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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Demonstration of Essential Reliability Services by a 300-MW Solar Photovoltaic Power Plant

The California Independent System Operator (CAISO), First Solar, and the National Renewable Energy Laboratory (NREL) conducted a demonstration project on a large utility-scale photovoltaic (PV) power plant in California to test its ability to provide essential ancillary services to the electric grid. With increasing shares of solar- and wind-generated energy on the electric grid, traditional generation resources equipped with automatic governor control (AGC) and automatic voltage regulation controls -- specifically, fossil thermal -- are being displaced. The deployment of utility-scale, grid-friendly PV power plants that incorporate advanced capabilities to support grid stability and reliability is essential for the large-scale integration of PV generation into the electric power grid, among other technical requirements. A typical PV power plant consists of multiple power electronic inverters and can contribute to grid stability and reliability through sophisticated 'grid-friendly' controls. In this way, PV power plants can be used to mitigate the impact of variability on the grid, a role typically reserved for conventional generators. In August 2016, testing was completed on First Solar's 300-MW PV power plant, and a large amount of test data was produced and analyzed that demonstrates the ability of PV power plants to use grid-friendly controls to provide essential reliability services. These data showed how the development of advanced power controls can enable PV to become a provider of a wide range of grid services, including spinning reserves, load following, voltage support, ramping, frequency response, variability smoothing, and frequency regulation to power quality. Specifically, the tests conducted included various forms of active power control such as AGC and frequency regulation; droop response; and reactive power, voltage, and power factor controls. This project demonstrated that advanced power electronics and solar generation can be controlled to contribute to system-wide reliability. It was shown that the First Solar plant can provide essential reliability services related to different forms of active and reactive power controls, including plant participation in AGC, primary frequency control, ramp rate control, and voltage regulation. For AGC participation in particular, by comparing the PV plant testing results to the typical performance of individual conventional technologies, we showed that regulation accuracy by the PV plant is 24-30 points better than fast gas turbine technologies. The plant's ability to provide volt-ampere reactive control during periods of extremely low power generation was demonstrated as well. The project team developed a pioneering demonstration concept and test plan to show how various types of active and reactive power controls can leverage PV generation's value from being a simple variable energy resource to a resource that provides a wide range of ancillary services. With this project's approach to a holistic demonstration on an actual, large, utility-scale, operational PV power plant and dissemination of the obtained results, the team sought to close some gaps in perspectives that exist among various stakeholders in California and nationwide by providing real test data.

14 SOLAR ENERGY↗
DOE OSTI2017

Multi-Time Step Service Restoration for Advanced Distribution Systems and Microgrids

Modern power systems are facing increased risk of disasters that can cause extended outages. The presence of remote control switches (RCSs), distributed generators (DGs), and energy storage systems (ESS) provides both challenges and opportunities for developing post-fault service restoration methodologies. Inter-temporal constraints of DGs, ESS, and loads under cold load pickup (CLPU) conditions impose extra complexity on problem formulation and solution. In this paper, a multi-time step service restoration methodology is proposed to optimally generate a sequence of control actions for controllable switches, ESSs, and dispatchable DGs to assist the system operator with decision making. The restoration sequence is determined to minimize the unserved customers by energizing the system step by step without violating operational constraints at each time step. The proposed methodology is formulated as a mixed-integer linear programming (MILP) model and can adapt to various operation conditions. Furthermore, the proposed method is validated through several case studies that are performed on modified IEEE 13-node and IEEE 123-node test feeders.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Consensus-Based Control and Optimization of Power System Inertia

The integration of distributed energy resources (DERs), such as solar, wind, and energy storage systems, into power grids through inverter-based resources reduces power system inertia, leading to faster frequency dynamics and potential grid instability. To address this challenge, this paper proposes a distributed, consensus-based approach for the real-time control and optimization of inertia sources (synchronous generators and/or DERs) during system disturbances, enhancing both system stability and economic performance. The distributed control and optimization approach assumes each inertia source exchanges information solely with its neighbor ones, making it easily scalable to large power grid networks. The impacts of the communication connectivity among the inertia sources as well as their generation capacity limits on the distributed approach are investigated. We also demonstrate the approach’s robustness in scenarios involving communication time delays and packet losses, validating its effectiveness through numerical simulations on a 4-bus test system and a two-area 8-bus test system.

