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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Electric Power Grid and Natural Gas Network Operations and Coordination

In this report, we present findings from three studies related to the coordination of natural gas and electricity system operations. We first propose and demonstrate a modeling platform for examining the interdependence of natural gas and electricity networks based on a direct current unit-commitment and economic dispatch model for the power system and a transient hydraulic gas model for the gas system. We use this platform to analyze the value of day-ahead coordination of power and natural gas network operations and to show the importance of considering gas system constraints when analyzing power systems operation with high penetration of gas generators and variable renewable energy sources. In the second study, we utilize our modeling platform to consider the U.S. Federal Energy Regulatory Commission (FERC) Order 809, issued in 2015 to improve day-ahead and intraday coordination of power and gas systems. Finally, in the third study we expand our modeling platform to focus on market-based coordination of electricity and natural gas system operations for a real system, namely a subset of the power and gas networks in the Front Range region of Colorado. We use real system data to evaluate the benefits of coordination operations under different conditions, including different levels of renewable penetration and the use of time-variant, shaped flow nominations. Our results indicate that coordination at various timescales can contribute to a reduction in curtailed gas in high-stress periods (such as those with large ramps in gas offtakes) and a reduction in energy consumption of gas compressor stations. We find that intraday coordination can reduce total power system production costs and natural gas deliverability constraints, yielding cost and reliability benefits. We observe these benefits for the test system as well as in the Colorado case study, where we find that coordination and shaped flows may provide additional value for systems with high penetration of variable renewable energy. Together, these three studies demonstrate a pathway for integrated gas and electricity grid modeling and for studying the benefits of coordinated operations of these increasingly interdependent energy systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Natural Gas - Electric Interface Study

In this presentation, the authors share an overview of the natural gas-electric interface study, why it was started, an overview of existing and proposed approaches so far, a description of the proposed coordination framework, and a case study for Colorado's electricity and natural gas system.

03 NATURAL GAS↗
DOE OSTI2024

Convex Relaxations of Maximal Load Delivery for Multi-Contingency Analysis of Joint Electric Power and Natural Gas Transmission Networks

Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems. These interdependencies have amplified existing vulnerabilities in gas and power grids, where disruptions can require the curtailment of load in one or both systems. Although typically operated independently, coordination of these systems during severe disruptions can allow for targeted delivery to lifeline services, including gas delivery for residential heating and power delivery for critical facilities. To address the challenge of estimating maximum joint network capacities under such disruptions, we consider the task of determining feasible steady-state operating points for severely damaged systems while ensuring the maximal delivery of gas and power loads simultaneously, represented mathematically as the nonconvex joint Maximal Load Delivery (MLD) problem. To increase its tractability, we present a mixed-integer convex relaxation of the MLD problem. Then, to demonstrate the relaxation’s effectiveness in determining bounds on network capacities, exact and relaxed MLD formulations are compared across various multi-contingency scenarios on nine joint networks ranging in size from 25 to 1191 nodes. The relaxation-based methodology is observed to accurately and efficiently estimate the impacts of severe joint network disruptions, often converging to the relaxed MLD problem’s globally optimal solution within ten seconds.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Natural Gas-Electric Interdependency Through 2030

Presentation to IEEE Power and Engineering Society 2022 General Meeting on natural-gas electric interdependency results from Grid Modernization Initiative Near-Term Reliability and Resilience project.

Brewer, John↗
DOE OSTI2020

An Uncertainty Management Framework for Integrated Gas-Electric Energy Systems

In many parts of the world, electric power systems have seen a significant shift toward generation from renewable energy and natural gas. Because of their ability to flexibly adjust power generation in real time, gas-fired power plants are frequently seen as the perfect partner for variable renewable generation. However, this reliance on gas generation increases interdependence and propagates uncertainty between power grids and gas pipelines and brings coordination and uncertainty management challenges. To address these issues, we propose an uncertainty management framework for uncertain, but bounded gas consumption by gas-fired power plants. The admissible ranges are computed based on a joint optimization problem for the combined gas and electricity networks, which involves chance-constrained scheduling for the electric grid and a novel robust optimization formulation for the natural-gas network. This formulation ensures feasibility of the integrated system with a high probability, while providing a tractable numerical formulation. A key advance with respect to existing methods is that our method is based on a physically accurate, validated model for transient gas pipeline flows. Our case study benchmarks our proposed formulation against methods that ignore how reserve activation impacts the fuel use of gas power plants and only consider predetermined gas consumption. Here, the results demonstrate the importance of considering uncertainty to avoid operating constraint violations and curtailment of gas to the generators.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Coordinated Modeling of Electric Grid and Natural Gas Network Operations

