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223 records · Page 13

Ensemble Manufacturing Techniques for Steam Turbine Components Across Length Scales

Faster design to manufacturing requirements were sought for steam turbine components to meet the changing demands of today’s power grid of improved efficiency through operating temperature increases and enhanced operational flexibility from baseload to cyclic operations. Advances in multiple advanced manufacturing (AM) process enabled redesign of turbine components for extreme environments with the potential to reduce cost. AM is of particular interest to improve component functionality, higher temperature capability, and superior durability in large scale steam turbine applications. AM methods have an immense potential to open-up the design space by working directly with the 3D model to produce near-net shapes, enable fast design-manufacturing iterations, thereby significantly reducing product cost and lead-time up to 25 % from current baseline. However, these benefits cannot be fully realized due to the potential for unknown AM processing defects and their resultant effect upon component performance in service. Siemens is partnering with Oak Ridge National Laboratory (ORNL), Electric Power Research Institute (EPRI), and Connecticut Center for Advanced Technology (CCAT) to advance the knowledge of complex process-material interactions for desired microstructures and properties that are closely interlinked to component geometries across different length scales. The proposed program utilized an ensemble of multidisciplinary technologies to accelerate the development of materials, high-throughput experiments for their qualification, and design flexibility/topology optimization for repair/redesign of components to address critical failure mechanisms for improved performance and increased reliability of existing power plant components. The proposed activities, if successfully demonstrated for identified components, will enable paradigm shift in customized manufacturing and accelerated qualification/certification towards increased steam turbine component durability, increased turbine efficiency, and reduced CO 2 emissions in load-following environments compared to today’s technology. Technology maturation is built into the project as successful research will include customized process-component down-selection enabling AM methodologies to be incorporated directly into the existing supply chain. The specific activities of the proposed effort are: 1. Topology optimization of down-selected steam turbine parts that are amenable to additive and hybrid manufacturing for cost/performance improvement. 2. Process-structure-property relationships for five AM processes for steam turbine materials of interest to compare with conventional materials. 3. Perform part/assembly build process using advanced additive/hybrid machine tools followed by quality inspection of the built components for insight into qualification for production scale-up. Steam turbine rig testing of printed components under targeted, well monitored and characterized environmental conditions of for performance comparison of baseline and redesigned components.

36 MATERIALS SCIENCE↗

Renewable Energy and Efficiency Technologies in Scenarios of U.S. Decarbonization in Two Types of Models: Comparison of GCAM Modeling and Sector-Specific Modeling

Energy system projections from quantitative models inform actions ranging from short-term and local decisions, such as those about technology and infrastructure deployment, and global and long-term negotiations and targets. Computational limits require model designers to balance coverage and resolution (i.e., breadth versus depth). Some models, such as the Global Change Analysis Model (GCAM), represent all energy sources and uses with less resolution than models that focus on a single sector's energy use. GCAM balances global supply and demand of all energy carriers projecting prices using internal calculations for energy sources and costs of greenhouse gas mitigation while capturing interlinkages between the energy system, water, agriculture and land use, the economy, and the climate. This globally comprehensive model was used to frame the Long-Term Strategy of the United States: Pathways to Net-Zero Greenhouse Gas Emissions by 2050, which the White House released in 2021 and has been used to inform national and global economy-wide climate change mitigation discussions and strategy development for decades. Unlike GCAM, sectoral models focus on a portion of the energy sector and with greater detail and resolution. The Regional Energy Deployment System (ReEDS) electricity-sector model, for example, projects electricity system capacity expansion and operation with high-fidelity representation of emerging technologies for deep decarbonization, such as variable renewable energy and energy storage, and integration of these technologies into the electric grid. The Transportation Energy and Mobility Pathway Options (TEMPO) transportation-sector model enables analysis of household choices, with a focus on adoption, charging, and use of electric vehicles. The Scout buildings-sector model supports detailed consideration of the policies and markets that can accelerate the adoption of electrification and energy conservation measures in buildings. Such sector-specific models are instrumental in informing technology research, sectoral planning strategies, and sector-specific aspects of greenhouse gas mitigation strategies in the United States. The integrated multisector and sector-specific modeling approaches represented by GCAM and these sectoral models are complementary. The integrated multisector approach calculates energy pricing and resource allocation within the model, which is important for consistency when future conditions substantially diverge from current conditions in transformative scenarios. The sector-specific approach facilitates representation of granular details across spatial, temporal, technological, and market dimensions that enable exploration of particular interactions and trade-offs. This report presents the results of recent work to explore the differences and trade-offs between these approaches by comparing GCAM with the sector-specific ReEDS, TEMPO, and Scout models. The report compares both model structures and results, and it addresses their potential relevance and applications.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Modeling and Analysis of Stirling Power Convertors

