Metastability-Containing Circuits

In digital circuits, metastability can cause deteriorated signals that neither are logical 0 or logical 1, breaking the abstraction of Boolean logic. Unfortunately, any way of reading a signal from an unsynchronized clock domain or performing an analog-to-digital conversion incurs the risk of a metastable upset; no digital circuit can deterministically avoid, resolve, or detect metastability (Marino, 1981). Synchronizers, the only traditional countermeasure, exponentially decrease the odds of maintained metastability over time. Trading synchronization delay for an increased probability to resolve metastability to logical 0 or 1, they do not guarantee success. We propose a fundamentally different approach: It is possible to contain metastability by fine-grained logical masking so that it cannot infect the entire circuit. This technique guarantees a limited degree of metastability in---and uncertainty about---the output. At the heart of our approach lies a time- and value-discrete model for metastability in synchronous clocked digital circuits. Metastability is propagated in a worst-case fashion, allowing to derive deterministic guarantees, without and unlike synchronizers. The proposed model permits positive results and passes the test of reproducing Marino's impossibility results. We fully classify which functions can be computed by circuits with standard registers. Regarding masking registers, we show that they become computationally strictly more powerful with each clock cycle, resulting in a non-trivial hierarchy of computable functions

Advanced Modeling, Design, and Control of ac-dc Microgrids

An interconnected dc grid that comprises resistive and constant-power loads (CPLs) that is fed by Photovoltaic (PV) units is studied first. All the sources and CPLs are connected to the grid via dc-dc buck converters. Nonlinear behavior of PV units in addition to the effect of the negative-resistance CPLs can destabilize the dc grid. A decentralized nonlinear model and control are proposed where an adaptive output-feedback controller is employed to stabilize the dc grid with assured stability through Lyapunov stability method while each converter employs only local measurements. Adaptive Neural Networks (NNs) are utilized to overcome the unknown dynamics of the dc-dc converters at Distributed Energy Resources (DERs) and CPLs and those of the interconnected network imposed on the converters. Additionally, the use of the output feedback control makes possible the utilization of other measured signals, in case of loss of main signal, at the converter location and creates measurement redundancy that improves reliability of the dc network. The switching between measurement signals of different types are performed through using the NNs without the need to further tuning. Then, in a small-scale ac grid, PV-based Distributed Generation (DG) units, including dc/dc converters and inverters, are controlled such that mimic a synchronous generator behavior. While other control schemes such as Synchronverters are used to control the inverter frequency and power at a fixed dc link voltage, the proposed approach considers both the dc-link voltage and the inverter ac voltage and frequency regulation. The dc-link capacitor stores kinetic energy similar to the rotor of a synchronous generator, providing inertia and contributes to the system stability. Additionally, a reduced Unified Power Flow Controller (UPFC) structure is proposed to enhance transient stability of small-scale micro grids. The reduced UPFC model exploits dc link of the DG unit to generate appropriate series voltage and inject it to the power line to enhance transient stability. It employs optimal control to ensure that the stability of the system is realized through minimum cost for the system. A neural network is used to approximate the cost function based on the weighted residual method

A pulsed Sagnac source of narrowband polarization-entangled photons

We demonstrate pulsed operation of a bidirectionally pumped polarization Sagnac interferometric down-conversion source and its generation of narrowband, high-visibility polarization-entangled photons. Driven by a narrowband, mode-locked pump at 390.35 nm, the phase-stable Sagnac source with a type-II phase-matched periodically poled KTiOPO$_4$ crystal is capable of producing 0.01 entangled pair per pulse in a 0.15-nm bandwidth centered at 780.7 nm with 1 mW of average pump power at a repetition rate of 31.1 MHz. We have achieved a mean photon-pair generation rate of as high as 0.7 pair per pulse, at which multi-pair events dominate and significantly reduce the two-photon quantum-interference visibility. For low generation probability $\alpha$, the reduced visibility $V=1-\alpha$ is independent of the throughput efficiency and of the polarization analysis basis, which can be utilized to yield an accurate estimate of the generation rate $\alpha$. At low $\alpha$ we have characterized the source entanglement quality in three different ways: average quantum-interference visibility of 99%, the Clauser-Horne-Shimony-Holt $S$ parameter of $2.739 \pm 0.119$, and quantum state tomography with 98.85% singlet-state fidelity. The narrowband pulsed Sagnac source of entangled photons is suitable for use in quantum information processing applications such as free-space quantum key distribution.Comment: 10 pages, 6 figures, accepted for publication in Phys. Rev.

