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This paper explores the detection and localization of cyber-attacks on time-series measurements data in power systems, focusing on comparing conventional machine learning (ML) like k-means, deep learning method like autoencoder, and graph neural network (GNN)-based techniques. We assess the detection accuracy of these approaches and their potential to pinpoint the locations of specific sensor measurements under attack. Given the demonstrated success of GNNs in other time-series anomaly detection applications, we aim to evaluate their performance within the context of power systems cyber-attacks on sensor measurements. Utilizing the IEEE 68-bus system, we simulated four types of false data attacks, including scaling attacks, additive attacks, and their combinations, to test the selected approaches. Our results indicate that GNN-based methods outperform k-means and autoencoder in detection. Additionally, GNNs show promise in accurately localizing attacks for simple scenarios, although they still face challenges in more complex cases, especially ones that involve combinations of scaling and additive attacks.

With the emergence of low-inertia microgrids powered by inverter-based generation, there remains a concern about the operational resilience of these systems. Grid-forming inverters (GFMs), enabled by various device-level (primary) and system-level (secondary) control methods, are poised to play a significant role in achieving certain operational objectives, such as the effective utilization of clean energy resources while maintaining stability. However, despite the recent advances in GFMs, there is a lack of suitable controls that can ascertain resilience-constrained operations, like maintaining critical operational safety limits during transients under various cyber-physical disruptions. In this work, we develop decentralized autonomous controllers (DACs) that enforce resilience-constrained operation via local, minimally invasive adjustments (e.g., changes in set-points) while co-existing within the hierarchy of existing (primary and secondary) controls. The DACs work autonomously by sensing only local GFM measurements and act only when operational resilience constraints are violated. The proposed DAC scheme is computationally efficient (only algebraic computations), which enables fast, real-time execution and demonstrates the efficacy of the proposed control framework on GridLAB-D-HELICS-based control-grid co-simulations on the IEEE 123-node networked microgrid. Finally, we show how the developed DACs empower the grid by utilizing the available resources entirely to ensure resilience (maintain frequency safe limits)., Comment: This paper is currently under review in a journal

The paper discusses fast frequency control in bulk power systems using embedded networks of grid-forming energy storage resources. Differing from their traditional roles of regulating reserves, the storage resources in this work operate as fast-acting grid assets shaping transient dynamics. The storage resources in the network are autonomously controlled using local measurements for distributed frequency support during disturbance events. Further, the grid-forming inverter systems interfacing with the storage resources, are augmented with fast-acting safety controls designed to contain frequency transients within a prescribed tolerance band. The control action, derived from the storage network, improves the frequency nadirs in the system and prevents the severity of a disturbance from propagating far from the source. The paper also presents sensitivity studies to evaluate the impacts of storage capacity and inverter controller parameters on the dynamic performance of frequency control and disturbance localization. The performance of the safety-constrained grid-forming control is also compared with the more common grid-following control. The results are illustrated through case studies on an IEEE test system., Comment: accepted at the IEEE PES Electrical Energy Storage Applications and Technologies Conference (EESAT)

Inverter-based storages are poised to play a prominent role in future power grids with massive renewable generation. Grid-forming inverters (GFMs) are emerging as a dominant technology with synchronous generators (SG)-like characteristics through primary control loops. Advanced secondary control schemes, e.g., consensus algorithms, allow GFM-interfaced storage units to participate in frequency regulations and restore nominal frequency following grid disturbances. However, it is imperative to ensure transient frequency excursions do not violate critical safety limits while the grid transitions from pre- to post-disturbance operating point. This paper presents a hierarchical safety-enforced consensus method -- combining a device-layer (decentralized) transient safety filter with a secondary-layer (distributed) consensus coordination -- to achieve three distinct objectives: limiting transient frequency excursions to safe limits, minimizing frequency deviations from nominal, and ensuring coordinated power sharing among GFM-storage units. The proposed hierarchical (two-layered) safety-consensus technique is illustrated using a GFM-interfaced storage network on an IEEE 68-bus system under multiple grid transient scenarios., Comment: accepted for presentation at the IEEE Electrical Energy Storage Applications and Technologies Conference (EESAT)

