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Due to its multiple advantages, the grid-forming, droop-controlled (GFDC) inverter is a strong contender for large-scale deployment in the future power systems. However, it is still unclear whether higher harmonics can play an important role in the dynamics of GFDC inverter networks. The major objective of this article is to gain insight into whether certain higher harmonics influence or interact with GFDC inverter network dynamics and to characterize this harmonic interaction. For this purpose, a multiple-harmonic dynamic phasor model (DPM) of a representative GFDC network is derived, which can be conveniently extended to hundreds of DPM equations in order to rigorously investigate the effects of dc offsets and/or second-harmonic content, six-step switching harmonics, and unbalance. For a representative network, the results from eigenvalue migration studies show that GFDC dynamics are not strongly influenced by the presence of six-step switching harmonics nor unbalance. For the first time, it is shown that under conditions of high droop slope and high-bandwidth power filtering, dc offsets and second-harmonic content can excite a resonance within the network and even influence the location of the eigenvalues of the linearized DPM. All DPM results are thoroughly validated using Simulink, and the selected results are validated experimentally using the Wisconsin Energy Institute (WEI) microgrid testbed.

This paper presents a new modeling and analysis approach to address the small-signal stability issues among interconnected grid-forming (GFM) inverters. A novel phasor domain “power impedance” model is developed to capture the terminal characteristics of GFM inverters. Based on the developed models, a sum-type impedance stability criterion is proposed to analyze the power oscillations between GFM Inverters. The developed models are validated with EMT simulations and the stability analysis results using the proposed stability criterion can match both EMT simulations and eigenvalue analysis. In addition, the application of the developed model can be extended to the stability analysis of large-scale power system with high penetration of GFM inverters.

There is an increasing need to apply rigorous model-order-reduction techniques in the analysis of large-scale networks of inverter-based distributed generation resources due to the limitations of existing simulation tools. Various coherency-based aggregation techniques have long been used to construct reduced-order dynamic models of large-scale synchronous machine (SM) networks. Such techniques have the advantage of preserving the nonlinear nature of the dynamic model throughout the order-reduction process, enabling the efficient and accurate analysis of large-scale network dynamics during large disturbances such as fault events. This paper proposes the application of a rigorous coherency-based aggregation technique to the analysis of large-scale networks of grid-forming droop-controlled inverters. A rapid and powerful generalized eigenvalue perturbation technique for coherency identification, previously only applied to SM networks, is adapted to grid-forming droop-controlled inverter networks. The resulting reduced-order models are physically insightful and are capable of accurately reproducing the system response in the aftermath of large disturbances. For some networks, a rigorously-derived condition of coherency can be difficult to achieve, given the expected range of L–C–L filter impedances. To remedy this limitation, the potential for high-bandwidth inverter control to enforce the conditions that allow for coherency of droop-controlled inverters has been investigated and confirmed using a controller hardware-in-the loop testbed. Using this approach, the use of simple nonlinear aggregate inverter models to accurately model large sections of the inverter network can be more rigorously justified.

The discovery of ‘event signatures’ and useful insights from very large historical Phasor Measurement Unit (PMU) datasets is predicated on offline Big Data analysis approaches that rely on the generation of predictive features on a massive scale. This paper presents lessons learned from a data platform perspective towards reducing barriers to adoption of Big Data analytics against a real dataset of almost half a trillion data points drawn from over 400 PMUs distributed across the North American power grid. We demonstrate software abstractions and targeted performance optimizations that can lead to significant productivity gains for power systems researchers seeking to perform offline exploratory temporal analysis and modeling tasks, with a focus on feature generation. We describe how our optimized approach goes beyond a naive application of mainstream Big Data technologies, enabling feature generation tasks, that previously took days or even weeks, to now be completed in just a few hours.

The day-to-day operation of modern power systems is highly reliant on prompt and adequate situational-awareness. This can be achieved via various system monitoring functions such as anomaly detection, in which static thresholds are commonly utilized to distinguish the normal and the abnormal system states. However, a predetermined static threshold usually lacks the flexibility to adapt to unobserved scenarios. In this paper, we propose two self-adaptive synchrophasor data driven anomaly detection approaches based on Chebyshev’s Inequality. The proposed approaches have been evaluated with Kundur’s 2area system and Mini-WECC system. Experimental results verify that the proposed approaches can dynamically adapt to unprecedented scenarios, and detect anomalous events with lower false alarm rate compared to static threshold based detection.

