The large-scale penetration of inverter-based resources in power systems has challenged protection engineers because of the different fault behaviors these sources provide compared to conventional generation systems. The main challenges include a low level of fault current magnitude, unpredictable angles of sequence currents, and lack of inertia that can lead to maloperation of conventional phasor-based protection elements. This paper presents a sensitivity analysis of transmission line distance protection elements during phase-to-ground and phase-to-phase faults for different inverter controllers and power system conditions. It also summarizes which line protection elements remain secure near IBR terminations and identifies the ones affected by the inverter-based response. The paper concludes by highlighting that regulating negative-sequence current injection during the fault aids correct protection decisions, but does not address the entire challenge. Finally, alternative protection elements to those affected by the inverter fault response are discussed.

The energy needed to pump water from the Snake River Basin to the Boise metropolitan area in southern Idaho is determined in this study by utilizing updated datasets and modeling approaches. We refine previous methods based on power-consumption coefficients (PCCs) and K-factors by using recent U.S. Geological Survey (USGS) data from 39 pump locations, including elevation measurements and discharge rates. Regression analysis allows us to derive a more accurate model that shows significant agreement with observed data for estimating energy demands related to water withdrawals. When direct monitoring is not feasible, the results demonstrate how these enhanced coefficients can be applied to contemporary water systems, providing a dependable and affordable method of calculating withdrawals. Given the conflicting demands of population increase, climate unpredictability and competing water rights in the Snake River Basin, our model offers a comprehensive framework for measuring energy-water interdependence. When compared to historical methods, the improved PCC approach significantly lowers withdrawal estimation errors, providing utilities with a vital tool for infrastructure design in the face of hydrological uncertainty. This work helps sustainable resource management in the area and provides water districts with a scalable tool for estimating withdrawals in unmonitored locations.

There are several methods for estimating the parameters of a signal in the time domain. Some linear methods are based on polynomials, while others rely on singular value decomposition. These techniques are usually applied to analyze signals offline, that is, as a postanalysis of an event occurring in a physical system. To perform online signal analysis, it is necessary to reduce the number of samples to process by using a sliding window that contains enough information to determine the parameters of the signal of interest. Multiple nonlinear methods have also been developed for online parameter estimation, each defining a data window within its own implementation. This chapter presents state-of-the-art methods for parameter estimation employing the sliding window technique to accelerate the convergence of the linear algorithms. To demonstrate the implementation of the sliding window technique, a simple moving average low-pass filter is employed. To evaluate their performance, two cases are considered. First, an electric power system with a programmable source is used to simulate voltage magnitude and frequency change, and the resulting voltage signal is processed using the proposed algorithms to estimate its magnitude and frequency. Then, one of the proposed methods is successfully incorporated into a control system known as Extremum Seeking Control, an adaptive control technique used to determine optimal inputs or tune systems parameters. In this work, the terms “method” and “algorithm” are used interchangeably to refer to the proposed signal processing techniques.

The growing penetration of inverter-based resources (IBRs) in bulk power systems demands short-circuit models that capture both device-level dynamics and protection-relevant behaviors while remaining computationally efficient. Conventional voltage-source–behind–impedance models neglect control interactions, sequence coupling, and fault ride-through (FRT) behaviors, whereas electromagnetic transient (EMT) models, though accurate, are computationally intensive and lack interoperability in planning workflows. This paper presents a compact, parametric reduced-order model (ROM) for grid-following inverters that reproduces IBR fault current trajectories—including subtransient, transient, and steady-state phases—across a range of fault types, locations, and pre-fault operating points. The proposed model is tuned using detailed EMT simulations under multiple control configurations, including negative-sequence current control in the dq frame. Validation against EMT benchmarks demonstrates the ROM’s ability to capture magnitude, phase, and oscillatory content within 1.5 cycles of fault inception, using a single parameter set for diverse fault scenarios. This capability makes the ROM suitable for protection studies, grid code compliance verification, and integration into planning-grade short-circuit tools.