The paper presents a theoretical study on small-signal stability and damping in bulk power systems with multiple grid-forming inverter-based storage resources. A detailed analysis is presented, characterizing the impacts of inverter droop gains and storage size on the slower eigenvalues, particularly those concerning inter-area oscillation modes. From these parametric sensitivity studies, a set of necessary conditions are derived that the design of droop gain must satisfy to enhance damping performance. The analytical findings are structured into propositions highlighting potential design considerations for improving system stability. The findings are illustrated via numerical studies on an IEEE 68-bus grid-forming storage network., Comment: accepted for presentation at The 63rd IEEE Conference on Decision and Control

In a controlled cyber-physical network, such as a power grid, any malicious data injection in the sensor measurements can lead to widespread impact due to the actions of the closed-loop controllers. While fast identification of the attack signatures is imperative for reliable operations, it is challenging to do so in a large dynamical network with tightly coupled nodes. A particularly challenging scenario arises when the cyberattacks are strategically launched during a grid stress condition, caused by non-malicious physical disturbances. In this work, we propose an algorithmic framework -- based on Koopman mode (KM) decomposition -- for online identification and visualization of the cyberattack signatures in streaming time-series measurements from a power network. The KMs are capable of capturing the spatial embedding of both natural and anomalous modes of oscillations in the sensor measurements and thus revealing the specific influences of cyberattacks, even under existing non-malicious grid stress events. Most importantly, it enables us to quantitatively compare the outcomes of different potential cyberattacks injected by an attacker. The performance of the proposed algorithmic framework is illustrated on the IEEE 68-bus test system using synthetic attack scenarios. Such knowledge regarding the detection of various cyberattacks will enable us to devise appropriate diagnostic scheme while considering varied constraints arising from different attacks., Comment: accepted as a work-in-progress paper at the 2024 Annual Conference of the IEEE Industrial Electronics Society (IECON)

Net load forecasting is crucial for energy planning and facilitating informed decision-making regarding trade and load distributions. However, evaluating forecasting models' performance against benchmark models remains challenging, thereby impeding experts' trust in the model's performance. In this context, there is a demand for technological interventions that allow scientists to compare models across various timeframes and solar penetration levels. This paper introduces a visual analytics-based application designed to compare the performance of deep-learning-based net load forecasting models with other models for probabilistic net load forecasting. This application employs carefully selected visual analytic interventions, enabling users to discern differences in model performance across different solar penetration levels, dataset resolutions, and hours of the day over multiple months. We also present observations made using our application through a case study, demonstrating the effectiveness of visualizations in aiding scientists in making informed decisions and enhancing trust in net load forecasting models., Comment: Accepted for publication in the proceedings of 2025 IEEE PES Grid Edge Technologies Conference & Exposition (Grid Edge)

The modern power grid has seen a rise in the integration of non-linear loads, presenting a significant concern for operators. These loads introduce unwanted harmonics, leading to potential issues such as overheating and improper functioning of circuit breakers. In pursuing a more sustainable grid, the adoption of electric vehicles (EVs) and photovoltaic (PV) systems in residential networks has increased. Understanding and examining the effects of high-order harmonic frequencies beyond $1.5$ kHz is crucial to understanding their impact on the operation and planning of electrical distribution systems under varying nonlinear loading conditions. This study investigates a diverse set of critical power electronic loads within a household modeled using PSCAD/EMTdc, analyzing their unique harmonic spectra. This information is utilized to run the time-series harmonic analysis program in OpenDSS on a modified IEEE 34 bus test system model. The impact of high-order harmonics is quantified using metrics that evaluate total harmonic distortion (THD), transformer harmonic-driven eddy current loss component, and propagation of harmonics from the source to the substation transformer., Comment: accepted for presentation at the 2024 IEEE Energy Conversion Conference and Expo (ECCE)