Power system inertia↗
DOE OSTI2019

Diesel Generator Controller Evaluation via Controller-Hardware-in-the-Loop for Various Microgrid Operation Modes

This paper presents the Controller-Hardware-in-the-Loop (CHIL) evaluation of a diesel generator controller for various microgrid operation modes. The model of the diesel generator (governor, exciter, and primary control) is simulated in real time, and the secondary control is implemented in a real hardware controller, Woodward easYgen, which is tested via CHIL with different microgrid configurations under microgrid transition operations. The experimental results demonstrate that the control settings and configuration of the Woodward controller work correctly for different microgrids under microgrid transition operations, which provides confidence for site commissioning.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

Accelerating Development of Advanced Inverters.

Increasing the penetration of distributed renewable sources, including photovoltaic (PV) generators, poses technical challenges for grid management. The grid has been optimized over decades to rely on large centralized power plants with well-established feedback controls. Conventional generators provide relatively constant dispatchable power and help to regulate both voltage and frequency. In contrast, photovoltaic (PV) power is variable, is only as predictable as the weather, and provides no control action. Thus, as conventional generation is displaced by PV power, utility operation stake holders are concerned about managing fluctuations in grid voltage and frequency. Furthermore, since the operation of these distributed resources are bound by certain rules that require they stop delivering power when measured voltage or frequency deviate from the nominal operating point, there are also concerns that a single grid event may cause a large fraction of generation to turn off, triggering a black out or break-up of an electric power system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

On the impact of tidal generation and energy storage integration in PV-rich electric distribution systems

Deep decarbonization of power system operations requires the maximal utilization of available renewable resources. At distribution-level operations, however, grid operators can face numerous challenges in integrating renewables at scale owing to the inherent intermittence of renewable energy resources. These include phenomena such as voltage fluctuations, which are typically mitigated through control actuators such as on-load tap changers (OLTC) as well as energy storage devices, such as battery energy storage systems (BESS). On the one hand, high intermittence of the available renewable portfolio may require increasingly aggressive control of actuators, thereby accelerating the probability of equipment failure. On the other hand, integrating BESS operations and having a diverse renewable generation portfolio can typically help stagger power/energy flow to mitigate the aforementioned adverse impacts. In this paper, we employ a Bayesian framework for equipment lifetime estimation to understand the impact of including tidal energy resources and BESS in distribution system operations for feeders having substantial distribution photovoltaic generation. Our results indicate that while tidal energy alone may slightly decrease equipment reliability, the adverse impact on reliability is significantly magnified by a generation portfolio consisting of tidal generation and photovoltaic generation. Here, we also study the tidal and photovoltaic hosting capacity problem with and without energy storage systems using equipment reliability as an added constraint. We conclude that energy storage increases the reliability-constrained hosting capacity of the distribution system.

14 SOLAR ENERGY↗
DOE OSTI2020

A Cost-Performance Analysis of a Sodium Heat Engine for Distributed Concentrating Solar Power

We present that a sodium thermal electrochemical converter (Na-TEC) generates electricity directly from heat through isothermal expansion of sodium ions across a beta"-alumina solid-electrolyte. This heat engine has been considered for use with conventional concentrating solar power (CSP) systems before. However, unlike previous single-stage devices, the improved design uses two stages with an interstage reheat, allowing more economical and efficient conversion up to 29% at a hot side temperature of 850 °C. Herein, a cost-performance analysis for this improved design assesses opportunities for distributed-CSP in the context of micro-combined heat and power systems. A high-level techno-economic analysis (TEA) is presented that explores four scenarios where a Na-TEC is used as the heat engine for a distributed-CSP system. Overnight capital cost and levelized cost of electricity (LCOE) are estimated for a system lifetime of 30 years, revealing that overnight capital costs in a range from $3.57 to $17.71 per W e are feasible, which equate to LCOEs from 6.9 to 17.2 cents kWh e -1 . This analysis makes a significant contribution by concurrently quantifying the efficiency and unit costs for a range of multistage configurations, and demonstrating that a Na-TEC may be a promising alternative to Stirling engines for distributed-CSP systems at residential scale of 1–5 kW e .