Presentation based upon full report of a Colorado case study and coordination framework, which is available at https://www.nrel.gov/docs/fy20osti/77096.pdf. JISEA analysts Brian Sergi, Omar Guerra, and Bri-Mathias Hodge will present on recent JISEA work on coordination between the natural gas and electricity sectors. Power and gas are becoming increasingly interdependent but weren't designed to function together. How does greater coordination impact system operations with different levels of solar and wind penetrations? This free JISEA presentation will take place in a Webinar on Tuesday, May 11, 2021 at 12 p.m.: Learn how greater coordination between the natural gas and electricity sectors impacts system operations with different levels of solar and wind penetrations. Presentation information includes: Historical and projected data for natural gas consumption and power generation in the United States as demonstrated by 2014 East Coast Polar Vortex, 2021 Texas Winter Storm Uri. Showing coupling points, FERC identified need for better coordination, different levels of coordination (decision making and optimization control), coordination framework. Case study on Colorado Front Range, ramping requirements and gas nominations, real-time dispatch (June and December scenarios), results of analysis of impacts of coordination on unserved load. Total real-time gas offtakes by node, impacts on unserved gas, effect on CO2 emissions. Discussions on clusions drawn from Colorado Case study expanded co-simulation via HELICS, objectives of the HELICS+ natural gas use case, modeling of hydrogen blending, techno economic assessment of blending, and blending impacts on energy content and pressure.

analysis↗
DOE OSTI2023

Resilience assessment and planning in power distribution systems: Past and future considerations

High impact low probability (HILP) events such as hurricanes, heat waves, and floods have instigated widespread power outages and blackouts around the globe in the past decade. With the increasing challenges concerning the threats to the power distribution systems and the growing need to mitigate the impacts of the HILP events, resilience has become a crucial requirement for the power grid infrastructures. Numerous efforts have been made to define, measure, and characterize the resilience of power distribution systems. This study thoroughly reviews the state-of-the-art methods on the existing resilience evaluation framework and metrics. Here, the desirable characteristics of resilience metrics are highlighted, and the challenges associated with formulating, developing, and calculating such metrics are discussed. Next, we detail the state-of-the-art literature on planning solutions to ensure distribution system resilience. This paper aims to extract a deep insight into this challenging and critical research area and envision future opportunities that can guide the power distribution system operators/planners to formulate more effective mitigation strategies to enhance the resilience of power distribution systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Resilience-Motivated Distribution System Restoration Considering Electricity-Water-Gas Interdependency

A major outage in the electricity distribution system may affect the operation of water and natural gas supply systems, leading to an interruption of multiple services to critical customers. Therefore, enhancing resilience of critical infrastructures requires joint efforts of multiple sectors. In this paper, a distribution system service restoration method considering the electricity-water-gas interdependency is proposed. The objective is maximizing the supply of electricity, water, and gas to critical customers after an extreme event. The operational constraints of electricity, water, and natural gas networks are considered. Additionally, the characteristics of electricity-driven coupling components, including water pumps and gas compressors, are also modeled. Relaxation techniques are applied to non convex constraints posed by physical laws of those networks. Consequently, the restoration problem is formulated as a mixed-integer second-order cone program, which can readily be solved by the off-the-shelf solvers. The proposed method is validated by numerical simulations on an electricity-water-gas integrated system, developed based on benchmark models of the subsystems. The results indicate that considering the interdependency refines the allocation of limited generation resources and demonstrate the exactness of the proposed convex relaxation

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Could on-site fuel storage economically reduce power plant-gas grid dependence in pipeline constrained areas like New England?

