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We propose a three-stage stochastic programming model to inform risk-averse investment in power system resilience to winter storms. The first stage pertains to long-term investment in generator winterization and mobile battery energy storage system (MBESS) resources, the second stage to MBESS deployment prior to an imminent storm, and the third stage to operational response. Serving as a forecast update, an imminent winter storm’s severity is assumed to be known at the time the deployment decisions are made. We incorporate conditional value-at-risk (CVaR) as the risk measure in the objective function to target loss, represented in our model by unserved energy, experienced during high-impact, low-frequency events. We apply the model to a Texas-focused case study based on the ACTIVS 2000-bus synthetic grid with winter storm scenarios generated using historical Winter Storm Uri data. Results demonstrate how the optimal investments are affected by parameters like cost and risk aversion, and also how effectively using CVaR as a risk measure mitigates the outcomes in the tail of the loss distribution over the winter storm impact uncertainty.

This article studies the Transmission Restoration Problem with Mobile Substation Resources, a novel mixed-integer linear programming model that prescribes the most effective usage of mobile-substation resources to enhance the resilience of a power transmission system against a particular, widespread flood event. The model is a two-stage stochastic program in which each scenario captures a different potential progression of flood heights at substations over the event horizon. The first stage concerns the pre-event selection and positioning of mobile-substation resources. The second stage concerns the coordination of mobile-substation resource deployment and permanent-substation restoration to maintain and recover service within the horizon. Experiments in the IEEE 24-Bus System and a synthetic Houston grid confirm the efficacy of the model. Even when isolated from effects related to restoration of permanent substations, the effect of four mobile transformers and eight mobile breakers for a realistic set of flood scenarios in the synthetic Houston grid was found to be an average total-cost reduction of approximately ${\$}$ 35MM (i.e., approximately 8% of a default optimal objective value). Additionally, a novel, parallel heuristic is designed that can efficiently solve the problem as well as, with minor modifications, similar stochastic problems on pre-selection of mobile resources or placement of static ones. For a 40-scenario model instance in the IEEE 24-Bus System, the extensive form was not able to find an integer-feasible solution in six hours, yet the heuristic achieved an optimality gap no worse than 4.5% in two hours.

Optimal power flow (OPF) analysis enables the in-depth study and examination of islanded microgrid design and operation. The development of the analysis framework, including modeling, formulating, and selecting effective OPF solvers, however, is a nontrivial task. As a result, this paper presents a tutorial on an OPF modeling framework, offering a mathematical model that can be readily implemented using established open-source software tools such as OpenDSS, Pyomo, and IPOPT. The framework is versatile, capable of representing single-phase and unbalanced three-phase islanded microgrids. Various inverter models, such as those of grid forming and following equipped with their operating characteristics, can be incorporated. The efficacy of the proposed framework is demonstrated in studying the OPF of single-phase and three-phase microgrids.

The objective of this paper is to analyze and identify the range of voltage balancing capability of grid-forming inverters serving three-phase unbalanced loads. These inverters are designed to compensate for voltage imbalance by controlling the negative-sequence components of voltage and current. However, the magnitude of the negative-sequence current an inverter can supply is limited by its relatively low rated current. Moreover, it becomes more challenging to estimate the amount of current needed for an unbalanced load when the inverter is interfaced using a delta-wye grounded interconnection transformer. Therefore, we investigate the range of negative-sequence current the inverter can supply and derive formulas to determine the minimum inverter’s capacity required to compensate for voltage imbalance while supplying unbalanced loads connected through a delta-wye grounded transformer. The proposed formulas can be used to estimate the capacity of an inverter in lieu of detailed analyses and electromagnetic transient simulations. The proposed equation is implemented in small and large scale microgrid systems and validated using a detailed model developed in PSCAD/EMTDC.