Recent Odessa disturbance events have brought attention to the challenges associated with the interaction between Inverter-Based Resources (IBRs) and the transmission and distribution system. The NERC event diagnosis report has highlighted several issues, emphasizing the need for continuous performance monitoring of these IBRs by system operators. Key areas of concern include the mismatch of control and protection performance of IBRs between the original equipment manufacturer (OEM)-provided models and field measurements. The inability to replicate the realistic response can result in incorrect reliability and resilience studies. In this paper, we developed an approach on how to emulate the behavior of an IBR using measurement data obtained for system operators to utilize in real-time and long-term planning. Two experiments are conducted in the phasor domain and electromagnetic transients (EMT) domain to emulate the behavior for grid forming and grid following inverters under various operating conditions and the effectiveness of the proposed model is demonstrated in terms of accuracy and ease of utilizing user-defined models (UDMs)., Comment: accepted for presentation at The 2024 Annual Conference of the IEEE Industrial Electronics Society (IECON)

This paper addresses the following fundamental research question: how does the integration of grid-forming inverters (GFMs) replacing conventional synchronous generators (SGs) impact the slow coherent eigen-structure and the low-frequency oscillatory behavior of future power systems? Due to time-scale separated dynamics, generator states inside a coherent area synchronize over a fast time-scale due to stronger coupling, while the areas themselves synchronize over a slower time scale. Our mathematical analysis shows that due to the large-scale integration of GFMs, the weighted Laplacian structure of the frequency dynamics is preserved, however, the entries of the Laplacian may be significantly modified based on the location and penetration levels of the GFMs. This can impact and potentially significantly alter the coherency structure of the system. We have validated our findings with numerical results using the IEEE 68-bus test system., Comment: 10 pages, 5 figures

Forecasting load at the feeder level has become increasingly challenging with the penetration of behind-the-meter solar, as this self-generation (also called total generation) is only visible to the utility as aggregated net-load. This work proposes a methodology for creation of scenarios of solar penetration at the feeder level for use by forecasters to test the robustness of their algorithm to progressively higher penetrations of solar. The algorithm draws on publicly available observations of weather \emph{condition} (e.g., rainy/cloudy/fair) for use as proxies to sky clearness. These observations are used to mask and weight the interval deviations of similar native usage profiles from which average interval usage is calculated and subsequently added to interval net generation to reconstruct interval total generation. This approach improves the estimate of annual energy generation by 23\%; where the net generation signal currently only reflects 52\% of total annual generation, now 75\% is captured via the proposed algorithm. This proposed methodology is data driven and extensible to service territories which lack information on irradiance measurements and geo-coordinates., Comment: accepted for presentation at the IEEE PES General Meeting 2024

The development and progression of arthritis is strongly associated with osteophytes, which are small and elusive bone growths. This paper presents one of the first efforts towards automated spinal osteophyte detection in spinal X-rays. A novel automated patch extraction process, called SegPatch, has been proposed based on deep learning-driven vertebrae segmentation and the enlargement of mask contours. A final patch classification accuracy of 84.5\% is secured, surpassing a baseline tiling-based patch generation technique by 9.5%. This demonstrates that even with limited annotations, SegPatch can deliver superior performance for detection of tiny structures such as osteophytes. The proposed approach has potential to assist clinicians in expediting the process of manually identifying osteophytes in spinal X-ray., Comment: ISBI'24 Full Paper

Accurate net load forecasting is vital for energy planning, aiding decisions on trade and load distribution. However, assessing the performance of forecasting models across diverse input variables, like temperature and humidity, remains challenging, particularly for eliciting a high degree of trust in the model outcomes. In this context, there is a growing need for data-driven technological interventions to aid scientists in comprehending how models react to both noisy and clean input variables, thus shedding light on complex behaviors and fostering confidence in the outcomes. In this paper, we present Forte, a visual analytics-based application to explore deep probabilistic net load forecasting models across various input variables and understand the error rates for different scenarios. With carefully designed visual interventions, this web-based interface empowers scientists to derive insights about model performance by simulating diverse scenarios, facilitating an informed decision-making process. We discuss observations made using Forte and demonstrate the effectiveness of visualization techniques to provide valuable insights into the correlation between weather inputs and net load forecasts, ultimately advancing grid capabilities by improving trust in forecasting models., Comment: Accepted for publication in the proceedings of 2024 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference, North America (ISGT NA)

