We put forth a hybrid-computing solution to a class of constrained nonlinear optimization problems involving nonlinear cost and linear constraints. This is accomplished by realizing gradient-flow dynamics for a reformulated penalty program with a combination of operational amplifiers, discrete linear and nonlinear circuit elements, and a digital microcontroller. Convergence of the voltages of the circuit to stationary points of the original mathematical optimization problem, as well as local asymptotic stability of the equilibria, are established analytically. Leveraging numerical tools catering to delayed differential equations, design strategies to ensure the circuit is parametrized to be robust to delays attributable to the digital microcontroller are presented. Hardware results for a representative problem involving minimizing selected harmonics from a pulse-width modulated waveform validate the analytical developments.

Assessing set-membership and evaluating distances to the related set boundary are problems of widespread interest, and can often be computationally challenging. Seeking efficient learning models for such tasks, this paper deals with voltage stability margin prediction for power systems. Supervised training of such models is conventionally hard due to high-dimensional feature space, and a cumbersome label-generation process. Nevertheless, one may find related easy auxiliary tasks, such as voltage stability verification, that can aid in training for the hard task. This paper develops a novel approach for such settings by leveraging transfer learning. A Gaussian process-based learning model is efficiently trained using learning- and physics-based auxiliary tasks. Numerical tests demonstrate markedly improved performance that is harnessed alongside the benefit of uncertainty quantification to suit the needs of the considered application.

In modern machine learning systems, distributed algorithms are deployed across applications to ensure data privacy and optimal utilization of computational resources. This work offers a fresh perspective to model, analyze, and design distributed optimization algorithms through the lens of stochastic multi-rate feedback control. We show that a substantial class of distributed algorithms—including popular Gradient Tracking for decentralized learning, and FedPD and Scaffold for federated learning—can be modeled as a certain discrete-time stochastic feedback-control system, possibly with multiple sampling rates. This key observation allows us to develop a generic framework to analyze the convergence of the entire algorithm class. It also enables one to easily add desirable features such as differential privacy guarantees, or to deal with practical settings such as partial agent participation, communication compression, and imperfect communication in algorithm design and analysis.

In this paper, we compare the performance of grid-forming (GFM) and grid-following (GFL) inverters during unbalanced grid faults. By performing an exhaustive time-domain electromagnetic transient (EMT) simulation study of an allinverter network, we compute a variety of transient and steadystate fault signatures including peak current, transient time, sequence voltages, and harmonic distortion with computational methods spanning wavelet, Fourier, and Forstescue transforms. Simulation results quantitatively establish that: i) GFM control architectures offer superior transient and steady-state fault performance compared to GFL architectures, ii) the performance of the virtual-impedance current limiter in GFM inverters offers better performance compared to current-reference saturation limiter, and iii) the specific choice of primary-control method has minimal impact on fault behavior of GFM inverters.

This paper demonstrates how equivalent-circuit representations of grid-following power-electronic inverters can be realized within a SPICE-based development environment using common circuit components and VerilogA code. This facilitates computationally lean simulations of inverter networks leveraging the strengths of SPICE in large-scale simulations. We validate the approach with time-domain simulations for a modified version of the IEEE standard 118-bus system modeled in Virtuoso (a SPICE-based solver). Simulation results are compared-focusing on accuracy and computation speed-with results from a commonly used power-electronics simulation package. We note a significant decrease in simulation time with comparable signal resolution when simulating the network in SPICE.

Virtual oscillator control (VOC) is a time-domain strategy for regulating the operation of grid-forming (GFM) inverters. The premise of this method is to leverage the dynamics of nonlinear oscillator circuits to realize controllers; the time-domain nature of the resulting implementation is starkly different from classical droop control methods. This paper considers VOC realized with the dynamics of the Andronov-Hopf oscillator, a second-order nonlinear dynamical system that enables GFM inverters to be dispatched and generate low-harmonic outputs while not compromising dynamic performance. Leveraging an equilibrium analysis of the involved dynamics and small-signal models, we put forth a side-by-side comparison of dynamic performance and small-signal stability with classical droop control. The results demonstrate superior dynamic performance of VOC, and broadly, the paper furthers efforts focused on modeling and analysis of this general class of GFM controllers.

