Basilio Gentile

On reactive power flow and voltage stability in microgrids

This paper focuses on reactive power flow and voltage stability in electrical grids. We provide novel analytical understanding of the solutions to the classic nonlinear polynomial equations describing the decoupled reactive power flow. As of today, solutions to these equations can be found only via numerical methods. Yet an analytical understanding would be beneficial to the rigorous design of future electrical grids. This paper has two main contributions. First, for sufficiently high reference voltages, we guarantee the existence of a high-voltage solution for the reactive power flow equations and provide its approximate analytical expression. We bound the approximation error in terms of network topology and parameters. Second, we consider a recently proposed droop control strategy for voltage stabilization in a microgrid equipped with inverters. For sufficiently high reference voltages, we prove the existence and the exponential stability of a high-voltage fixed point of the closed-loop dynamics. We provide an approximate expression for this fixed point and bound the approximation error in terms of the network topology and parameters. Finally, we validate the accuracy of our approximations through numerical simulation of the IEEE 37 standard test case.

Distributed computation of generalized Nash equilibria in quadratic aggregative games with affine coupling constraints

We analyse deterministic aggregative games, with large but finite number of players, that are subject to both local and coupling constraints. Firstly, we derive sufficient conditions for the existence of a generalized Nash equilibrium, by using the theory of variational inequalities together with the specific structure of the objective functions and constraints. Secondly, we present a coordination scheme, belonging to the class of asymmetric projection algorithms, and we prove that it converges R-linearly to a generalized Nash equilibrium. To this end, we extend the available results on asymmetric projection algorithms to our setting. Finally, we show that the proposed scheme can be implemented in a decentralized fashion and it is suitable for the analysis of large populations. Our theoretical results are applied to the problem of charging a fleet of plug-in electric vehicles, in the presence of capacity constraints coupling the individual demands.

A Mean Field control approach for demand side management of large populations of Thermostatically Controlled Loads

This paper presents a Mean Field (MF) control approach for demand side management of large populations of flexible electric loads, such as electrical cooling/heating appliances, called Thermostatically Controlled Loads (TCLs). We model the switching dynamics of each individual TCL as the solution of a local optimization problem, characterized by individual cost function, comfort constraints, cooling/heating rates and external temperature. We consider that a central utility company broadcasts macroscopic incentives to steer the overall TCL population towards a convenient equilibrium, to avoid power demand peaks due to possible synchronization of the TCL duty cycles. To find such pricing schemes we propose an iterative algorithm where, at every step, a simple model-free feedback law is used to update the incentives, given the current aggregate demand of the TCL population only. The convergence of such algorithm is ensured for any population size, even in the presence of heterogeneous convex constraints. We illustrate our MF control approach via numerical analysis.