This work aims to explore the community structure of Santiago de Chile by analyzing the movement patterns of its residents. We use a dataset containing the approximate locations of home and work places for a subset of anonymized residents to construct a network that represents the movement patterns within the city. Through the analysis of this network, we aim to identify the communities or sub-cities that exist within Santiago de Chile and gain insights into the factors that drive the spatial organization of the city. We employ modularity optimization algorithms and clustering techniques to identify the communities within the network. Our results present that the novelty of combining community detection algorithms with segregation tools provides new insights to further the understanding of the complex geography of segregation during working hours., Comment: 6 pages excluding References

The influx of non-linear power electronic loads into the distribution network has the potential to disrupt the existing distribution transformer operations. They were not designed to mediate the excessive heating losses generated from the harmonics. To have a good understanding of current standing challenges, a knowledge of the generation and load mix as well as the current harmonic estimations are essential for designing transformers and evaluating their performance. In this paper, we investigate a mixture of essential power electronic loads for a household designed in PSCAD/EMTdc and their potential impacts on transformer eddy current losses and derating using harmonic analysis. The various scenarios have been studied with increasing PV penetrations. The peak load conditions are chosen for each scenario to perform a transformer derating analysis. Our findings reveal that in the presence of high power electronic loads (especially third harmonics), along with increasing PV generation may worsen transformer degradation. However, with a low amount of power electronic loads, additional PV generation helps to reduce the harmonic content in the current and improve transformer performance., Comment: The paper has been accepted at ISGT NA 2023 and will be presented there

Critical energy infrastructure are constantly understress due to the ever increasing disruptions caused by wildfires, hurricanes, other weather related extreme events and cyber-attacks. Hence it becomes important to make critical infrastructure resilient to threats from such cyber-physical events. Such events are however hard to predict and numerous in nature and type, making it infeasible to become resilient to all possible cyber-physical event as such an approach would make the system operation overly conservative. Furthermore, distributions of such events are hard to predict and historical data available on such events is sparse. To deal with these issues, we present a policy-mode framework that enumerates and predicts the probability of various cyber-physical events on top of a distributionally robust optimization (DRO) that is robust to the sparsity of the available historical data. The proposed algorithm is illustrated on an islanded microgrid example: a modified IEEE 123-node feeder with distributed energy resources (DERs) and energy storage.

Critical energy infrastructures are increasingly relying on advanced sensing and control technologies for efficient and optimal utilization of flexible energy resources. Algorithmic procedures are needed to ensure that such systems are designed to be resilient to a wide range of cyber-physical adversarial events. This paper provides a robust optimization framework to quantify the range of adversarial perturbations that a system can accommodate without violating pre-specified resiliency metrics. An inner-approximation of the set of adversarial events which can be mitigated by the available flexibility is constructed using an optimization based approach. The proposed algorithm is illustrated on an islanded microgrid example: a modified IEEE 123-node feeder with distributed energy resources. Simulations are carried out to validate that the resiliency metrics are met for any event sampled from the constructed adversarial set for varying levels of available flexibility (energy reserves)., Comment: accepted at the IEEE American Control Conference 2022

With the expected rise in behind-the-meter solar penetration within the distribution networks, there is a need to develop time-series forecasting methods that can reliably predict the net-load, accurately quantifying its uncertainty and variability. This paper presents a deep learning method to generate probabilistic forecasts of day-ahead net-load at 15-min resolution, at various solar penetration levels. Our proposed deep-learning based architecture utilizes the dimensional reduction, from a higher-dimensional input to a lower-dimensional latent space, via a convolutional Autoencoder (AE). The extracted features from AE are then utilized to generate probability distributions across the latent space, by passing the features through a kernel-embedded Perron-Frobenius (kPF) operator. Finally, long short-term memory (LSTM) layers are used to synthesize time-series probability distributions of the forecasted net-load, from the latent space distributions. The models are shown to deliver superior forecast performance (as per several metrics), as well as maintain superior training efficiency, in comparison to existing benchmark models. Detailed analysis is carried out to evaluate the model performance across various solar penetration levels (up to 50\%), prediction horizons (e.g., 15\,min and 24\,hr ahead), and aggregation level of houses, as well as its robustness against missing measurements., Comment: presently under review at a IEEE PES journal