We present a small-signal stability study of a coupled synchronous generator and inverter system, where the inverter is controlled by virtual oscillator control (VOC). VOC is a recently proposed grid-forming inverter control strategy, which acts on faster time scales compared to droop control. In our study, we leverage a scalable VOC controller (that is by design agnostic of power levels) to test the system's small-signal stability at different inverter penetration levels. The impact of rotational inertia, reactive power support, and filter parameters on stability is then investigated. Results highlight possible issues that might arise in these mixed machine-inverter systems further motivating the need to develop next generation stabilizing grid-forming controllers.

This paper presents analytical closed-form expressions that map the contributions of nodal active- and reactive-power injections to the branch active- and reactive-power flows in an AC electrical network that is operating in sinusoidal steady state. We term these as the power divider laws, since they are derived leveraging, and their form and functionality are similar to, the ubiquitous current divider law. Distinct from the current divider law that only depends on the topology and constitution of the electrical network, the power divider laws are a function of the topology as well as the sinusoidal-steady-state voltage profile of the network.

In this paper, the three-port Ćuk converter interfaces one unidirectional input power port (envisioned to be a DC power source such as PV, or fuel cell) and two bidirectional output ports, representing the grid-tied inverter dc bus and a storage port respectively, and combines all the magnetics into a single core. The well-known property of the basic Ćuk converter that emulates an ideal dc-dc transformer (zero ripple terminal currents) is extended to three ports and is analyzed in detail. Two methods, one involving the physical structure of the core, and the other, a circuit-based dual approach, which is directly related to the core structure, are applied to solve the zero-ripple problem, and the accuracy of one of them over the other is verified with simulation results. Three different power transfer modes in this three-port converter are compared using the two methods mentioned above.

A three-port converter (TPC) based on the Ćuk topology is proposed in this paper. The proposed converter interfaces one unidirectional input power port (envisioned to be a DC power source such as PV, or fuel cell) and two bidirectional output ports, representing the grid-tied inverter dc bus and a storage port respectively. This converter utilizes a single integrated magnetic core on which all the inductor and the transformer windings are wound. The proposed structure utilizes only three power switches, and does not require output capacitors on the output ports on account of the zero-ripple property. Depending on utilization state of the battery, three different power operation modes are defined for the converter. The features of the proposed converter are analyzed and then verified by means of simulation results for different operation conditions.

This paper proposes a set-theoretic method to capture the effect of parametric uncertainty in reliability and performability indices obtained from Markov reliability and reward models. We assume that model parameters, i.e., component failure and repair rates, are not perfectly known, except for upper and lower bounds obtained from engineering judgment or field data. Thus, the values that these parameters can take are constrained to lie within a set. In our method, we first construct a minimum volume ellipsoid that upper bounds this set, and hence contains all possible values that the parameters can take. This ellipsoid is then propagated via set operations through a second-order Taylor series expansion of the Markov chain stationary distribution, resulting in a set that provides approximate bounds on reliability and performability indices of interest. Case studies pertaining to a two-component shared load system with common-cause failures, and preventative maintenance of an electric-power distribution transformer, are presented.

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 uncertainty to reliability and performability indices of interest. The Taylor series coefficients are expressed in closed form as functions of the Markov chain generator-matrix group inverse. Then, to compute the probability density functions of the reliability and performability indices, random variable transformations are applied to the polynomial approximations that result from the Taylor series expansion. Additionally, closed-form expressions that approximate the expectation and variance of the indices are also derived. A significant advantage of the proposed framework is that only the parametrized Markov chain generator matrix is required as an input, i.e., closed-form expressions for the reliability and performability indices as a function of the model parameters are not needed. Several case studies illustrate the accuracy of the proposed method in approximating distributions of reliability and performability indices. Additionally, analysis of a large model demonstrates lower execution times compared to Monte Carlo simulations.

Highly detailed models of power converters can be slow to simulate due to the wide disparity in transient time scales. This is further pronounced in the presence of nonlinear components, e.g., saturated inductors. Variable-resolution simulation provides an alternative method by providing an appropriate amount of detail based on the time scale and phenomenon being considered. First, a high-fidelity detailed full-order model of the converter is built that accounts for the system parasitics and higher order effects, component nonlinearity, etc. Efficient order-reduction techniques are then used to extract several lower order models for the desired resolution of the simulation. The state continuity across different resolutions and switching events is ensured using appropriate similarity transforms. The proposed variable-resolution simulation framework is demonstrated on a boost converter with a saturated inductor. Significant improvement in simulation speed (orders of magnitude) is reported.