Abstract-Motivated by the power-grid-side challenges in the integration of electric vehicles, we propose a decentralized protocol for negotiating day-ahead charging schedules for electric vehicles. The overall goal is to shift the load due to electric vehicles to fill the overnight electricity demand valley. In each iteration of the proposed protocol, electric vehicles choose their own charging profiles for the following day according to the price profile broadcast by the utility, and the utility updates the price profile to guide their behavior. This protocol is guaranteed to converge, irrespective of the specifications (e.g., maximum charging rate and deadline) of electric vehicles. At convergence, the l2 norm of the aggregated demand is minimized, and the aggregated demand profile is as "flat" as it can possibly be. The proposed protocol needs no coordination among the electric vehicles, hence requires low communication and computation capability. Simulation results demonstrate convergence to optimal collections of charging profiles within few iterations.

The optimal power flow (OPF) problem determines power generation/demand that minimize a certain objective such as generation cost or power loss. It is nonconvex. We prove that, for radial networks, after shrinking its feasible set slightly, the global optimum of OPF can be recovered via a second-order cone programming (SOCP) relaxation under a condition that can be checked a priori. The condition holds for the IEEE 13-, 34-, 37-, 123-bus networks and two real-world networks, and has a physical interpretation.

Abstract-Motivated by the power-grid-side challenges in the integration of electric vehicles, we propose a decentralized protocol for negotiating day-ahead charging schedules for electric vehicles. The overall goal is to shift the load due to electric vehicles to fill the overnight electricity demand valley. In each iteration of the proposed protocol, electric vehicles choose their own charging profiles for the following day according to the price profile broadcast by the utility, and the utility updates the price profile to guide their behavior. This protocol is guaranteed to converge, irrespective of the specifications (e.g., maximum charging rate and deadline) of electric vehicles. At convergence, the l2 norm of the aggregated demand is minimized, and the aggregated demand profile is as "flat" as it can possibly be. The proposed protocol needs no coordination among the electric vehicles, hence requires low communication and computation capability. Simulation results demonstrate convergence to optimal collections of charging profiles within few iterations.

Distribution networks are usually multiphase and radial. To facilitate power flow computation and optimization, two semidefinite programming (SDP) relaxations of the optimal power flow problem and a linear approximation of the power flow are proposed. We prove that the first SDP relaxation is exact if and only if the second one is exact. Case studies show that the second SDP relaxation is numerically exact and that the linear approximation obtains voltages within 0.0016 per unit of their true values for the IEEE 13, 34, 37, 123-bus networks and a real-world 2065-bus network.

We propose an online algorithm for solving optimal power flow (OPF) problems on radial networks where the controllable devices continuously interact with the network that implicitly computes a power flow solution given a control action. Collectively the controllable devices and the network implement a gradient projection algorithm for the OPF problem in real time. The key design feature that enables this approach is that the intermediate iterates of our algorithm always satisfy power flow equations and operational constraints. This is achieved by explicitly exploiting the network to implicitly solve power flow equations for us in real time at scale. We prove that the proposed algorithm converges to the set of local optima and provide sufficient conditions under which it converges to a global optimum. We derive an upper bound on the suboptimality gap of any local optimum. This bound suggests that any local minimum is almost as good as any strictly feasible point. We explain how to greatly reduce the gradient computation in each iteration by using approximate gradient derived from linearized power flow equations. Numerical results on test networks, ranging from 42-bus to 1990-bus, show a great speedup over a second-order cone relaxation method with negligible difference in objective values. Index Terms-Branch flow model, distflow equations, interior point method, online optimization algorithm, optimal power flow (OPF). I. INTRODUCTION O PTIMAL power flow (OPF) is fundamental in power system operations as it underlies many applications such as economic dispatch, unit commitment, state estimation, stability and reliability assessment, volt/var control, demand response, etc. There has been a great deal of research on OPF since Carpentier's first formulation in 1962 [6]. An early solution appears in [11], [33] and extensive surveys can be found in e.g. [5], [7], [8], [16], [17], [23], [25]-[32]. Almost all algorithms in this literature are offline where one must wait till the iteration has converged to obtain a solution that can be applied to the network because the intermediate iterates of these algorithms do not satisfy power flow equations and therefore are not implementable. In this paper, we propose a different approach, motivated by the need to optimize the operation of a large network of distributed energy resources in distribution systems of the future, such as distributed wind and solar generations, Manuscript