On the Outage Probability of Localization in Randomly Deployed Wireless Networks

This paper analyzes the localization outage probability (LOP), the probability that the position error exceeds a given threshold, in randomly deployed wireless networks. Two typical cases are considered: a mobile agent uses all the neighboring anchors or select the best pair of anchors for self-localization. We derive the exact LOP for the former case and tight bounds for the LOP for the latter case. The comparison between the two cases reveals the advantage of anchor selection in terms of LOP versus complexity tradeoff, providing insights into the design of efficient localization systems

Differential Privacy of Aggregated DC Optimal Power Flow Data

We consider the problem of privately releasing aggregated network statistics obtained from solving a DC optimal power flow (OPF) problem. It is shown that the mechanism that determines the noise distribution parameters are linked to the topology of the power system and the monotonicity of the network. We derive a measure of "almost" monotonicity and show how it can be used in conjunction with a linear program in order to release aggregated OPF data using the differential privacy framework.Comment: Accepted by 2019 American Control Conference (ACC

A Note on Branch Flow Models with Line Shunts

When the shunt elements in the Π circuit line model are assumed zero, it has been proved that branch flow models are equivalent to bus injection models and that the second-order cone relaxation of optimal power flow problems on a radial network is exact under certain conditions. In this note we propose a branch flow model that includes nonzero line shunts and prove that the equivalence and the exactness of relaxation continue to hold under essentially the same conditions as for zero shunt elements

A Note on Branch Flow Models with Line Shunts

When the shunt elements in the Pi circuit line model are assumed zero, it has been proved that branch flow models are equivalent to bus injection models and that the second-order cone relaxation of optimal power flow problems on a radial network is exact under certain conditions. In this note we propose a branch flow model that includes nonzero line shunts and prove that the equivalence and the exactness of relaxation continue to hold under essentially the same conditions as for zero shunt elements.Comment: 6 pages, 1 figur

An Energy Sharing Game with Generalized Demand Bidding: Model and Properties

This paper proposes a novel energy sharing mechanism for prosumers who can produce and consume. Different from most existing works, the role of individual prosumer as a seller or buyer in our model is endogenously determined. Several desirable properties of the proposed mechanism are proved based on a generalized game-theoretic model. We show that the Nash equilibrium exists and is the unique solution of an equivalent convex optimization problem. The sharing price at the Nash equilibrium equals to the average marginal disutility of all prosumers. We also prove that every prosumer has the incentive to participate in the sharing market, and prosumers' total cost decreases with increasing absolute value of price sensitivity. Furthermore, the Nash equilibrium approaches the social optimal as the number of prosumers grows, and competition can improve social welfare.Comment: 16 pages, 7 figure

Sufficient Conditions for Exact Semidefinite Relaxation of Optimal Power Flow in Unbalanced Multiphase Radial Networks

This paper proves that in an unbalanced multi-phase network with a tree topology, the semidefinite programming relaxation of optimal power flow problems is exact when critical buses are not adjacent to each other. Here a critical bus either contributes directly to the cost function or is where an injection constraint is tight at optimality. Our result generalizes a sufficient condition for exact relaxation in single-phase tree networks to tree networks with arbitrary number of phases.Comment: Accepted by 2019 Conference on Decision and Control (CDC