This paper proposes decentralized resource-aware coordination schemes for solving network optimization problems defined by objective functions which combine locally evaluable costs with network-wide coupling components. These methods are well suited
for a group of supervised agents trying to solve an optimization problem under mild coordination requirements. Each agent has information on its local cost and coordinates with the network supervisor for information about the coupling term of the cost. The proposed approach is feedback-based and asynchronous by design, guarantees anytime feasibility, and ensures the asymptotic convergence of the network state to the desired optimizer. Numerical simulations on a power system example illustrate our results.
Distribution grids constitute complex networks of lines often times reconfigured to minimize losses, balance loads, alleviate faults, or for maintenance purposes. Topology monitoring becomes a critical task for optimal grid scheduling. While synchrop
hasor installations are limited in low-voltage grids, utilities have an abundance of smart meter data at their disposal. In this context, a statistical learning framework is put forth for verifying single-phase grid structures using non-synchronized voltage data. The related maximum likelihood task boils down to minimizing a non-convex function over a non-convex set. The function involves the sample voltage covariance matrix and the feasible set is relaxed to its convex hull. Asymptotically in the number of data, the actual topology yields the global minimizer of the original and the relaxed problems. Under a simplified data model, the function turns out to be convex, thus offering optimality guarantees. Prior information on line statuses is also incorporated via a maximum a-posteriori approach. The formulated tasks are tackled using solvers having complementary strengths. Numerical tests using real data on benchmark feeders demonstrate that reliable topology estimates can be acquired even with a few smart meter data, while the non-convex schemes exhibit superior line verification performance at the expense of additional computational time.
