In recent years complex networks have gained in-
creasing attention in different fields of science and engineering.
The problem of controlling these networks is an interesting and
challenging problem to investigate. In this paper we look at the
controllability problem focusing on the energy needed for the
control. Precisely not only we want to analyze whether a network
can be controlled, but we also want to establish whether the
control can be performed using a limited amount of energy.
We restrict our study to irreducible and (marginally) stable
networks and we find that the leading right and left eigenvectors
of the network matrix play a crucial role in this analysis.
Interestingly, our results suggest the existence of a connection
between controllability and network centrality, a well-known
concept in network science. In case the network is reversible, the
latter connection involves the PageRank, an extensively studied
type of centrality measure. Finally, the proposed results are
applied to examples concerning random graphs.

We consider the problem of optimal reactive power compensation for the minimization of power distribution losses in a smart microgrid. We first propose an approximate model for the power distribution network, which allows us to cast the problem into the class of convex quadratic, linearly constrained, optimization problems. Then, we design a randomized, gossip-like optimization algorithm based on that model. We show how a distributed approach is possible, where agents have a partial knowledge of the problem parameters and state, and can only perform local measurements. For the proposed algorithm, we provide conditions for convergence together with an analytic characterization of the convergence speed. The analysis shows that the best performance can be achieved when we command cooperation among agents that are neighbors in the electric topology. Numerical simulations are included to validate the proposed model and to confirm the analytic results about the performance of the proposed algorithm.

We consider the problem of commanding the electronic power interfaces of the microgenerators in a low voltage microgrid for the task of optimal reactive power compensation. In this work, we analyze the convergence of the strategy proposed by Tenti et al. in 2012. The proof of convergence gives some additional insight on the behavior of the algorithm and allows the characterization of its rate of convergence as a function of the microgrid parameters.

In this paper we address the problem of exploitingthe distributed energy resources (DER) available in a smartmicro-grid to minimize the power distribution losses via optimalreactive power compensation. Due to their typically smallsize, the amount of reactive power provided by each micro-generator is subject to tight saturation constraints. As aconsequence, it might be impossible to achieve convergence tothe global optimum based on algorithms that rely on short-range, gossip-type communication. We therefore propose arandomized multi-hop protocol that guarantees convergence ofthe distributed optimization algorithm also when only short-range communications are possible, at the expense of someadditional communication overhead.

We considered the problem of minimizing reactive power flows in a smart microgrid. First we modeled this problem as a linearly constrained quadratic optimization, in which the decision variables are the amount of reactive power that compensators inject into the network. Then, we designed a distributed algorithm in which agents are clustered into overlapping subsets, according to a given communication graph that allows them to coordinate and to exchange information. At each time, one subset is triggered, and agents belonging to it update their states in order to minimize the reactive power flows on the grid. We showed that, by sensing the network at their points of connection, agents can perform this minimization with just the data that they can gather from the other agents belonging to the subset. We characterized convergence of this algorithm in term of conditions on the subsets and on the randomized triggering sequence. Moreover, we studied the rate of convergence, obtaining also a convenient upper bound. We finally analyzed the rate of convergence for some specic topologies of the grid and for some choices of the agents communication topologies.

We consider the problem of optimal reactive power compensation for the minimization of power distribution losses in a smart microgrid. We first propose an approximate model for the power distribution network, which allows us to cast the problem into the class of convex quadratic, linearly constrained, optimization problems.

We also show how this model provides the tools for a distributed approach, in which agents have a partial knowledge of the problem parameters and state, and can only perform local measurements.

Then, we design a randomized, gossip-like optimization algorithm, providing conditions for convergence together with an analytical characterization of the convergence speed. The analysis shows that the best performance can be achieved when we command cooperation among agents that are neighbors in the smart microgrid topology. Numerical simulations are included to validate the proposed model and to confirm the analytical results about the performance of the proposed algorithm.

We consider a distributed system of N agents, on which we define a quadratic optimization problem subject to a linear equality constraint. We assume that the nodes can estimate the gradient of the cost function by measuring the steady state response of the system. Even if the cost function cannot be decoupled into individual terms for the agents, and the linear constraint involves the whole system state, we are able to design a distributed, gradient-driven, algorithm, for the solution of the optimization problem. This algorithm belongs to the class of quasi-Newton methods and requires minimal knowledge of the system to behave fairly well. We proved finite time convergence of the algorithm in its centralized version, and we designed its distributed implementation in the case in which a communication graph is given. In this latter case, the tool of average consensus results to be fundamental for the distribution of the algorithm. As a testbed for the proposed method, we consider the problem of optimal distributed reactive power compensation in smart microgrids.

In this paper a distributed clock synchronization algorithm is proposed. The algorithm requires gossip asynchronous communication between the nodes of the network, and because of its proportional-integral (PI) structure it is able to compensate both initial offsets and different clock speeds. Convergence of the algorithm is proved and analysed with respect to the controller parameter, while scalability issues are addressed by simulations.