We present a hierarchical optimization architecture for large-scale power networks that overcomes limitations of fully centralized and fully decentralized architectures. The architecture leverages principles of multigrid computing schemes, which are widely used in the solution of partial differential equations on massively parallel computers. The top layer of the architecture uses a coarse representation of the entire network while the bottom layer is composed of a family of decentralized optimization agents each operating on a network subdomain at full resolution. We use an alternating direction method of multipliers (ADMM) framework to drive coordination of the decentralized agents. We show that state and dual information obtained from the top layer can be used to accelerate the coordination of the decentralized optimization agents and to recover optimality for the entire system. We demonstrate that the hierarchical architecture can be used to manage large collections of microgrids.

The wide area monitoring system (WAMS) is critical for power system situational awareness, but represents a growing cybersecurity vulnerability. Malicious adversaries may seek to compromise one or more PMUs in order to effect control decisions that unnecessarily disrupt typical grid operations. One example of a particularly pernicious attack vector is the spoofing or replaying of a fault event using one or more compromised PMUs. This work documents the development and validation of a coherency-based cyberattack detection algorithm that integrates a sliding-window singular value decomposition (SVD) with physics-based partitioning analysis to achieve accurate classification of events. Special consideration is given to discerning a sophisticated fault-replay or fault spoofing attack from actual faults. A software-based cybersecurity testbed has been developed for rigorous testing of the algorithm. The algorithm is further validated using simulated synchrophasor datasets obtained from a MinniWECC 63-bus test system. Results show that the algorithm can successfully detect fault-replay attacks even when over half of the PMUs are compromised.

There is an increasing need to model large networks of inverter-based distributed generation due to the limits of existing simulation tools. A deliberate enforcement of intra-feeder coherency between adjacent droop-controlled inverters is a worthwhile objective, as phase angle coherency will allow for a deliberate partitioning of fast and slow dynamics within the network. This partitioning, in turn, results in simpler and more tractable reduced-order network dynamics that are easier to model. This paper presents the adaptation of the generalized eigenvalue perturbation approach to the identification of coherent groups within grid-forming, droop-controlled inverter networks. For many networks, a rigorously-derived condition of coherency can be difficult to achieve, given the expected range of L-C-L filter and grid-tie impedances. To remedy this limitation, this paper investigates the use of multi-loop voltage regulation and virtual impedance to enforce the conditions that allow for coherency, and thereby more rigorously justify the use of simple nonlinear aggregate inverter models to accurately model large sections of the inverter network.

A droop-controlled, hybrid ac/dc microgrid represents a robust architecture that can coordinate the operation of multiple distributed sources while minimizing the power conversion stages. While the reduced-order nonlinear dynamics of grid-forming, droop-controlled inverter-based microgrids have been rigorously shown to be stable for a wide range of operating parameters, the problem of analyzing the transient stability characteristics of droop-controlled hybrid ac/dc architectures has not been adequately addressed. This work reviews the link between the Virtual Synchronous Machine control concept and grid-forming droop control, and introduces a new droop control strategy for ac/dc hybrid microgrids, termed ‘symmetric droop control’ (SDC). SDC better addresses the dynamic interactions between the ac and dc sub-grids of the hybrid microgrid, by ensuring that the interfacing inverter appropriately represents the dc sub-grid dynamics when interacting with other inverters. SDC can help to ensure that the reduced-order, nonlinear dynamics in both the ac and dc networks remain predictable and well-behaved during large disturbances in the ac network.

This work describes the development of a reduced-order nonlinear dynamic phasor modeling tool for distribution networks containing a large number of P-f and Q-v droop-controlled inverters. Attention is focused on constructing reduced-order models that accurately predict the nonlinear behavior of coherent clusters of droop-controlled inverters in response to a large disturbance, such as an asymmetric fault. In such a scenario, dynamic phasor models are shown to offer valuable insights into how the signal conditioning associated with local power measurement can have a significant effect on the large-signal stability of a droop-controlled inverter or inverter cluster. An algorithm conventionally used to identify coherent groups of synchronous generators is adopted for the investigation of coherency between large numbers of droop-controlled inverters within a distribution network. The coherency results help guide the aggregation of droop-controlled inverters and enable nonlinear reduced-order dynamic phasor modeling. For large disturbances, a reduced-order dynamic phasor simulation of a 50-inverter system is validated against full-order simulation results obtained using an OPAL-RT power system simulator.

In order to ensure resilient and high power quality microgrid operation, P-f and Q-V microgrid droop control algorithms rely on the calculation of active and reactive power outputs based on locally-measured voltage and current. A low-pass filter (LPF) on the calculated power signal is often incorporated by design into the droop controller, but the complete effect of the LPF on microgrid dynamics has not been adequately studied in the literature. This paper analytically and experimentally investigates the impact of the power measurement LPF bandwidth on several important aspects of microgrid performance. These include the dynamics of the interaction between network swing modes, voltage regulator dynamics, and filter dynamics as the filter bandwidth is swept across a large range. Three different voltage regulators are studied. Additionally, the role of the controller's LPF characteristics on the reduced-order large-signal nonlinear dynamics of inverter-based microgrids is investigated using an equivalent electromechanical system. Using a Lyapunov energy function, a family of linear power measurement filters is identified that ensures stability for a grid-tied frequency-droop-controlled inverter.