Modern safety-critical energy infrastructures are increasingly operated in a hierarchical and modular control framework which allows for limited data exchange between the modules. In this context, it is important for each module to synthesize and communicate constraints on the values of exchanged information in order to assure system-wide safety. To ensure transient safety in inverter-based microgrids, we develop a set invariance-based distributed safety verification algorithm for each inverter module. Applying Nagumo's invariance condition, we construct a robust polynomial optimization problem to jointly search for safety-admissible set of control set-points and design parameters, under allowable disturbances from neighbors. We use sum-of-squares (SOS) programming to solve the verification problem and we perform numerical simulations using grid-forming inverters to illustrate the algorithm.

Continuous monitoring of the spatio-temporal dynamic behavior of critical infrastructure networks, such as the power systems, is a challenging but important task. In particular, accurate and timely prediction of the (electro-mechanical) transient dynamic trajectories of the power grid is necessary for early detection of any instability and prevention of catastrophic failures. Existing approaches for the prediction of dynamic trajectories either rely on the availability of accurate physical models of the system, use computationally expensive time-domain simulations, or are applicable only at local prediction problems (e.g., a single generator). In this paper, we report the application of two broad classes of data-driven learning models -- along with their algorithmic implementation and performance evaluation -- in predicting transient trajectories in power networks using only streaming measurements and the network topology as input. One class of models is based on the Koopman operator theory which allows for capturing the nonlinear dynamic behavior via an infinite-dimensional linear operator. The other class of models is based on the graph convolutional neural networks which are adept at capturing the inherent spatio-temporal correlations within the power network. Transient dynamic datasets for training and testing the models are synthesized by simulating a wide variety of load change events in the IEEE 68-bus system, categorized by the load change magnitudes, as well as by the degree of connectivity and the distance to nearest generator nodes. The results confirm that the proposed predictive models can successfully predict the post-disturbance transient evolution of the system with a high level of accuracy., Comment: 17 pages, this paper is currently under review in a journal

This report documents recent technical work on developing and validating stochastic occupancy models in commercial buildings, performed by the Pacific Northwest National Laboratory (PNNL) as part of the Sensor Impact Evaluation and Verification project under the U.S. Department of Energy (DOE) Building Technologies Office (BTO). In this report, we present our work on developing and validating inhomogeneous semi-Markov chain models for generating sequences of zone-level occupancy presence and occupancy counts in a commercial building. Real datasets are used to learn and validate the generative occupancy models. Relevant metrics such as normalized Jensen-Shannon distance (NJSD) are used to demonstrate the ability of the models to express realistic occupancy behavioral patterns.

Integration of electronics-based residential appliances and distributed energy resources in homes is expected to rise with grid decarbonization. These devices may introduce significant harmonics into power networks that need to be closely studied in order to accurately model and forecast load. However, it can be difficult to obtain harmonic-rich voltage and current data -- necessary for identifying accurate load models -- for residential electrical loads. Recognizing this need, first a set of electronics-based end-use loads is identified and modeled in an electromagnetic transients program tool for a residence. Second, an impedance-varying method is proposed to generate harmonic data that captures harmonic propagation to the supply voltage and harmonic interactions among end-use loads connected to the same supply voltage. Third, a harmonic-rich dataset produced via the proposed methodology is demonstrated to successfully identify frequency coupling matrix-based harmonic load models using the least-squares method. Numerical results demonstrate the accuracy of the model. The impact of limited data availability on model identification is also explored., Comment: Accepted at the IEEE ISGT 2022 Conference