14 SOLAR ENERGY↗
DOE OSTI2020

NH 4 OH Looping with Membrane CO 2 Absorber and Distributed Stripper for Enhanced Algae Growth

The University of Kentucky Center for Applied Energy (UK CAER) has devised a unique, integrated CO2 capture and utilization technology. CO2 from coal-fired power generation flue gas is first captured at half the operating cost of a typical aqueous CO2 capture system (CCS), distributed in an aqueous stream and then fixed by algae in bioreactors where the algae production is increased by 50% over that with a typical intermittent nutrient feeding system. Lower CCS operating cost is achieved by eliminating the flue gas pretreatment step for cooling and SO2 removal, eliminating steam extraction from the power generation steam cycle for solvent regeneration, and eliminating CO2 compression. Higher algae production is achieved by continuous, just-in-time nutrient feed to the bioreactors directly from a distributed solvent regenerator, which maintains the bioreactor pH for optimum growth. The process starts with a uniquely configured membrane absorber, where the flue gas is indirectly contacted with an ammonium hydroxide (NH4OH) solvent. Dissolved NH3 is attractive for both CO2 capture and as an algae nutrient. For CO2 capture it is inexpensive, has a low regeneration energy, is thermally- and oxidatively-stable and has a viscosity near that of water, which makes is easy to transport. Numerous studies have shown that the scrubbing capacity of NH3 is approximately 0.9-1.2 kg of CO2/kg of NH3, with a CO2 removal efficiency of ~99% and half the solvent regeneration energy than that of 30 wt% MEA[1, 2, 3]. NH3 is attractive as an algae nutrient due to its low cost. The rich NH4OH solvent is pumped to a set of distributed regenerators which are co-located with the algae bioreactors. Solvent pumping, transport and distribution reduces the balance of plant (BOP) cost compared to a typical aqueous CCS related to the flue gas duct and boost fan required to transport the flue gas. The energy required for the distributed solvent regeneration is supplied by solar-thermal panels eliminating the need for steam extraction from the power generation steam cycle. After solvent regeneration, the product stream contains both the CO2 captured from the flue gas and volatized NH3 from the solvent. This product stream is fed directly to the bioreactors, eliminating the need for compression of the CO2 stream. The relative amounts of CO2 and NH3 in the product stream are adjusted and controlled by a controlling the regeneration conditions (pressure and temperature). The continuous feed of the right ratio of nutrients overcomes the typical inhibition of algae growth resulting from frequent pH swings in the bioreactor due to unbalanced (intermittent) feeding systems for CO2 and N. Also, because the regenerators will operate at pressure and be located in close proximity to the bioreactors, there is no worry about pressure drop when sparging the gas into the algae. Sparging produces small bubbles which is beneficial for mass transfer efficiency. One known challenge when using an NH4OH solvent is high NH3 emission. Hydrophobic membranes are used for CO2 capture using an aqueous NH3 solution[4, 5] without the direct contact between flue gas and aqueous solution. Additionally, UK CAER CO2 capture and utilization process manages NH3 slip in three extra measures. First, NH3 slip is minimized by working with minimal species partial pressure, which is proportional to the concentration in the liquid. Hence, lowering the capture solvent concentration will lower the NH3 partial pressure. Second, UK CAER’s previous work has demonstrated that the addition of Zn2+ into NH3 solutions to chelate the NH3 can reduce NH3 volatility. Third, the configuration of the membrane CO2 absorber utilizes condensed water from the flue gas to continually wash the gas-side of the membrane to reduce fouling and recapture NH3 slip. Additional details about the UK CAER unique, integrated CO2 capture and utilization technology will be presented along with technology development plans. Diao, N., Q. Li, and Z. Fang. 2004. Heat transfer in ground heat exchangers with groundwater advection. International Journal of Thermal Sciences. 43: 1203-1211, He, Q., M. Chen, L. Meng, K. Liu, and W. Pan. 2004. Study on Carbon Dioxide Removal from Flue Gas by Absorption of Aqueous Ammonia. Western Kentucky University. Yeh, A.C., and H. Bai. 1999. Comparison of ammonia and monoethanolamine solvents to reduce CO2 greenhouse gas emissions. The Science of the Total Environment. 228: 121-133, Villeneuve, K., D. Roizard, J.C. Remigy, M. Iacono, and S. Rode. 2018. CO2 capture by aqueous ammonia with hollow fiber membrane contactors: Gas phase reactions and performance stability. Separation and Purification Technology, 199: 189-197, Toro Molina, C., and C. Bouallou. 2016. Carbon dioxide absorption by ammonia intensified with membrane contactors. Clean Techn Environ Policy 18, 2133–2146 (2016)

