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Person# Eleni Stai

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Jean-Yves Le Boudec, Ehsan Mohammadpour, Eleni Stai

In time-sensitive networks, bounds on worst-case delays are typically obtained by using network calculus and assuming that flows are constrained by bit-level arrival curves. However, in IEEE TSN or IETF DetNet, source flows are constrained on the number of packets rather than bits. A common approach to obtain a delay bound is to derive a bit-level arrival curve from a packet-level arrival curve. However, such a method is not tight: we show that better bounds can be obtained by directly exploiting the arrival curves expressed at the packet level. Our analysis method also obtains better bounds when flows are constrained with g-regulation, such as the recently proposed Length-Rate Quotient rule. It can also be used to generalize some recently proposed network-calculus delay-bounds for a service curve element with known transmission rate.

Jean-Yves Le Boudec, Eleni Stai, Cong Wang

We study the admissibility problem in multivariate algebraic systems, such as ac electrical networks, where the power injection is quadratic in the state. The goal of such systems is to ensure that the state stays in some security set (e.g., magnitudes of nodal voltages and branch currents are within safety bounds). A common practice is to implicitly control the state by controlling the injection; a difficulty is that the number of states that correspond to a given injection can be zero or many. Further, the injection is subject to some uncertainty. The admissibility problem is whether it is possible to ensure that the state stays in the security set, given that the only available information is some uncertainty set that constrains the injection. We extend the recently proposed V-control theory, design a solution framework to test if a given uncertainty set is admissible, and develop a concrete method for ac electrical networks.

Jean-Yves Le Boudec, Eleni Stai, Cong Wang

We study a multiperiod optimal power flow (OPF) problem in unbalanced three-phase radial distribution networks with batteries. To address this problem, we first take the resistance-line battery model that treats lossy batteries by adding resistive lines and virtual buses. Then, we derive a linearization for the power flow equations, called generalized three-phase simplified DistFlow, which accounts for shunt elements. Also, it is exact at a freely chosen point while having globally good performance. Using it, we extend the heuristic iterative OPF algorithm, CoDistFlow, to unbalanced three-phase networks. At convergence, three-phase CoDistFlow gives a solution that satisfies the exact nonlinear power-flow equations and the exact security constraints. To theoretically guarantee the convergence of three-phase CoDistFlow, we develop the forced convergent three-phase CoDistFlow. Moreover, we show how to adapt the three-phase CoDistFlow to solve a scenario-based OPF in the presence of uncertainties, whereas other existing OPF solution methods may not offer this possibility. Finally, we perform evaluations on the IEEE 123-bus test feeder and comparisons with Ipopt.