Recent studies have demonstrated the potential of flexible loads in providing frequency response services. However, uncertainty and variability in various weather-related and end-use behavioral factors often affect the demand-side control performance. This work addresses this problem with the design of a demand-side control to achieve frequency response under load uncertainties. Our approach involves modeling the load uncertainties via stochastic processes that appear as both multiplicative and additive to the system states in closed-loop power system dynamics. Extending the recently developed mean square exponential stability (MSES) results for stochastic systems, we formulate multi-objective linear matrix inequality (LMI)-based optimal control synthesis problems to not only guarantee stochastic stability, but also promote sparsity, enhance closed-loop transient performance, and maximize allowable uncertainties. The fundamental trade-off between the maximum allowable (\textit{critical}) uncertainty levels and the optimal stochastic stabilizing control efforts is established. Moreover, the sparse control synthesis problem is generalized to the realistic power systems scenario in which only partial-state measurements are available. Detailed numerical studies are carried out on IEEE 39-bus system to demonstrate the closed-loop stochastic stabilizing performance of the sparse controllers in enhancing frequency response under load uncertainties; as well as illustrate the fundamental trade-off between the allowable uncertainties and optimal control efforts., Comment: accepted for publication at the IEEE Transactions on Power Sysems

For effective integration of building operations into the evolving demand response programs of the power grid, real-time decisions concerning the use of building appliances for grid services must excel on multiple criteria, ranging from the added value to occupants' comfort to the quality of the grid services. In this paper, we present a data-driven decision-support framework to dynamically rank load control alternatives in a commercial building, addressing the needs of multiple decision criteria (e.g. occupant comfort, grid service quality) under uncertainties in occupancy patterns. We adopt a stochastic multi-criteria decision algorithm recently applied to prioritize residential on/off loads, and extend it to i) complex load control decisions (e.g. dimming of lights, changing zone temperature set-points) in a commercial building; and ii) systematic integration of zonal occupancy patterns to accurately identify short-term grid service opportunities. We evaluate the performance of the framework for curtailment of air-conditioning, lighting, and plug-loads in a multi-zone office building for a range of design choices. With the help of a prototype system that integrates an interactive \textit{Data Analytics and Visualization} frontend, we demonstrate a way for the building operators to monitor the flexibility in energy consumption and to develop trust in the decision recommendations by interpreting the rationale behind the ranking., Comment: accepted in the 2021 American Control Conference

Convolutional Neural Networks have been known as black-box models as humans cannot interpret their inner functionalities. With an attempt to make CNNs more interpretable and trustworthy, we propose IS-CAM (Integrated Score-CAM), where we introduce the integration operation within the Score-CAM pipeline to achieve visually sharper attribution maps quantitatively. Our method is evaluated on 2000 randomly selected images from the ILSVRC 2012 Validation dataset, which proves the versatility of IS-CAM to account for different models and methods., Comment: 8 pages

Malicious activities on measurements from sensors like Phasor Measurement Units (PMUs) can mislead the control center operator into taking wrong control actions resulting in disruption of operation, financial losses, and equipment damage. In particular, false data attacks initiated during power systems transients caused due to abrupt changes in load and generation can fool the conventional model-based detection methods relying on thresholds comparison to trigger an anomaly. In this paper, we propose a Koopman mode decomposition (KMD) based algorithm to detect and identify false data attacks in real-time. The Koopman modes (KMs) are capable of capturing the nonlinear modes of oscillation in the transient dynamics of the power networks and reveal the spatial embedding of both natural and anomalous modes of oscillations in the sensor measurements. The Koopman-based spatio-temporal nonlinear modal analysis is used to filter out the false data injected by an attacker. The performance of the algorithm is illustrated on the IEEE 68-bus test system using synthetic attack scenarios generated on GridSTAGE, a recently developed multivariate spatio-temporal data generation framework for simulation of adversarial scenarios in cyber-physical power systems., Comment: This work has been accepted in the 2020 IEEE SmartGridComm