A reduced-order model is used to derive a candidate energy function for a system that includes an infinite bus connected with a single frequency-droop-controlled inverter (a ‘MicroSource’) whose frequency command is actuated according to its low-pass-filtered active power measurement. The analysis of the large-signal stability of such a system is important in understanding the duration that a frequency-droop-controlled inverter can withstand a particular grid transient before islanding or tripping offline becomes mandatory. It is shown that a large-signal instability for this system can occur under abnormal grid conditions. Additionally, for poor selections of droop gain and low-pass cutoff frequency, these control parameters can potentially have a significant effect on the ability of the system to maintain synchronism after a fault on the main grid is cleared. The proposed energy function is shown through simulation to provide insight on the impact of the frequency droop gain and filter time constant on this instability during and after faulted conditions, particularly for high levels of droop gain and/or measurement filter time constant.

Usability is an important topic in the field of telerehabilitation research. Older users with disabilities in particular, present age-related and disability-related challenges that should be accommodated for in the design of a user interface for a telerehabilitation system. This paper describes the design, implementation, and assessment of a telerehabilitation system user interface that tries to maximize usability for an elderly user who has experienced a stroke. An Internet-connected Nintendo(®) Wii™ gaming system is selected as a hardware platform, and a server and website are implemented to process and display the feedback information. The usability of the interface is assessed with a trial consisting of 18 subjects: 10 healthy Doctor of Physical Therapy students and 8 people with a stroke. Results show similar levels of usability and high satisfaction with the gaming system interface from both groups of subjects.

A second-life battery is an electric vehicle battery pack that has reached an end-of-life condition for its vehicular use, yet retains enough performance to be re-purposed for another application. One promising application of a second-life battery is stationary energy storage within a CERTS microgrid. This paper investigates the modeling of multiple paralleled traction battery packs within a CERTS microgrid, examining the impacts of elevated internal pack impedance on microgrid system operation. Impedance spectroscopy and hybrid-pulse power characterization are used to model vehicular Li-ion cells under a range of conditions that include second-life aging. The ac bus dynamics of the microgrid model are validated experimentally. Second-life battery models are incorporated into two CERTS microgrid architectures and system-level effects of changing the battery impedance are explored. Simulation results indicate that the modeled EV second-life batteries deliver promising performance characteristics in both CERTS microgrid architectures that were investigated.

In this paper, we investigate the feasibility of linking amateur weather ballooning, amateur radio, and emergency communications for the purpose of creating low-cost, easily-reproducible emergency Deployable Aerial Communications Architecture (DACA). Amateur radio and other line-of-sight communications are already widely used during disaster relief, so the vision of our work is to explore to what extent already-existing volunteer groups, which use amateur radio and other line-of-sight communications, can be better enabled to function immediately following a disaster where terrestrial infrastructure can become interrupted, especially without the need for those groups to acquire any new equipment. In this paper, we build upon ideas previously discussed by the FCC and FEMA, and discuss our experimental findings on the feasibility of using weather balloons in a DACA solution; in particular, our work especially attempts to leverage existing, already-deployed amateur radio capabilities. We conclude by evaluating our findings, mentioning some of our ongoing work in this space, including research in how to build highly-available and reusable weather balloon DACA solutions, and discuss future work we hope to see in this space. In analyzing our data, we find that our experimental weather balloon was able to successfully make radio contacts across an approximately 300-mile radius.

Advances in sensor technologies provide a method to accurately assess activity levels of people with stroke in their community. This information could be used to determine the effectiveness of rehabilitation interventions as well as provide behavior-enhancing feedback. The purpose of this study was to assess the accuracy of a novel shoe-based sensor system (SmartShoe) to identify different functional postures and steps in people with stroke. The SmartShoe system consists of five force-sensitive resistors built into a flexible insole and an accelerometer on the back of the shoe. Pressure and acceleration data are sent via Bluetooth to a smart phone.Participants with stroke wore the SmartShoe while they performed activities of daily living (ADLs) in sitting, standing, and walking positions. Data from four participants were used to develop a multilayer perceptron artificial neural network (ANN) to identify sitting, standing, and walking. A signal-processing algorithm used data from the pressure sensors to estimate the number of steps taken while walking. The accuracy, precision, and recall of the ANN for identifying the three functional postures were calculated with data from a different set of participants. Agreement between steps identified by SmartShoe and actual steps taken was analyzed by the Bland Altman method.The SmartShoe was able to accurately identify sitting, standing, and walking. Accuracy, precision, and recall were all greater than 95%. The mean difference between steps identified by SmartShoe and actual steps was less than one step.The SmartShoe was able to accurately identify different functional postures, using a unique combination of pressure and acceleration data, of people with stroke as they performed different ADLs. There was a strong level of agreement between actual steps taken and steps identified by the SmartShoe. Further study is needed to determine whether the SmartShoe could be used to provide valid information on activity levels of people with stroke while they go about their daily lives in their home and community.