Abstract Impedance‐based fault location (IBFL) approaches are the most commonly used fault location methods in digital relays. However, each IBFL approach is designed specific to a line or network configuration and thus is not universal. For example, complex line configurations such as lines with mutual coupling between them and three‐terminal lines have to employ individual IBFL algorithms derived specifically for them. Furthermore, they suffer from several sources of errors such as non‐homogeneous system, and CT saturation. Hence, this paper presents a novel fault location approach that utilises a system model to overcome these limitations. The proposed model‐based fault location (MBFL) approach estimates the fault location by identifying the closest match among various anticipated fault scenarios obtained using the system model and the actual fault scenario. It uses a dynamic search technique to implement the MBFL efficiently. A key highlight of the proposed approach is identifying the location of a fault on a neighbouring line using limited measurements, as few as only the through fault current flowing in a neighbouring line. The advantages of the approach and its practical applicability have been demonstrated by implementing it in complex network configurations as well as field data.

The capability of routing power from one phase to another, interphase power flow (IPPF) control, has the potential to improve power systems efficiency, stability, and operation. To date, existing works on IPPF control focus on unbalanced compensation using three-phase devices. An IPPF model is proposed for capturing the general power flow caused by single-phase elements. The model reveals that the presence of a power quantity in line-to-line single-phase elements causes an IPPF of the opposite quantity; line-to-line reactive power consumption causes real power flow from leading to lagging phase while real power consumption causes reactive power flow from lagging to leading phase. Based on the model, the IPPF control is proposed for line-to-line single-phase power electronic interfaces and static var compensators (SVCs). In addition, the control is also applicable for the line-to-neutral single-phase elements connected at the wye side of delta-wye transformers. Two simulations on a multimicrogrid system and a utility feeder are provided for verification and demonstration. The application of IPPF control allows single-phase elements to route active power between phases, improving system operation and flexibility. A simple IPPF control for active power balancing at the feeder head shows reductions in both voltage unbalances and system losses.

This work proposes positive- and negative-sequence equivalent circuits of grid-forming inverters for steady-state analysis. The proposed models are especially attractive for performing long-duration voltage regulation analysis and short-circuit studies involving grid-forming inverters. Our proposed equivalent circuit models are based on the inverter’s voltage and current control loops in the $\alpha \beta $ and dq frames. For this reason, they operate according to prescribed control functions and specified impedances (i.e., filter impedance, current limiter block, virtual admittance block, and PI/PR controller block). The equivalent circuit model accuracy is validated by comparing system steady-state voltage and current responses obtained by detailed time-domain models in PSCAD/EMTDC to those by the equivalent circuit models implemented in steady-state load flow program (e.g., OpenDSS). Two distinct control structures implemented in the $\alpha \beta $ and dq frames are used for the validation. Single line-to-ground and line-to-line-to-ground faults are simulated in a small islanded microgrid as well as the IEEE 34-node test feeder. Fault impedances varying from 0 to 5 ohms are simulated. We show that the equivalent models precisely replicate the steady-state response of the detailed time-domain models.

Recent advances in inverter-based distributed energy resources (DERs) allow microgrids to operate in grid-connected and islanded modes with ease. However, determining a steady-state load flow solution of a real-world unbalanced and islanded three-phase microgrid remains a challenge. Existing methods are either unsuitable, labor-intensive or computationally demanding for a long-term analysis of islanded microgrids. To address these issues, we propose a practical solution framework that employs externally-updated system frequency, power quantities, and droop characteristics governing the voltage and phase angle of DERs in every iteration as inputs to an off-the-shelf open-source multi-phase, multi-wire, unbalanced power flow software tool to solve an islanded-microgrid power flow. Using our framework, users only need to implement a set of droop equations and update system variables. The power flow solution is accomplished entirely by an off-the-shelf power flow tool, e.g., OpenDSS. Our proposed framework can model a microgrid of any arbitrary configuration and operating condition. We demonstrate and validate the proposed method’s efficacy by comparing its results with those modeled using a time-domain simulation with PSCAD/EMTDC. Finally, an example of a quasi-static time-series study is presented to better illustrate the application of such a tool.