The proliferation of inverter-based resources (IBRs) in modern power systems introduces fault characteristics that substantially differ from those of synchronous machines, posing challenges to conventional protection schemes. Although open-source generic IBR models provide full control transparency and tunability, their fault responses often diverge from trusted original equipment manufacturer (OEM) black-box models—particularly from the perspective of protection relays that rely on specific current magnitude, phase, and sequence component dynamics. Tuning the open-source generic IBR ensures its fault response matches the OEM black-box model, enabling protection engineers to design relay logic using the tuned open-source IBR model as a substitute for the OEM black-box model. This paper proposes a systematic framework for tuning open-source, multifunctional generic IBR models to emulate OEM-equivalent fault dynamics as observed by protection relay elements. The framework introduces structured guidelines for adjusting key parameters of inner control loops and current limiters to align the fault current magnitude, sequence content, and phase trajectories with those of OEM models across diverse fault types and locations. The tuned model’s fidelity is validated through comparative analysis with an OEM black-box reference, assessing both the fault response and the operation of multiple relay functions—including distance, directional, and fault identification elements—adapted from a commercial protective relay. The results demonstrate that the tuned generic model can trigger relay decision logic that is identical or nearly identical to that of the OEM model, enabling intellectual property-compliant fault studies that directly inform protection design for IBR-rich grids.

This work analytically establishes a multi-variable energy function for a three-phase grid-following inverter leveraging a unified equivalent-circuit model for its physical- and control-layer subsystems. This is a significant contribution to the prior art in which analytical approaches to large-signal stability for inverters have largely been attempted with simplified models. Central to our effort is to cast physical- and control-layer dynamics of each dynamical subsystem as an equivalent circuit consisting of familiar circuit elements adopting a positive-sequence modeling framework. An energy function for the inverter is then constructively synthesized by summing the energy functions across the various subsystems that are readily derived from circuit-theoretic principles. Numerical simulations are presented to validate the equivalent-circuit model of the inverter as well as the efficacy of the synthesized energy function in characterizing large-signal stability following a disturbance.

Power system transmission line protective relays are supervised by a number of elements to ensure the security and selectivity of protection decisions. Supervising elements are important for fault direction determination and they are typically designed based on the properties of sequence currents and voltages. Superconducting fault current limiters (SFCLs) could potentially affect the profiles of sequence currents and voltages, which could have further influence on the performance of supervising elements. This article is one of the first works that investigate the impact of resistive SFCLs on supervising elements in power system transmission line protection. A resistive SFCL and an electric power system are modeled in an electromagnetic transients simulation program. Single-line-to-ground faults are simulated on the transmission line. The acquired fault voltages and currents are processed by a transmission line impedance-based protective relay model to investigate the responses of supervising elements. The results are analyzed and discussed.

AC-DC converters with cascaded units are gaining popularity for medium voltage level grid connection however, as the number of cascaded stages increase, their widespread application are limited by existing centralized and distributed control schemes. In this article, a completely decentralized control scheme has been proposed for cascaded-type ac-dc converters with integrated energy storage. The proposed control method is capable of locally controlling both the active and reactive power processed by an individual unit and thereby achieve State-of-Charge (SOC) balancing of the energy storage units integrated with each converter. In this framework, the reactive power control loops achieve voltage synchronization among the converters and the grid, and the active power control loops modulate the terminal voltage amplitudes that influence power delivery. The proposed control is inspired from conventional droop control used for parallel connected converters, however, it has been modified by incorporating state feedback of voltage angle in order to facilitate stable bidirectional power flow in series connected systems. The stability analysis and simulation results have been presented along with relevant experimental results.