In the Northeastern United States, natural gas supply constraints have led to periods when gas shortages have caused up to a quarter of all unscheduled power plant outages. Dual fuel oil/gas generators or local gas storage might mitigate gas supply shortages. We use historical power plant operational and availability data to develop a supply curve of the costs required for generators to mitigate fuel shortage failures in New England. Based on 2012–2018 data, we find that the historical fuel shortages at approximately 2 GW worth of gas-fired capacity could be mitigated using on-site fuel storage. For comparison, New England’s average reserve margin was 1.7–2.8 GW over our sample period. Oil dual fuel plants would recoup their investment if compensated with a reliability adder of $\$ 3-7$/MWh during their normal operations, while $\$ 7-16$/MWh would incentivize using onsite, compressed natural gas storage. We estimate that the capital expenses associated with the fuel storage options would be less expensive than installing battery backup for resource adequacy at current battery prices.

03 NATURAL GAS↗
DOE OSTI2024

Joint Management and Optimization of Residential Natural Gas and Electricity Distribution Networks Coupled via Fuel Cells

The attractive features of natural gas as well as the growing electric power demand worldwide have created increasing interest in natural-gas-based distributed generation applications for electric distribution networks. Here, this paper investigates the interdependency between a residential natural gas network and an electric distribution network that are linked together via fuel cells. The modeling of the natural gas network is introduced first, and then the algorithm for gas flow study is presented. The optimal placement and sizing of fuel cell based distributed generation systems are formulated to minimize the losses in both the natural gas network and the electric distribution grid, subject to the constraints imposed by both networks. In addition, a probabilistic model for both gas and electricity demands is developed based on historical electricity and natural gas demand data. A K-means clustering method is used to determine the hourly load states to solve the joint probabilistic optimization problem. Simulation studies are carried out on an integrated system consisting of the IEEE 69-bus distribution network and a radial 27-node natural gas network to verify the developed optimization model and the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Joint Management and Optimization of Residential Natural Gas and Electricity Distribution Networks Coupled via Fuel Cells

The interesting properties of natural gas as well as the growing electric power demand worldwide have led to increasing attention to natural-gas-based distributed generation applications in electric distribution systems. This paper goes over the interdependency between a residential natural gas network and an electric distribution network that are coupled via fuel cells. The modeling of the gas network is introduced first, and then the algorithm for gas flow study is presented. The optimal placement and sizing of fuel cell based distributed generation systems are formulated to minimize the losses in both the gas and electric distribution networks, subject to their model constraints. In addition to this, in order to capture the probabilistic nature of the optimization problem under study, the K-means clustering algorithm is applied to the gas and electricity demands to determine hourly load states and their corresponding probabilities. Furthermore, simulation studies are carried out on an integrated system consisting of the IEEE 69-bus distribution feeder and a radial 27-node natural gas network to verify the developed optimization model and the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1984