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2023

Subordinated Gaussian Processes for Solar Irradiance

Traditionally the power grid has been a one-way street with power flowing from large transmission-connected generators through the distribution network to consumers. This paradigm is changing with the introduction of distributed renewable energy resources (DERs), and with it, the way the grid is managed. There is currently a dearth of high fidelity solar irradiance datasets available to help grid researchers understand how expansion of DERs could affect future power system operations. Realistic simulations of by-the-second solar irradiances are needed to study how DER variability affects the grid. Irradiance data are highly non-stationary and non-Gaussian, and even modern time series models are challenged by their distributional properties. We develop a subordinated non-Gaussian stochastic model whose simulations realistically capture the distribution and dependence structure in measured irradiance. We illustrate our approach on a fine resolution dataset from Hawaii, where our approach outperforms standard nonlinear time series models.

MATHEMATICS AND COMPUTING,SOLAR ENERGY↗
DOE OSTI2023

Net Load Forecasting With Disaggregated Behind-the-Meter PV Generation

As worldwide use of residential photovoltaic (PV) systems grows, system operators and utilities will need to transition from forecasting pure demand to forecasting net load with behind-the-meter (BTM) PV generation. However, PV generation can be difficult to predict and the measurements of PV generation from BTM residential systems are often invisible behind a measurement of the net load, making net load forecasting challenging. This paper proposes a novel two-stage framework for net load forecasting in areas with limited observability and high BTM PV generation. First, the profiles of observable customers are used to disaggregate the net load measurements into the pure load and PV generation. Then, separate models are used to forecast the PV generation and pure load individually, and the results are combined for a net load forecast. Further, this paper also proposes a compensator for correcting the error of the net load forecast, using historical forecast errors of the PV generation, pure load, and net load. The proposed framework is tested through two case studies for areas with high BTM PV penetration and less than 10% observable customers. The two-stage forecasting model is compared to two benchmark methods - a time series forecasting model, and a model that forecasts the net load directly using historical net load measurements. Results show that the proposed disaggregation-forecasting framework reduces the error of the net load forecast compared to both benchmark models. In addition, when the net load forecast error is periodic, the compensator can correct the error to improve the forecast accuracy.

14 SOLAR ENERGY↗
DOE OSTI2019

Optimal Operation of Soft Open Points in Active Distribution Networks Under Three-Phase Unbalanced Conditions

The asymmetric integration of distributed generators (DGs) exacerbates the three-phase unbalanced condition in distribution systems. The serious unbalanced operation causes inefficient utilization of network assets and security risks in the system. Soft open point (SOP) is a flexible power electronic device which can achieve accurate active and reactive power flow control to balance the power flow among phases. This paper proposes an SOPs-based operation strategy for unbalanced active distribution networks (ADNs). By regulating the operation of SOPs, the strategy can reduce power losses and simultaneously mitigate the three-phase unbalance of the upper-level grid. Semidefinite programming (SDP) relaxation is advocated to convert the original non-convex, nonlinear optimization model into an SDP formulation, which can be efficiently solved to meet the requirement of rapid adjustment. Case studies are conducted on the modified IEEE 33-node and IEEE 123-node distribution system to verify the effectiveness and efficiency of the proposed strategy.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