As batteries become more prevalent in grid energy storage applications, the controllers that decide when to charge and discharge become critical to maximizing their utilization. Controller design for these applications is based on models that mathematically represent the physical dynamics and constraints of batteries. Unrepresented dynamics in these models can lead to suboptimal control. Our goal is to examine the state-of-the-art with respect to the models used in optimal control of battery energy storage systems (BESSs). This review helps engineers navigate the range of available design choices and helps researchers by identifying gaps in the state-of-the-art. BESS models can be classified by physical domain: state-of-charge (SoC), temperature, and degradation. SoC models can be further classified by the units they use to define capacity: electrical energy, electrical charge, and chemical concentration. Most energy based SoC models are linear, with variations in ways of representing efficiency and the limits on power. The charge based SoC models include many variations of equivalent circuits for predicting battery string voltage. SoC models based on chemical concentrations use material properties and physical parameters in the cell design to predict battery voltage and charge capacity. Temperature is modeled through a combination of heat generation and heat transfer. Heat is generated through changes in entropy, overpotential losses, and resistive heating. Heat is transferred through conduction, radiation, and convection. Variations in thermal models are based on which generation and transfer mechanisms are represented and the number and physical significance of finite elements in the model. Modeling battery degradation can be done empirically or based on underlying physical mechanisms. Empirical stress factor models isolate the impacts of time, current, SoC, temperature, and depth-of-discharge (DoD) on battery state-of-health (SoH). Through a few simplifying assumptions, these stress factors can be represented using regularization norms. Physical degradation models can further be classified into models of side-reactions and those of material fatigue. This article demonstrates the importance of model selection to optimal control by providing several example controller designs. Simpler models may overestimate or underestimate the capabilities of the battery system. Adding details can improve accuracy at the expense of model complexity, and computation time. Our analysis identifies six gaps: deficiency of real-world data in control literature, lack of understanding in how to balance modeling detail with the number of representative cells, underdeveloped model uncertainty based risk-averse and robust control of BESS, underdevelopment of nonlinear energy based SoC models, lack of hysteresis in voltage models used for control, lack of entropy heating and cooling in thermal modeling, and deficiency of knowledge in what combination of empirical degradation stress factors is most accurate. These gaps are opportunities for future research.

Abstract Current and voltage waveforms recorded by intelligent electronic devices (IEDs) are more useful than just performing post-fault analysis. The objective of this paper is to present techniques to estimate the zero-sequence line impedance of all sections of a three-terminal line and the Thevenin equivalent impedance of the transmission network upstream from the monitoring location using protective relay data collected during short-circuit ground fault events. Protective relaying data from all three terminals may not be always available. Furthermore, the data from each terminal may be unsynchronized and collected at different sampling rates with dissimilar fault time instants. Hence, this paper presents approaches which use unsynchronized measurement data from all the terminals as well as data from only two terminals to estimate the zero-sequence line impedance of all the sections of a three-terminal line. An algorithm to calculate positive-, negative- and zero-sequence Thevenin impedance of the upstream transmission network has also been presented in this paper. The efficacy of the proposed algorithms are demonstrated using a test case. The magnitude error percentage in determining the zero-sequence impedance was less than 1% in the test case presented.

Abstract Introduction Event reports recorded by intelligent electronic devices (IEDs) such as digital relays and fault recorders during disturbances depict the status and system parameters of the power system. Incorrect relay settings and unknown system parameters can lead to relay misoperation but information regarding these are available by performing a comprehensive analysis of fault records. Hence, it is necessary to regularly make a comprehensive assessment of the functioning of the relay to ensure reliable operation. Case description The objective of this paper is to demonstrate various aspects of evaluating relay performance and verifying circuit parameters which are used in relay settings using field data in two case studies. Discussion and Evaluation While scrutinizing the relay’s operation, this paper also presents key insights on verifying circuit parameters using the same relay event records. Conclusions The lessons learned from the case studies presented in this paper will equip a protection engineer to inspect the operation of a relay during a transmission line fault, help gain a better understanding of the fault event and take possible actions to prevent future occurrence of similar events.