Report of the Panel on Propulsion

Propulsion, while conventionally included on the list of important aeronautical disciplines along with aerodynamics, structures, etc., is in itself a systems endeavor, analogous to the engineering of the entire vehicle; indeed propulsion encompasses important aspects of all the other disciplines. In recognition of this fact, the panel focused its discussion on those aspects of the key disciplines that are especially or uniquely important to propulsion. From the initial development of the airplane, the propulsion system has been recognized as one of the pacing technologies. It is perhaps because of the technological disparity between the reciprocating engine and the primitive airframe that the two remained relatively and separate, were developed somewhat independently, usually by different organizations. In recent years, the maturing of the gas turbine power plant and the advance in high-speed airframes have rendered this separation somewhat artificial. The power plant and the airframe now share common structural and aerodynamic elements; as the flight Mach number rises, the degree of interaction increases. By the year 2000, this interdependence will have increased in many respects to a point where independent design may not be practical or possible. During the period since the initiation of the aircraft gas turbine, the solid propellant rocket and the liquid propellant rocket, a vast array of other novel engines have been studied, covering the full spectrum of flight conditions from low subsonic to hypersonic and transatmospheric flight. In each instance, performance limits have been investigated under the assumption that current technology or reasonably foreseeable technology would be available for their development. Among the extensive list of advanced, high-performance concepts and cycles examined are the hypersonic ramjet, the variable cycle, runway-to-orbit airbreathing engine, the ram rocket (airbreathing and rich solid propellant rocket), and the air turborocket. At various times, these systems have come relatively close to meriting development and application. In many instances, limitations of materials and technologies curtailed development. As important and with almost equal frequency, the lack of commercial or military utility of the concept precluded the necessary funding. It is instructive to note that two former items on this list, the turbofan (bypass engine) and the high-speed turboprop, are respectively a mainstay engine and a promising development. In the case of the turbofan, its full potential could not be realized until turbine cooling technology had been developed and new materials developed to permit the construction of transonic fans. In the case of the highspeed turbopropeller engine, not only were the material and turbine technologies needed, but, in addition, the rise in fuel costs provided the impetus to take advantage of its favorable fuel consumption characteristic. As the basic technologies progress and as new missions become attractive, the engines in the foregoing list become candidates for new feasibility studies and further technology development. At the present time, the ram rocket is the prime contender to augment the range of small missiles. Of interest also is the hypersonic ram jet and its logical extension, the runway-to-orbit airbreathing engine. Much of this report deals with the development of current or near-future power plant concepts. First, the motivating factors for aeronautical propulsion research are reviewed as a reminder of the importance of continued effort in a field that has often been characterized as mature. Next, technical areas are discussed in which the panel feels additional research effort is warranted and would lead to the realization of the technological potentials between now and the year 2000. Under these guidelines, new cycles (e.g., isothermal energy exchange) were not considered by the panel. Finally, although facility requirements were not a prime consideration in the current projections, the panel believes that the increasing complexity of propulsion systems; the need for more refined interaction between propulsion system, airframe, and controls; and increasing operation in adverse weather will require test capabilities beyond those now available (see appendix). Enhanced test capability is needed in the areas of propulsion airframe integration and in largescale icing research with proper concurrent treatment of altitude, temperature, and speed.

Kerrebrock, Jack L.↗
DOE OSTI2020

Coordinated operation of electricity and natural gas systems from day-ahead to real-time markets

Power systems worldwide are becoming more reliant on energy from natural gas, wind, and solar, posing possible reliability and coordination challenges from the tighter coupling of these infrastructure systems. This paper proposes a framework for the market-based coordination of electricity and natural gas system operations. The proposed framework includes a power system model that accounts for flexibility in the commitment of power plants with short start-up and shut-down times, coupled with a dynamic gas model that simulates when gas cannot be delivered to generators. The capabilities of the framework are illustrated using real-world electric power and gas systems, including scenarios around wind and solar penetrations and the analysis of time-variant, “shaped flow” gas nominations. Our results indicate that coordination between power and gas systems improves total gas delivery and reduces out-of-merit order dispatch in the electricity system, and that shaped flows may reduce unserved gas in systems with high penetrations of wind and solar. Coordination can have mixed effects on carbon-dioxide emissions, with emissions increasing with coordination for current systems during high load weeks but decreasing for systems with high renewable penetrations, particularly during periods of high variability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Near-Term Reliability and Resilience (NTRR) (Final Report)