Interpretation of the underlying mechanisms of Deep Convolutional Neural Networks has become an important aspect of research in the field of deep learning due to their applications in high-risk environments. To explain these black-box architectures there have been many methods applied so the internal decisions can be analyzed and understood. In this paper, built on the top of Score-CAM, we introduce an enhanced visual explanation in terms of visual sharpness called SS-CAM, which produces centralized localization of object features within an image through a smooth operation. We evaluate our method on the ILSVRC 2012 Validation dataset, which outperforms Score-CAM on both faithfulness and localization tasks., Comment: 7 pages, 4 figures and 4 tables

Unlike conventional generators, inverter-based generation do not possess any rotational inertia. While grid-forming inverters can synthesize small (virtual) inertia via advanced feedback control loops, additional control mechanisms are needed to ensure safety and security of the power grid during transients. In this paper, we propose novel real-time safety-constrained feedback controllers ("safety filters") for droop-based (grid-forming) inverters to ensure transient security of the grid. The safety filter acts as a buffer between the network operational layer and the inverter-control layer, and only lets those dispatch control signals pass to the inverter droop-controller, which are guaranteed to not violate the safety specifications (frequency, voltage, current limits). Using a distributed barrier certificates method, we construct state-inclusive bounds on the allowable control inputs, which guarantee the satisfaction of transient safety specifications. Sum-of-square programming is used to synthesize the safety filters. Numerical simulation results are provided to illustrate the performance of the proposed filter in inverter-based microgrids., Comment: accepted for presentation at the 2020 American Control Conference. arXiv admin note: text overlap with arXiv:1903.09743

Effective utilization of flexible loads for grid services, while satisfying end-user preferences and constraints, requires an accurate estimation of the aggregated predictive flexibility offered by the electrical loads. Virtual battery (VB) models are often used to quantify the predictive flexibility in thermostatic loads (e.g. residential air-conditioners, electric water-heaters), which model the temporal evolution of a (virtual) energy state via a first order dynamics including self-dissipation rate, and power and energy capacities as parameters. Uncertainties and lack of information regarding end-usage and equipment models render deterministic VB models impractical. In this paper, we introduce the notion of stochastic VB models, and propose a \textit{variational autoencoder}-based deep learning algorithm to identify the probability distribution of the VB model parameters. Using available sensors and meters data, the proposed algorithm generates not only point estimates of the VB parameters, but also confidence intervals around those values. Effectiveness of the proposed frameworks is demonstrated on a collection of electric water-heater loads, whose operation is driven by uncertain water usage profiles., Comment: accepted for presentation at the 2020 American Control Conference

The proliferation of inverter-based generation and advanced sensing, controls, and communication infrastructure have facilitated the accelerated deployment of microgrids. A coordinated network of microgrids can maintain reliable power delivery to critical facilities during extreme events. Low inertia offered by the power electronics interfaced energy resources however, can present significant challenges to ensuring stable operation of the microgrids. In this work, distributed small-signal stability conditions for inverter-based microgrids are developed that involve the droop controller parameters and the network parameters such as line impedances, loads, etc. The distributed closed-form parametric stability conditions derived in this paper can be verified in a computationally efficient manner, facilitating the reliable design and operations of networks of microgrids. Dynamic phasor models have been used to capture the effects of electromagnetic transients. Numerical results are presented, along with PSCAD simulations, to validate the analytical stability conditions. Effects of design choices, such as the conductor types, and inverter sizes, on the small-signal stability of inverter-based microgrids are investigated to identify interpretable stable or unstable region estimates., Comment: This paper is accepted in IEEE Transactions on Power Systems

Protection equipment is used to prevent damage to induction motor loads by isolating them from power systems in the event of severe faults. Modeling the response of induction motor loads and their protection is vital for power system planning and operation, especially in understanding system's dynamic performance and stability after a fault occurs. Induction motors are usually equipped with several types of protection with different operation mechanisms, making it challenging to develop adequate yet not overly complex protection models and determine their parameters for aggregate induction motor models. This paper proposes an optimization-based nonlinear regression framework to determine protection model parameters for aggregate induction motor loads in commercial buildings. Using a mathematical abstraction, the task of determining a suitable set of parameters for the protection model in composite load models is formulated as a nonlinear regression problem. Numerical examples are provided to illustrate the application of the framework. Sensitivity studies are presented to demonstrate the impact of lack of available motor load information on the accuracy of the protection models., Comment: accepted for presentation at The Eleventh Conference on Innovative Smart Grid Technologies (ISGT 2020)