The inclusion of distributed renewable energy sources, new goals of efficiency and reliability, and the technological advancement of the power grid has led to a significant increase in the complexity of distribution systems. Although multiple devices can be controlled to achieve these objectives during smart grid operation, many proposed algorithms are based on ideal scenarios where the complex distribution system is assumed to be fully observable or measurable. As this condition obstructs many advanced applications, it is necessary to implement novel alternatives that provide support and validation in the field. In this paper, we show that embedded simulation is capable of providing accurate results of the system real-time condition. The designed platform exploits the technological development of mobile devices, a specific purpose solver, and concurrent processing to embed the power systems simulation into small, flexible, and affordable devices. Simulation results demonstrate the accuracy and timeliness of the proposed realtime simulation based on the IEEE 37 bus test feeder emulation and other large-scale scenarios such as the IEEE 8500 node test feeder. We anticipate that this simulation approach will be useful for applications covering advanced protection relaying, volt-var control, topological reconfiguration, distributed generation management, storage control, and cyber security assessment among others.

Impedance-based algorithms commonly used for determining the fault location in transmission lines are prone to several sources of error and are specific to the line and system configuration. Furthermore, these algorithms do not utilise available valuable information about the power system surrounding the faulted line. These issues can be overcome using a model-based fault location (MBFL) approach. It uses a circuit model to simulate possible fault scenarios and compares the simulated fault currents with the measured currents recorded by the relay to identify the fault location. However, there are several difficulties and limitations while applying MBFL. There is a loss in accuracy and precision based on the number of simulated scenarios and a requirement to store voluminous simulation results. Hence, this study presents a novel application technique for implementing model-based approach efficiently to estimate the fault location and fault resistance using artificial neural networks-based approach. A key highlight of the proposed approach is the ability to identify the location of a fault present on neighbouring lines using the measured through fault current. The study also presents representative scenarios to demonstrate the capability and potential of the proposed approach.

In recent years, machine learning applications have received increasing interest from power system researchers. The successful performance of these applications is dependent on the availability of extensive and diverse datasets for the training and validation of machine learning frameworks. However, power systems operate at quasi-steady-state conditions for most of the time, and the measurements corresponding to these states provide limited novel knowledge for the development of machine learning applications. In this paper, a data mining approach based on optimization techniques is proposed for filtering root-mean-square (RMS) voltage profiles and identifying unusual measurements within triggerless power quality datasets. Then, datasets with equal representation between event and non-event observations are created so that machine learning algorithms can extract useful insights from the rare but important event observations. The proposed framework is demonstrated and validated with both synthetic signals and field data measurements.

Widespread deployment of large-scale photovoltaics (PVs) and energy storage systems (ESSs) in distribution networks necessitates the development of methods to assess their possible system impacts. One of the primary concerns related to the integration of these systems is short-circuit overcurrent protection problems. Present techniques use simulations of full and detailed distribution circuit models with a large number of scenarios to estimate the PV and ESS sizes a distribution feeder can accommodate without causing adverse impacts. As this process requires considerable time and effort, this paper develops a practical and simplified analytical approach to conservatively estimate a utility distribution feeder's accommodation limits without causing protection problems. Sympathetic tripping and relay insensitivity problems are considered in this paper under both symmetrical and unsymmetrical fault conditions. Using the analysis presented, the factors influencing these protection problems are determined to provide insights into relay settings. The feeder accommodation limits obtained using the proposed analytical approach are compared with those obtained using simulations of an actual detailed distribution circuit model. The findings show that the proposed approach is accurate in estimating the feeder's accommodation limits for integrating large-scale PV and ESS.

Series arc faults are challenging to detect in low-voltage dc (LVDC) distribution systems because, unlike other fault types, series arc faults result in only small changes in the current and voltage waveforms. Though there have been several approaches proposed to detect series arc faults, each approach has its requirements and limitations. A step change in the current and voltage waveforms at the arc inception is one of the characteristic signatures of these faults that can be extracted without requiring one to sample the waveforms at a very high frequency. This characteristic feature is utilized to present a novel approach based on voltage differential protection to detect series arc faults in LVDC systems. The proposed method is demonstrated using an embedded controller and experimental data that emulate a hardware-in-the-loop (HIL) test environment. The successful detection of series arc faults on two sets of series arc fault experimental data validated the approach. The results presented also illustrate the computational feasibility in implementing the approach in a real-time environment using an embedded controller. In addition, the paper discusses the robustness of the approach to load changes and loss of time synchronization between measurements at the two terminals of the line.