Modeling and Analysis of Stirling Power Convertors Luis A. Rodriguez1 Steven M. Geng, Terry V. Reid, Scott D. Wilson NASA Glenn Research Center, Cleveland, OH, 44135, USA NASA Glenn’s Thermal Energy Conversion Branch is supporting the development of the next generation free-piston Stirling power convertors. American Superconductor (AMSC) and Sunpower Inc. are the two firms under contract to develop the Flexure Isotope Stirling Convertor (FISC) and the Sunpower Robust Stirling Convertor (SRSC), respectively. To comprehend and forecast convertor performance, Sage, ANSYS® Maxwell, and ANSYS® Fluent were used to model the Stirling thermodynamic cycle, alternator electromagnetics, and piston and displacer dynamics. I. Introduction Stirling convertors are being developed by NASA as a potential steady source of electrical power for NASA’s future scientific space missions. Currently, NASA Glenn Research Center has two corporations under contract, American Superconductor (AMSC) and Sunpower Inc., for the development of the next generation of free-piston Stirling convertors for dynamic radioisotope power systems. AMSC is developing the Flexure Isotope Stirling Convertor (FISC), which uses flexures to prevent side motion and rubbing of the piston. Similarly, Sunpower Inc, is developing the Sunpower Robust Stirling Convertor (SRSC). The SRSC uses gas bearings to prevent radial contact of the moving piston. As convertor development continues, it is increasingly important to understand and predict the interactions of components in the system, how they respond to one another, and how they perform as a response to changes in operating conditions. A suitable and enlightening way to demonstrate and foresee these interactions is with the use of accurate modeling software. Sage, ANSYS® Maxwell, and ANSYS® Fluent are the current modeling tools used by NASA to analytically determine convertor performance. Sage is a one-dimensional object-oriented commercial software package used for modeling and optimizing Stirling convertors for Dynamic Radioisotope Power Systems (DRPS) and it is one of the most accurate Stirling convertor codes in use by NASA. This code is the successor to GLIMPS (Globally-Implicit Stirling Cycle Simulation) and GLOP (GLIMPS Optimization) software created by Gedeon Associates [1]. Model input parameters are typically material/gas type, component physical dimensions, temperatures, frequency, charge pressure, and number of time/space nodes. Sage is used to model both the FISC’s and SRSC’s Stirling cycle thermodynamics and piston/displacer dynamics. Performance maps were created and analyzed for both power systems to better understand the relationship between the following conditions: cold-end temperature, hot-end temperature, piston/displacer amplitudes, pressure drop, and thermal input power. The synergy between these conditions will help determine parameter sensitivity. ANSYS® Maxwell was used to create a three-dimensional (3-D) axisymmetric model for both FISC and SRSC alternators. The significant physical components included in each model are the magnets, magnet carrier, outer/inner laminations, and the coil. Inputs to the model are piston amplitude, piston frequency, alternator load, coil resistance, tuning capacitance, and specific material properties. The alternator models calculate terminal voltage, current, piston/current phase, voltage/current phase, coil inductance, terminal power and efficiency. The RI2 losses, core (hysteresis and eddy) losses, and magnet/can eddy losses are also a part of the final results. ANSYS® Fluent is used to build 3-D computational fluid dynamic (CFD) models to examine the Stirling cycle thermodynamics for both the FISC and SRSC systems. Three-dimensional Computer Aided Design (CAD) models were used to create the physical components of each convertor. Steady-state simulations were conducted for hardware testing, prediction of environmental losses during testing, and generation of radiation look-up tables. The model inputs to the aforementioned analysis are the material properties and boundary thermal conditions. The steady-state model calculates temperature and heat flow distributions. Transient 3-D calculations were also part of the CFD analysis. In this study a physically reduced version of the FISC is used to obtain a prediction of available engine power. For the gas bearing SRSC, the transient effort is used to obtain a prediction of bearing pad performance and its sensitivity to micro-channel geometric variation. The model inputs to the transient simulations are the piston amplitude, displacer amplitude, frequency, displacer/piston phase angle, dynamic deforming CFD grid, temperature boundary conditions, and user defined files describing motion profile of piston/displacer. The results of the model are temperature distributions, heat distributions, and PV power produced at pre-determined conditions.