This paper investigates the use of Infrastructure-To-Vehicle (I2V) communication to generate routing suggestions for drivers in transportation systems, with the goal of optimizing a measure of overall network congestion. We define link-wise levels of trust to tolerate the non-cooperative behavior of part of the driver population, and we propose a real-time optimization mechanism that adapts to the instantaneous network conditions and to sudden changes in the levels of trust. Our framework allows us to quantify the improvement in travel time in relation to the degree at which drivers follow the routing suggestions. We then study the resilience of the system, measured as the smallest change in routing choices that results in roads reaching their maximum capacity. Interestingly, our findings suggest that fluctuations in the extent to which drivers follow the provided routing suggestions can cause failures of certain links. These results imply that the benefits of using Infrastructure-To-Vehicle communication come at the cost of new fragilities, that should be appropriately addressed in order to guarantee the reliable operation of the infrastructure., Comment: Accepted for presentation at the IEEE 2019 American Control Conference

Low-to-medium voltage distribution networks are experiencing rising levels of distributed energy resources, including renewable generation, along with improved sensing, communication, and automation infrastructure. As such, state estimation methods for distribution systems are becoming increasingly relevant as a means to enable better control strategies that can both leverage the benefits and mitigate the risks associated with high penetration of variable and uncertain distributed generation resources. The primary challenges of this problem include modeling complexities (nonlinear, non-convex power-flow equations), limited availability of sensor measurements, and high penetration of uncertain renewable generation. This paper formulates the distribution system state estimation as a nonlinear, weighted, least squares problem, based on sensor measurements as well as forecast data (both load and generation). We investigate the sensitivity of state estimator accuracy to (load/generation) forecast uncertainties, sensor accuracy, and sensor coverage levels., Comment: accepted for presentation at the IEEE 2019 American Control Conference

Inverter-interfaced microgrids differ from the traditional power systems due to their lack of inertia. Vanishing timescale separation between voltage and frequency dynamics makes it critical that faster-timescale stabilizing control laws also guarantee by-construction the satisfaction of voltage limits during transients. In this article, we apply a barrier functions method to compute distributed active and reactive power setpoint control laws that certify satisfaction of voltage limits during transients. Using sum-of-squares optimization tools, we propose an algorithmic construction of these control laws. Numerical simulations are provided to illustrate the proposed method., Comment: accepted at the IEEE 2019 American Control Conference

As modern engineering systems grow in complexity, attitudes toward a modular design approach become increasingly more favorable. A key challenge to a modular design approach is the certification of robust stability under uncertainties in the rest of the network. In this paper, we consider the problem of identifying the parametric region, which guarantees stability of the connected module in the robust sense under uncertainties. We derive the conditions under which the robust stability of the connected module is guaranteed for some values of the design parameters, and present a sum-of-squares (SOS) optimization-based algorithm to identify such a parametric region for polynomial systems. Using the example of an inverter-based microgrid, we show how this parametric region changes with variations in the level of uncertainties in the network., Comment: accepted for presentation at the IEEE 2019 American Control Conference

The potential of distributed energy resources in providing grid services can be maximized with the recent advancements in demand side control. Effective utilization of this control strategy requires the knowledge of aggregate flexibility of the distributed energy resources (DERs). Recent works have shown that the aggregate flexibility of DERs can be modeled as a virtual battery (VB) whose state evolution is governed by a first order system including self-dissipation. The VB parameters (self-dissipation rate, energy capacity) are obtained by solving an optimization problem which minimizes the tracking performance of the ensemble and the proposed first-order model. For the identified first order model, time-varying power limits are calculated using binary search algorithms. Finally, this proposed framework is demonstrated for different homogeneous and heterogeneous ensembles consisting of air conditioners (ACs) and electric water heaters (EWHs)., Comment: This is a preprint version of PESGM 2019 (accepted) paper