the problem. Convergence of the algorithm to an optimizer is shown for a general class of quadratic programs, which includes a storage and reactive power control problem. In addition, a distributed implementation of the algorithm which is based on the Jacobi overrelaxation is presented. Simulations compare the algorithm performance with that of a purely dual decomposition approach over a set of standard distribution feeder test cases acting as grid-connected microgrid proxies.

Hierarchical management of demand response events with on/off loads

A suboptimal hierarchical approach for the management of demand response events (DRE) is proposed. We introduce a DRE model that explicitly accounts for on/off loads and leverages the inherent storage capacity of thermal loads provided by their inertia. Our approach can compute in a tractable time a feasible suboptimal solution to the DRE management problem, while user privacy is preserved. We present an MPC implementation of our approach and show the performance of our strategy in different DRE simulation scenarios.