The Energy Transition: Advanced Nuclear Needed but Address Climate Vulnerabilities Now

The term “Energy Transition” is an attempt to capture an elaborate set of activities related to the modernization and decarbonization of energy grids. Performed concurrently and often in an ad hoc manner across local, state, regional and national boundaries, it is bringing chaos to what should arguably be one of the most conservatively managed of all critical infrastructure sectors. What’s more, with climate change producing an increasing tempo of extreme events, confidence in the intended resilient and redundant structure of the electric grids is likely to ebb. Even without these climate induced stressors, the nation’s electric grid was built for an earlier century. In addition to a drive towards greater efficiency via digitization and a continuing price decline in distributed energy resources (DERs), one could argue that climate change concerns are the primary driver of the energy transition. Non-CO2 emitting generation sources like wind and solar have become an important part of the overall generation fleet, albeit ones that cannot be counted upon to provide dispatchable power. Current projections indicate deployment of even larger percentages of DERs in coming years. Until far better storage capabilities arrive, the variability of wind and solar, inconsistent performance of traditional thermal generation plants, and energy delivery failures associated with natural gas pipelines will reinforce mounting reliability concerns. This pertains to both electric transmission and distribution. The recent shuttering of nuclear power plants in Germany, Japan, the US and elsewhere are also putting more downward pressure on dispatchable generation. Russia’s attack on Ukraine has roiled energy markets worldwide and forced some countries to return to coal as a primary fuel. In view circumstances such as these, it is essential that significant changes be made to policies and planning criteria, and to the standards and code on which they are based. Given the accelerating pace of extreme weather events, this needs to occur as soon as possible.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Introduction to the Topical Collection on Regional Renewable Energy – Africa

The investments in and provision of power across the African continent are undergoing dramatic transitions brought on by unprecedented technological advances, falling generation costs, and utility business model changes. This transition, now at various stages across the diverse continent, will employ novel approaches and recognize a diverse group of energy users and decision makers - powering development with the region's abundant supply of renewable energy resources. Policymakers, planners, and the private sector in Africa, like those around the globe, are employing new approaches to take advantage of economically attractive renewable energy generation, ranging from innovations in distributed systems enabling higher penetrations of renewable energy, micro- and mini-grids powered entirely by solar photovoltaics and storage for energy access, to large-scale renewable power generation and grid and market integration.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Grid-Forming Frequency Shaping Control for Low-Inertia Power Systems

As power systems transit to a state of high renewable penetration, little or no presence of synchronous generators makes the prerequisite of well-regulated frequency for grid-following inverters unrealistic. Thus, there is a trend to resort to grid-forming inverters which set frequency directly. We propose a novel grid-forming frequency shaping control that is able to shape the aggregate system frequency dynamics into a first-order one with the desired steady-state frequency deviation and Rate of Change of Frequency (RoCoF) after a sudden power imbalance. The no overshoot property resulting from the first-order dynamics allows the system frequency to monotonically move towards its new steady-state without experiencing frequency Nadir, which largely improves frequency security. We prove that our grid-forming frequency-shaping control renders the system internally stable under mild assumptions. The performance of the proposed control is verified via numerical simulations on a modified Icelandic Power Network test case.

control systems↗
DOE OSTI2015

System and method for single-phase, single-stage grid-interactive inverter

The present invention provides for the integration of distributed renewable energy sources/storages utilizing a cascaded DC-AC inverter, thereby eliminating the need for a DC-DC converter. The ability to segment the energy sources and energy storages improves the maintenance capability and system reliability of the distributed generation system, as well as achieve wide range reactive power compensation. In the absence of a DC-DC converter, single stage energy conversion can be achieved to enhance energy conversion efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