In order to explain previously observed deviations of measured plasma velocities from velocities predicted by computer solutions based on a snowplow model, the experimental and computer data are here extended over a much wider range of electrode configurations, capacitor potentials, and gas densities in the shock tube. At low densities the experimental velocity curves fall below the predicted curves because of material evaporated from insulation and electrodes. At high gas densities the experimental velocity curve for the largest center electrode coincides with the predicted curve, but for center electrodes of successively smaller diameter the measured curves lie progressively farther above, but parallel to, those predicted, up to a factor of 5.5 times for the smallest electrode used. These results are explainable in terms of a modified snowplow model postulating an effective annular region adjacent to the center electrode, whose thickness is of the same order as the electrode radius, such that the force due to the magnetic pressure inside this annulus acts on only the gas contained within it to produce the measured velocity.

Pythagorean sets have interested mathematicians for over 2000 years. They may be of interest to some students in the mathematics classes of the senior high school and the college.

A fast but accurate relativistic method for determining the time variation of potential and field distributions, electron trajectories, and space‐charge‐limited current between parallel conducting walls is described. No limit is placed on how broad the energy spectrum of the emitted electrons may be, or in what manner the energy distribution and intensity may vary with time. A major simplification results from performing the basic calculations in terms of scalar potentials rather than vector fields. The emission of a group of charge sheets representing the existing energy spectrum is assumed for each closely spaced time interval. The incremental advance of each sheet is found from its starting velocity and acceleration as functions of the momentary potential distribution curve and of its past variations by a procedure which also compensates for ``self‐field'' effects. The new sheet positions define a new potential curve and the process is repeated. Trajectories calculated for monoenergetic electrons agree...

A simple method, utilizing a noninductive connection, is described for the direct measurement of the resistive component of the potential drop across a semi‐enclosed arc. By this method the resistance, power dissipation, and efficiency are determined for an arc due to a capacitor discharge having a peak current of about 2.5×105 A. The minimum resistivity is found to be 1.5×10−3 Ω cm, a value lower than values reported previously. A current curve is analyzed to determine resistance of the entire circuit. Inductance interrelation are considered further.

Although electromagnetic theory has been known for a century, and Biot's (also called Ampere's) formula in its simple form, dH = (1/4π)(Idl sinθ/r2), is often used, the corresponding relationship, dE = −(1/4π) (φdl sinθ/r2), for the electric field induced in space by a filament of time‐varying magnetic flux, seems not to have been recognized or used to any great extent. The discussion here presented, using the example afforded by coaxial conductors, illustrates some aspects of how this latter relationship may be used to solve for induced electric fields, including those for coaxial systems of both finite and infinite length with hollow or solid center conductors. The magnetically induced electric field fringes outward near the shorted end of a coaxial system, and a method is shown for finding the radial positions of a given line of electric force when coaxial conductors of different dimensions are connected together.

A method is described for determining the distribution of the radiation reflected from a mirror due to point source. In particular, the distribution from an elliptical cylinder, which apparently has not previously analyzed, is investigated and examples are given of the irradiance on surfaces of various configurations. In addition, the distribution from mirrors of ellipsoidal, paraboloidal, and parabolic cylinder form is considered. The method used may be extended to other types of mirrors.

The acceleration of a plasma by a capacitor discharge between coaxial electrodes is studied for (1) a shock tube having an initially uniform gas distribution and for (2) a plasma gun which accelerates a constant mass into a vacuum. Differential equations written for the first case for a simple snowplow model and solved by analog computer, are found to closely predict peak plasma velocities for a certain range of pressures. However, experimental study by means of a ``difference'' magnetic probe shows that the actual current distribution in the space between the electrodes is rather complex. Near the time when peak plasma velocity is reached, the first pulse splits into two pulses and persisting loop currents form in the plasma. An efficient mode of plasma acceleration which produces faster and more sharply defined shock waves is observed at low pressures when the center electrode is initially positive. Computer solutions are also obtained for the plasma gun, which seems to be intrinsically capable of greater efficiency than the shock tube.