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This paper summarizes a suite of methods that have recently been proposed for the control and synchronization of parallel single- and three-phase voltage source power electronics inverters. Inspired by the phenomenon of synchronization in networks of coupled oscillators, the premise of the proposed Virtual Oscillator Control (VOC) is to control an inverter(More)
—A framework to integrate reliability and performance analysis of grid-tied photovoltaic (PV) systems is formulated using Markov reward models (MRM). The framework allows the computation of performance metrics such as capacity and energy yield, and reliability metrics such as availability. The paper also provides an analytical method to compute the(More)
—Sufficient conditions are derived for the global asymptotic synchronization of a class of identical nonlinear oscillators coupled through a linear time-invariant network. In particular, we focus on systems where oscillators are connected to a common node through identical branch impedances. For such networks, it is shown that the synchronization condition(More)
—Sufficient conditions are derived for global asymp-totic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to settings where: i) the nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and(More)
—A control scheme is proposed for an islanded, low-inertia, three-phase, inverter-based microgrid with a high penetration of photovoltaic (PV) generation resources. The output of each inverter is programmed to emulate the dynamics of a nonlinear oscillator. The virtual oscillators within each controller are implicitly coupled through the physical electrical(More)
—We propose a framework to study the impact of stochastic active/reactive power injections on power system dynamics with a focus on time scales involving electromechan-ical phenomena. In this framework the active/reactive power injections evolve according to a continuous-time Markov chain (CTMC), while the power system dynamics are described by the standard(More)
This paper explores solutions to linearized power-flow equations with bus-voltage phasors represented in rectangular coordinates. The key idea is to solve for complex-valued perturbations around a nominal voltage profile from a set of linear equations that are obtained by neglecting quadratic terms in the original nonlinear power-flow equations. We prove(More)
—Efforts to ensure reliable operation of existing low-voltage distribution systems with high photovoltaic (PV) generation have focused on the possibility of inverters providing ancillary services such as active power curtailment and reactive power compensation. Major benefits include the possibility of averting overvoltages, which may otherwise be(More)
A common concern with Markov reliability and reward models is that model parameters, i.e., component failure and repair rates, are seldom perfectly known. This paper proposes a numerical method based on the Taylor series expansion of the underlying Markov chain stationary distribution (associated to the reliability and reward models) to propagate parametric(More)
In this paper, we propose a framework to analyze Markov reward models, which are commonly used in system performability analysis. The framework builds on a set of analytical tools developed for a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS). The state space of an SHS is comprised of: i) a discrete state that describes the(More)