John W. Simpson-Porco

John W. Simpson-Porco, Florian Dörfler, Francesco Bullo

Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers can be cast as a Kuramoto model of phase-coupled oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters and loads. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and locally exponentially stable. We present a selection of controller gains leading to a desirable sharing of power among the inverters, and specify the set of loads which can be serviced without violating given actuation constraints. Moreover, we propose a distributed integral controller based on averaging algorithms which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it maintains the power sharing properties of the primary droop controller. Our results hold without assumptions on identical line characteristics or voltage magnitudes.

John-Paolo Casasanta, John W. Simpson-Porco

The concept of matrix D-stability plays an important role in applications, ranging from economic and biological system models to decentralized control. Here we provide necessary and sufficient Lyapunov-type conditions for the robust (block) D-stability property. We leverage this characterization as part of a novel Lyapunov analysis of decentralized integral control for MIMO LTI systems, providing sufficient conditions guaranteeing stability under low-gain and under arbitrary connection and disconnection of individual control loops.

Xiangyu Zou, Amir Reza Nikzad, Ilyas Farhat et al.

Power system restoration following blackouts must ensure frequency stability throughout the recovery process. This paper proposes a frequency-constrained mixed-integer linear programming (MILP) framework for black-start restoration planning in transmission systems with synchronous machines and energy storage systems. To prevent excessive frequency deviations caused by restorative actions, a frequency nadir prediction method is developed for power systems with energy storage system (ESS) integration and incorporated into a multiperiod optimization framework. The formulation ensures that frequency deviations resulting from restorative actions remain within prescribed safe limits. Furthermore, the presented framework leverages ESSs to enhance frequency security and recovery speed. Case studies on a modified IEEE 9-bus system demonstrate that the computed restoration plan maintains frequency security, as validated through MATLAB and PSS/E simulations, while reducing restoration time through ESS coordination.