The Near-Term Reliability and Resiliency (NTRR) was awarded in December 2020 as an inter-lab project to examine the reliability and resilience of the electricity grid and natural gas transportation availability. The project builds on studies conducted by The North American Electric Reliability Corporation (NERC), the U.S. Department of Energy (DOE), and other non-governmental research and operational focused on reliability and resilience analyses challenges. The research was conceived to address near-term scenarios (within 10 years), when many local and regional policy transitions could begin to impact grid reliability, resilience, and supporting infrastructure availability. To integrate the natural gas interdependency, the team began with the generating capacity and demand projections from the 2020 NERC Long-Term Reliability Assessment and the Bulk Electric System (BES) transmission topologies defined in the Western Electricity Coordinating Council (WECC) Anchor Data Set, Eastern Interconnection Reliability Assessment Group Multi-Regional Modeling Working Group (ERAG/MMWG) Data Set, the team calculated baseline regional power sector gas demands from present electricity delivery year through the end of delivery year 2030/31 by applying security constrained economic dispatch. This demand was compiled along with demand projections for regional residential, commercial, and industrial natural gas demands from the most recent Energy Information Administration (EIA) Annual Energy Outlook Reference Case into Deloitte’s MarketBuilder® North American Gas Model. Through the application of these demands, MarketBuilder® was projected the topology of natural gas flows in the natural gas pipeline network across the interconnected North American system along with regional natural gas prices that may be seen by market participants in future years Additionally, contingencies and sensitivities focused on the built models of the Eastern Interconnection (EI) and Western Interconnection (WI). They address challenges from the following with the outcomes being an identification of performance under the extreme conditions and an identification of potential grid weaknesses that should be addressed to mitigate the reduced performance and improve the resilience and reliability of the specific regions as well as the National Grid: • Weather events including extreme heat, extreme cold, high wind, no wind, wind and solar forecasting errors, and wildfires. • Gas availability, factoring in supply disruption (contractual and physical), seasonal availability constraints, and infrastructure limitations; and • Transmission availability and congestion.

03 NATURAL GAS↗
DOE OSTI2020

A trilevel model against false gas-supply information attacks in electricity systems

The interdependence between natural gas and electricity systems is increasing rapidly due to the growing reliance on natural gas-fired generating units. Availability of natural gas for gas-fired generating units can impact the secure operation of electricity systems. Fuel supply shortage for gas-fired units can be caused by uncertain interruptible supply contracts and incorrect supply information. This article proposes a trilevel min-max-min defender-attacker-operator optimization problem to provide the power system operator a screening methodology that allocates a limited budget for best protecting critical fuel supply information, and also the strategies to sign firm supply contract to reduce natural gas supply uncertainties. We utilize a column and constraint generation (C&CG) algorithm to solve the proposed problem. We illustrate the effectiveness of this trilevel formulation using a case study based on IEEE 24-node test system.

42 ENGINEERING↗
DOE OSTI2022

Valuing Resilience for Microgrids: Challenges, Innovative Approaches, and State Needs

The United States depends on the delivery of reliable, affordable, clean, and safe electricity. Electric utilities invest billions of dollars each year in generation, transmission, and distribution assets to meet this need. However, experiences with recent natural disasters of increasing frequency and duration demonstrate the shortcomings of this approach in the face of modern threats. Further, as customers rely on electricity for a broader range of important needs, such as transportation, as well as critical life-saving services and mission critical facilities such as water treatment, medical care, shelters, telecommunications, and more, the need to minimize the likelihood and impacts of outages grows. Against this backdrop, resilience has emerged as a key consideration to guide electricity spending, whether from utilities, customers, or taxpayers. Although reliability has been defined and measured for decades with broadly accepted metrics that measure how many customers lose power and at what frequency and duration, resilience considers the electricity system’s response to a disruption and its subsequent impacts on customers. Developing tools and methods to accurately assess the costs and benefits of resilience investments is a critical step toward the goal of mitigating the impacts of outages on customers and society. Today, electric system resilience is largely treated as an externality due to challenges estimating the costs of long-duration outages, impacts of outages on society, and increasing reliance on electricity for a growing set of interdependent services. These interdependencies include the water, wastewater, telecommunications, natural gas, and health sectors. Without knowing how much a given resilience investment will benefit customers or society more broadly, investors, policymakers, and regulators are less likely to make or approve such investments, and less able to prioritize those investments. State Energy Offices and public utility commissions (PUCs) lead the development of state-level energy policy and utility regulation, respectively, and each has interests in encouraging appropriate public and private investments in resilience. To this end, the National Association of State Energy Officials (NASEO) and National Association of Regulatory Utility Commissioners (NARUC), with the support of the U.S. Department of Energy (DOE) Office of Electricity (OE), formed a joint Microgrids State Working Group to explore the costs and benefits of microgrids, barriers to broader deployment of microgrids to meet resilience and other objectives, and policy and regulatory strategies to optimize investments in resilience, including but not limited to microgrids. Although no universally accepted valuation tool for resilience exists, National Laboratories, utilities, researchers, and state and federal agencies have collaborated to develop, apply, and improve a number of approaches to quantify resilience, several of which are still in progress at the time this report is published. This report seeks to share these important advances by discussing current definitions of resilience (Section 1), how microgrids are defined and used to meet resilience objectives (Section 2), new approaches to valuing resilience (Section 3), steps State Energy Offices and PUCs have taken to further resilience valuation efforts (Section 4), and finally, considerations and suggested next steps for State Energy Offices and PUCs (Section 5). Relevant examples of specific microgrid projects and resilience valuation efforts are included throughout the report. While this report is written specifically for NASEO and NARUC members, it may be useful for utilities, local governments, and individual customers interested in improving the way public and private dollars are spent to achieve resilience outcomes.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Multiscale simulation of integrated energy system and electricity market interactions