This paper aims to understand, identify, and mitigate the impacts of residential electric vehicle (EV) charging on distribution system voltages. A thorough literature review on the impacts of residential EV charging is presented, followed by a proposed method for evaluating the impacts of EV loads on the distribution system voltage quality. Practical solutions to mitigate EV load impacts are discussed as well, including infrastructural changes and indirect controlled charging with time-of-use (TOU) pricing. An optimal TOU schedule is also presented, with the aim of maximizing both customer and utility benefits. This paper also presents a discussion on implementing smart charging algorithms to directly control EV charging rates and EV charging starting times. Finally, a controlled charging algorithm is proposed to improve the voltage quality at the EV load locations while avoiding customer inconvenience. The proposed method significantly decreases the impacts of EV load charging on system peak load demand and feeder voltages.

A number of impedance-based fault location algorithms have been developed for estimating the distance to faults in a transmission network. Each algorithm has specific input data requirements and makes certain assumptions that may or may not hold true in a particular fault location scenario. Without a detailed understanding of the principle of each fault-locating method, choosing the most suitable fault location algorithm can be a challenging task. This paper, therefore, presents the theory of one-ended (simple reactance, Takagi, modified Takagi, Eriksson, and Novosel et al.) and two-ended (synchronized, unsynchronized, and current-only) impedance-based fault location algorithms and demonstrates their application in locating real-world faults. The theory details the formulation and input data requirement of each fault-locating algorithm and evaluates the sensitivity of each to the following error sources: 1) load; 2) remote infeed; 3) fault resistance; 4) mutual coupling; 5) inaccurate line impedances; 6) DC offset and CT saturation; 7) three-terminal lines; and 8) tapped radial lines. From the theoretical analysis and field data testing, the following criteria are recommended for choosing the most suitable fault-locating algorithm: 1) data availability and 2) fault location application scenario. Another objective of this paper is to assess what additional information can be gleaned from waveforms recorded by intelligent electronic devices (IEDs) during a fault. Actual fault event data captured in utility networks is exploited to gain valuable feedback about the transmission network upstream from the IED device, and estimate the value of fault resistance.

Post-fault event report analysis is a crucial skill set for electric power engineers in the protection industry. This paper serves as a reference which elucidates the preprocessing procedures involved in transforming data present in event reports to phasors that can be used in various post-fault analysis application algorithms. The paper discusses key elements of this process such as interpreting the data and calculating voltage and current phasors from instantaneous sample values present in a fault record. A crucial component of event report analysis is choosing the appropriate time instant for calculating phasors for event report analysis. Conventionally, protection engineers manually perform event report analysis and arbitrarily select time instants after certain cycles of fault inception for this purpose. This approach prevents the process from being successfully automated. Furthermore, arbitrary selection of time instant does not utilize the entire fault data and may fail in several cases such as short time fault scenario and evolving fault scenario. For this purpose, this paper proposes an adaptive novel technique which utilizes the entire data present in the event report to select the most suitable time instant for event report analysis. The superiority of the proposed algorithm over conventional methods is demonstrated using three real-world scenarios.

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This paper describes an efficient yet accurate methodology for estimating system damping. The proposed technique is based on linear dynamic system theory and the Hilbert damping analysis. The proposed technique requires capacitor switching waveforms only. The detected envelope of the intrinsic transient portion of the voltage waveform after capacitor bank energizing and its decay rate along with the damped resonant frequency are used to quantify effective X/R ratio of a system. Thus, the proposed method provides complete knowledge of system impedance characteristics. The estimated system damping can also be used to evaluate the system vulnerability to various PQ disturbances, particularly resonance phenomena, so that a utility may take preventive measures and improve PQ of the system.