This paper examines the impact of inverter-based resource (IBR) momentary cessation timing on transmission system protection relays. IEEE Std. 2800 mandates voltage ride-through, requiring IBRs to remain online during voltage disturbances. However, for severe voltage dips (|V| <= 0.1 p.u.), the standard permits current blocking. In practice, vendors implement momentary cessation with varying delays, potentially affecting relay operation if IBRs cease too early. This article studies the impact of the time IBRs enter momentary cessation on transmission line protective relays. Using an electromagnetic transient (EMT) simulation, this study models IBR momentary cessation with tunable delays in a realistic transmission network. COMTRADE files generated from EMT simulations are analyzed in MATLAB using detailed protective relay models. Results indicate that IBRs must sustain operation for at least one cycle to ensure proper relay response; otherwise, relays may fail to operate. These findings guide IBR vendors in optimizing momentary cessation settings to enhance transmission line protection.

In this paper, our objective is to use notions of system energy to formulate closed-loop dc-dc converter controls that are nonlinear and satisfy passivity properties that guarantee stability. Port-Hamiltonian models are a particular form of models which can be used to describe the total energy in a converter, much like a Lyapunov function. In our approach, we first formulate a port-Hamiltonian model that represents the desired closed-loop dynamics we seek. However, the solution to this model is generally quite difficult for even the simplest of converters. To bypass this challenge, we offer a framework where a neural-network-based controller is trained to estimate the solution to this design problem. Essentially, our objective is to ensure that the energy dynamics of the dc-dc converter with a neural network as a controller closely match that of the target port-Hamiltonian model. This method circumvents the mathematical difficulties encountered when attempting to solve the closed-loop port-Hamiltonian model directly and gives a generalized framework. Our paper illustrates this approach and its versatile application towards boost, buck, buck-boost, and Cuk converters.

Classical transient stability assessment methods, such as the equal area criterion and Lyapunov energy function-based approaches, have long been used to analyze large-signal stability of power systems. However, when applied to grid-forming (GFM) inverters, these methods fail to account for key inverter-specific dynamic behaviors, including damping effects, reactive power versus voltage interactions, and the influence of current limiters. In recent literature, an alternative equivalent circuit-based energy function approach has been proposed to provide a more accurate transient stability assessment of GFM inverters. In this paper, we demonstrate how this circuit-based approach emerges from fundamental energy function principles and show how it addresses key limitations of classical transient stability assessment methods. Numerical simulations validate the effectiveness of the equivalent circuit-based energy function in characterizing the transient stability of GFM inverters.

This paper presents a practical teaching platform for understanding inverter-based resources (IBRs) in engineering courses and laboratory settings. This paper provides students with hands-on experience in setting transmission system protection, specifically focusing on examining the response of Mho distance protection in lines fed by IBRs. The laboratory setup consists of a real-time digital simulator, a digital relay for physical testing, and an electromagnetic transient (EMT) program power system model consisting of a transmission line integrating a photovoltaic farm with an transmission system. The voltage and current signals from fault studies performed using the EMT program are exported as COMTRADE files for playback tests in commercial protective relays. Students must configure the digital relay based on the system’s parameters and analyze the Mho distance protection performance through the real device response and software to visualize the relay event file. Students will be able to use multiple protection functions and evaluate which protection and supervisory elements are impacted by the IBR. The students also compare IBRs with fault response compliant with IEEE 2800-2022 to ones that are not compliant. Through these experiments, students will gain an understanding of protection challenges associated with protection in IBR-penetrated systems, bridging theoretical concepts with practical implementation.

This paper proposes an energy function-based direct method for large-signal stability assessment of grid-forming (GFM) inverters leveraging an equivalent-circuit representation of all involved control- and physical-layer dynamics. Three different primary controls, a standard inner-current outer-voltage cascaded-control architecture, output $LCL$ filter, and reference-current saturation limiting are featured in the modeling and analysis framework. A composite energy function for the GFM inverter is obtained by summing up individual energy contributions gleaned from the circuit representation. The approach can readily be generalized to different primary controls, output-filter arrangements, and current limiters since it is based on a circuit-theoretic foundation. Numerical simulations validate the efficacy of the approach in estimating the critical clearing time following a large-signal disturbance.