Accelerating the deep decarbonization of the world's electric grids requires the coordination of complex energy systems and infrastructures across timescales from seconds to decades. Here, we present a new multiscale simulation framework that integrates process- and grid-centric modeling paradigms to better design, operate, and control integrated energy systems (IESs), which combine multiple technologies, in wholesale energy markets. Traditionally, IESs are analyzed with a process-centric paradigm such as levelized cost of electricity (LCOE) or annualized net revenue, ignoring important interactions with electricity markets. This framework explicitly models the complex interactions between an IES's bidding, scheduling, and control decisions and the energy market's clearing and settlement processes, while incorporating operational uncertainties. Through two case studies, we show the importance of understanding and quantifying complex resource-grid interactions. In case study 1, we demonstrate that optimized bidding from one resource shifts the profit distribution for all energy systems in the market. This result suggests new and more flexible IES technologies can disrupt the economics of all market participants, possibly leading to accelerated retirements of less flexible resources. Interestingly, the optimized bidding has little impact on grid-level aggregate statistics, such as total generation costs and renewable penetration rate. While aggregate modeling strategies may remain valid under some IES adoption scenarios for analysis focused on regional outcomes, direct comparisons of IES technologies at specific locations without considering these interactions may lead to misleading or incorrect conclusions. In case study 2, we consider the design and flexible operation of IESs that hybridize conventional generators with energy storage. Through a sensitivity analysis, we find that as the size of the storage system increases, the total number of start-ups for coal- and natural gas-based IESs reduced by 25% and 33.6%, and the total thermal generator ramping (i.e., mileage) reduced by 86.5% and 62.5%, respectively. This shows the primary benefit of storage may not be reduced operational costs (which do not change significantly) but fewer start-ups and less ramping, which may greatly simplify the design, operation, and control of carbon capture systems. The new modeling and optimization capabilities from this work enable the coupling of rigorous, dynamic process models with grid-level production cost models to quantitatively identify the nuanced interdependencies across these vast timescales that must be addressed to realize clean, safe, and secure energy production. Moreover, the proposed general multiscale simulation framework is applicable to all IES technologies and can be easily extended to consider other energy carriers (e.g., hydrogen, ammonia) and energy infrastructures (e.g., natural gas pipelines).

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Chapter Ten - Power, Buildings, and Other Critical Networks: Integrated Multisystem Operation

The electrifying transportation sector, the increasing grid interactivity of the built environment, the rapidly expanding number of devices within the Internet-of-Things, and the overall trend toward highly connected systems and interdependent networks is revolutionizing the operation of the electric power grid. While these changes are presenting grid operators with new challenges to ensure an efficient, reliable, and sustainable operation of the grid, they also enable a new suite of resources that can be utilized for assisting the grid in times of need. In this chapter, we explore how these recent changes and trends are affecting modern power systems and discuss the benefits and challenges of an increasingly electrified and interconnected world. We will observe how various critical infrastructure, that is, buildings, water and gas, transportation, and telecommunication networks are highly dependent on power network operations but, with improved coordination and control, can also provide valuable assets to the grid in times of need.

electricity markets↗