Stability and Frequency Regulation of Inverters with Capacitive Inertia

In this paper, we address the problem of stability and frequency regulation of a recently proposed inverter. In this type of inverter, the DC-side capacitor emulates the inertia of a synchronous generator. First, we remodel the dynamics from the electrical power perspective. Second, using this model, we show that the system is stable if connected to a constant power load, and the frequency can be regulated by a suitable choice of the controller. Next, and as the main focus of this paper, we analyze the stability of a network of these inverters, and show that frequency regulation can be achieved by using an appropriate controller design. Finally, a numerical example is provided which illustrates the effectiveness of the method

Grid-Forming Converter Control Method to Improve DC-Link Stability in Inverter-Based AC Grids

As renewable energy sources with power-electronic interfaces become functionally and economically viable alternatives to bulk synchronous generators, it becomes vital to understand the behavior of these inverter-interfaced sources in ac grids devoid of any synchronous generation, i.e. inverter-based grids. In these types of grids, the inverters need to operate in parallel in grid-forming mode to regulate and synchronize their output voltage while also delivering the power required by the loads. It is common practice, therefore, to mimic the parallel operation control of the very synchronous generators that these inverter-based sources are meant to replace. This practice, however, is based on impractical assumptions and completely disregards the key differences between synchronous machines and power electronic inverters, as well as the dynamics of the dc source connected to the inverter. This dissertation aims to highlight the shortcomings of conventional controllers and derive an improved grid-forming inverter controller that is effective in parallel ac operation without sacrificing dc-link stability. This dissertation begins with a basis for understanding the control concepts used by grid-forming inverters in ac grids and exploring where existing ideas and methods are lacking in terms of efficient and stable inverter control. The knowledge gained from the literature survey is used to derive the requirements for a grid-forming control method that is appropriate for inverter-based ac grids. This is followed by a review and comparative analysis of the performance of five commonly used control techniques for grid-forming inverters, which reveal that nested loop controllers can have a destabilizing effect under changing grid conditions. This observation is further explored through an impedance-based stability analysis of single-loop and nested-loop controllers in grid-forming inverters, followed by a review of impedance-based analysis methods that can be used to assess the control design for grid-forming inverters. An improved grid-forming inverter controller is proposed with a demonstrated ability to achieve both dc-link and ac output stability with proportional power-sharing. This dissertation ends with a summary of the efforts and contributions as well as ideas for future applications of the proposed controller

Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation

This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters

Measurements, Models, Systems and Design

531 s.

A Novel Stochastic Predictive Stabilizer for DC Microgrids Feeding CPLs

In this work, a novel nonlinear approach is proposed for the stabilization of microgrids (MGs) with constant power loads (CPLs). The proposed method is constructed based on the incorporation of a pseudo-extended Kalman filter (EKF) into stochastic nonlinear model predictive control (MPC). In order to achieve high-performance and optimal control in dc MGs, estimating the instantaneous power flow of the uncertain CPLs and the available power units is essential. Thus, by utilizing the advantages of the stochastic MPC and the pseudo-EKF, an effective control solution for the stabilization of dc islanded MGs with CPLs is established. This technique develops a constrained controller for practical application to handle the states and control input constraints explicitly; furthermore, as it estimates the current by using the pseudo-EKF, it is a current-senseless approach. As noisy measurements are taken into account for the state estimation, it leads to a less conservative control action rather than the classical robust MPC, whereas it guarantees the global asymptotic stability in the presence of noisy measurements and parameter uncertainty. To validate the performance of the proposed controller, the attained results are compared with state-of-the-art controllers. Furthermore, the implementability of the proposed method is validated using real-time simulations on dSPACE hardware