Power quality monitoring has expanded from a means to investigate customer complaints to an integral part of power system performance assessments. Besides special purpose power quality monitors, power quality data are collected from many other monitoring devices on the system (intelligent relays, revenue meters, digital fault recorders, etc.). The result is a tremendous volume of measurement data that is being collected continuously and must be analyzed to determine if there are important conclusions that can be drawn from the data. It is a significant challenge due to the wide range of characteristics involved, ranging from very slow variations in the steady state voltage to microsecond transients and high frequency distortion. This paper describes some of the problems that can be evaluated with both offline and online analyses of power quality measurement data. These applications can dramatically increase the value of power quality monitoring systems and provide the basis for ongoing research into new analysis and characterization methods and signal processing techniques.

Background: The unpredictability of the progression of coronavirus disease 2019 (COVID-19) may be attributed to the low precision of the tools used to predict the prognosis of this disease. Objective: To identify the predictors associated with poor clinical outcomes in patients with COVID-19. Methods: Relevant articles from PubMed, Embase, Cochrane, and Web of Science were searched as of April 5, 2020. The quality of the included papers was appraised using the Newcastle-Ottawa scale (NOS). Data of interest were collected and evaluated for their compatibility for the meta-analysis. Cumulative calculations to determine the correlation and effect estimates were performed using the Z test. Results: In total, 19 papers recording 1,934 mild and 1,644 severe cases of COVID-19 were included. Based on the initial evaluation, 62 potential risk factors were identified for the meta-analysis. Several comorbidities, including chronic respiratory disease, cardiovascular disease, diabetes mellitus, and hypertension were observed more frequent among patients with severe COVID-19 than with the mild ones. Compared to the mild form, severe COVID-19 was associated with symptoms such as dyspnea, anorexia, fatigue, increased respiratory rate, and high systolic blood pressure. Lower levels of lymphocytes and hemoglobin; elevated levels of leukocytes, aspartate aminotransferase, alanine aminotransferase, blood creatinine, blood urea nitrogen, high-sensitivity troponin, creatine kinase, high-sensitivity C-reactive protein, interleukin 6, D-dimer, ferritin, lactate dehydrogenase, and procalcitonin; and a high erythrocyte sedimentation rate were also associated with severe COVID-19. Conclusion: More than 30 risk factors are associated with a higher risk of severe COVID-19. These may serve as useful baseline parameters in the development of prediction tools for COVID-19 prognosis.

Background: The unpredictability of the progression of coronavirus disease 2019 (COVID-19) may be attributed to the low precision of the tools used to predict the prognosis of this disease. Objective: To identify the predictors associated with poor clinical outcomes in patients with COVID-19. Methods: Relevant articles from PubMed, Embase, Cochrane, and Web of Science were searched and extracted as of April 5, 2020. Data of interest were collected and evaluated for their compatibility for the meta-analysis. Cumulative calculations to determine the correlation and effect estimates were performed using the Z test. Results: In total, 19 papers recording 1,934 mild and 1,644 severe cases of COVID-19 were included. Based on the initial evaluation, 62 potential risk factors were identified for the meta-analysis. Several comorbidities, including chronic respiratory disease, cardiovascular disease, diabetes mellitus, and hypertension were observed more frequent among patients with severe COVID-19 than with the mild ones. Compared to the mild form, severe COVID-19 was associated with symptoms such as dyspnea, anorexia, fatigue, increased respiratory rate, and high systolic blood pressure. Lower levels of lymphocytes and hemoglobin; elevated levels of leukocytes, aspartate aminotransferase, alanine aminotransferase, blood creatinine, blood urea nitrogen, high-sensitivity troponin, creatine kinase, high-sensitivity C-reactive protein, interleukin 6, D-dimer, ferritin, lactate dehydrogenase, and procalcitonin; and a high erythrocyte sedimentation rate were also associated with severe COVID-19. Conclusion: More than 30 risk factors are associated with a higher risk of severe COVID-19. These may serve as useful baseline parameters in the development of prediction tools for COVID-19 prognosis.