Decentralized control of units in smart grids for the support of renewable energy supply

Due to the significant environmental impact of power production from fossil fuels and nuclear fission, future energy systems will increasingly rely on distributed and renewable energy sources (RES). The electrical feed-in from photovoltaic (PV) systems and wind energy converters (WEC) varies greatly both over short and long time periods (from minutes to seasons), and (not only) by this effect the supply of electrical power from RES and the demand for electrical power are not per se matching. In addition, with a growing share of generation capacity especially in distribution grids, the top-down paradigm of electricity distribution is gradually replaced by a bottom-up power supply. This altogether leads to new problems regarding the safe and reliable operation of power grids. In order to address these challenges, the notion of Smart Grids has been introduced. The inherent flexibilities, i.e. the set of feasible power schedules, of distributed power units have to be controlled in order to support demand–supply matching as well as stable grid operation. Controllable power units are e.g. combined heat and power plants, power storage systems such as batteries, and flexible power consumers such as heat pumps. By controlling the flexibilities of these units we are particularly able to optimize the local utilization of RES feed-in in a given power grid by integrating both supply and demand management measures with special respect to the electrical infrastructure. In this context, decentralized systems, autonomous agents and the concept of self-organizing systems will become key elements of the ICT based control of power units. In this contribution, we first show how a decentralized load management system for battery charging/discharging of electrical vehicles (EVs) can increase the locally used share of supply from PV systems in a low voltage grid. For a reliable demand side management of large sets of appliances, dynamic clustering of these appliances into uniformly controlled appliance sets is necessary. We introduce a method for self-organized clustering for this purpose and show how control of such clusters can affect load peaks in distribution grids. Subsequently, we give a short overview on how we are going to expand the idea of self-organized clusters of units into creating a virtual control center for dynamic virtual power plants (DVPP) offering products at a power market. For an efficient organization of DVPPs, the flexibilities of units have to be represented in a compact and easy to use manner. We give an introduction how the problem of representing a set of possibly 10{sup 100} feasible schedules can be solved by a machine-learning approach. In summary, this article provides an overall impression how we use agent based control techniques and methods of self-organization to support the further integration of distributed and renewable energy sources into power grids and energy markets. - Highlights: • Distributed load management for electrical vehicles supports local supply from PV. • Appliances can self-organize into so called virtual appliances for load control. • Dynamic VPPs can be controlled by extensively decentralized control centers. • Flexibilities of units can efficiently be represented by support-vector descriptions.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Centralized and Decentralized Distributed Energy Resource Access Control Implementation Considerations.

A global transition to power grids with high penetrations of renewable energy generation is being driven in part by rapid installations of distributed energy resources (DER). New DER equipment includes standardized IEEE 1547-2018 communication interfaces and proprietary communications capabilities. Interoperable DER provides new monitoring and control capabilities. The existence of multiple entities with different roles and responsibilities within the DER ecosystem makes the Access Control (AC) mechanism necessary. In this paper, we introduce and compare two novel architectures, which provide a Role-Based Access Control (RBAC) service to the DER ecosystem’s entities. Selecting an appropriate RBAC technology is important for the RBAC administrator and users who request DER access authorization. The first architecture is centralized, based on the OpenLDAP, an open source implementation of the Lightweight Directory Access Protocol (LDAP). The second approach is decentralized, based on a private Ethereum blockchain test network, where the RBAC model is stored and efficiently retrieved via the utilization of a single Smart Contract. We have implemented two end-to-end Proofs-of-Concept (PoC), respectively, to offer the RBAC service to the DER entities as web applications. Finally, an evaluation of the two approaches is presented, highlighting the key speed, cost, usability, and security features.

42 ENGINEERING↗
DOE OSTI2026

Omega-Limit Sets and Input-To-State Stability in Power Grids with Switching Equilibria

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields - or modes -, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of ..omega.. -limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