Luis A Rodriguez↗

AVESTAR Center for Operational Excellence of Electricity Generation Plants

To address industry challenges in attaining operational excellence for electricity generation plants, the U.S. Department of Energy’s (DOE) National Energy Technology Laboratory (NETL) has launched a world-class facility for Advanced Virtual Energy Simulation Training and Research (AVESTARTM). This presentation will highlight the AVESTARTM Center simulators, facilities, and comprehensive training, education, and research programs focused on the operation and control of high-efficiency, near-zero-emission electricity generation plants. The AVESTAR Center brings together state-of-the-art, real-time, high-fidelity dynamic simulators with full-scope operator training systems (OTSs) and 3D virtual immersive training systems (ITSs) into an integrated energy plant and control room environment. AVESTAR’s initial offering combines--for the first time--a “gasification with CO2 capture” process simulator with a “combined-cycle” power simulator together in a single OTS/ITS solution for an integrated gasification combined cycle (IGCC) power plant with carbon dioxide (CO2) capture. IGCC systems are an attractive technology option for power generation, especially when capturing and storing CO2 is necessary to satisfy emission targets. The AVESTAR training program offers a variety of courses that merge classroom learning, simulator-based OTS learning in a control-room operations environment, and immersive learning in the interactive 3D virtual plant environment or ITS. All of the courses introduce trainees to base-load plant operation, control, startups, and shutdowns. Advanced courses require participants to become familiar with coordinated control, fuel switching, power-demand load shedding, and load following, as well as to problem solve equipment and process malfunctions. Designed to ensure work force development, training is offered for control room and plant field operators, as well as engineers and managers. Such comprehensive simulator-based instruction allows for realistic training without compromising worker, equipment, and environmental safety. It also better prepares operators and engineers to manage the plant closer to economic constraints while minimizing or avoiding the impact of any potentially harmful, wasteful, or inefficient events. The AVESTAR Center is also used to augment graduate and undergraduate engineering education in the areas of process simulation, dynamics, control, and safety. Students and researchers gain hands-on simulator-based training experience and learn how the commercial-scale power plants respond dynamically to changes in manipulated inputs, such as coal feed flow rate and power demand. Students also analyze how the regulatory control system impacts power plant performance and stability. In addition, students practice start-up, shutdown, and malfunction scenarios. The 3D virtual ITSs are used for plant familiarization, walk-through, equipment animations, and safety scenarios. To further leverage the AVESTAR facilities and simulators, NETL and its university partners are pursuing an innovative and collaborative R&D program. In the area of process control, AVESTAR researchers are developing enhanced strategies for regulatory control and coordinated plant-wide control, including gasifier and gas turbine lead, as well as advanced process control using model predictive control (MPC) techniques. Other AVESTAR R&D focus areas include high-fidelity equipment modeling using partial differential equations, dynamic reduced order modeling, optimal sensor placement, 3D virtual plant simulation, and modern grid. NETL and its partners plan to continue building the AVESTAR portfolio of dynamic simulators, immersive training systems, and advanced research capabilities to satisfy industry’s growing need for training and experience with the operation and control of clean energy plants. Future dynamic simulators under development include natural gas combined cycle (NGCC) and supercritical pulverized coal (SCPC) plants with post-combustion CO2 capture. These dynamic simulators are targeted for use in establishing a Virtual Carbon Capture Center (VCCC), similar in concept to the DOE’s National Carbon Capture Center for slipstream testing. The VCCC will enable developers of CO2 capture technologies to integrate, test, and optimize the operation of their dynamic capture models within the context of baseline power plant dynamic models. The objective is to provide hands-on, simulator-based “learn-by-operating” test platforms to accelerate the scale-up and deployment of CO2 capture technologies. Future AVESTAR plans also include pursuing R&D on the dynamics, operation, and control of integrated electricity generation and storage systems for the modern grid era. Special emphasis will be given to combining load-following energy plants with renewable and distributed generating supplies and fast-ramping energy storage systems to provide near constant baseload power.

97 MATHEMATICS AND COMPUTING↗

Langston University - High Energy Physics (LU-HEP)

This final report is presented by Langston University (LU) for the project entitled "Langston University High Energy Physics" (LUHEP) under the direction of principal investigator (PI) and project director Professor Joel Snow. The project encompassed high energy physics research performed at hadron colliders. The PI is a collaborator on the DZero experiment at Fermi National Accelerator Laboratory in Batavia, IL, USA and the ATLAS experiment at CERN in Geneva, Switzerland and was during the entire project period from April 1, 1999 until May 14, 2012. Both experiments seek to understand the fundamental constituents of the physical universe and the forces that govern their interactions. In 1999 as member of the Online Systems group for Run 2 the PI developed a cross-platform Python-based, Graphical User Interface (GUI) application for monitoring and control of EPICS based devices for control room use. This served as a model for other developers to enhance and build on for further monitoring and control tasks written in Python. Subsequently the PI created and developed a cross-platform C++ GUI utilizing a networked client-server paradigm and based on ROOT, the object oriented analysis framework from CERN. The GUI served as a user interface to the Examine tasks running in the D\O\ control room which monitored the status and integrity of data taking for Run 2. The PI developed the histogram server/control interface to the GUI client for the EXAMINE processes. The histogram server was built from the ROOT framework and was integrated into the D\O\ framework used for online monitoring programs and offline analysis. The PI developed the first implementation of displaying histograms dynamically generated by ROOT in a Web Browser. The PI's work resulted in several talks and papers at international conferences and workshops. The PI established computing software infrastructure at LU and U. Oklahoma (OU) to do analysis of DZero production data and produce simulation data for the experiment. Eventually this included the FNAL SAM data grid system, the SAMGrid (SG) infrastructure, and the Open Science Grid software stacks for computing and storage elements. At the end of 2003 Snow took on the role of global Monte Carlo production coordinator for the DØ experiment. A role which continues til this day. In January of 2004 Snow started working with the SAMGrid development team to help debug, deploy, and integrate SAMGrid with DØ Monte Carlo production. Snow installed and configured SG execution and client sites at LUHEP and OUHEP, and a SG scheduler site at LUHEP. The PI developed a python based GUI (DAJ) that acts as a front end for job submission to SAMGrid. The GUI interfaces to the DZero Mone Carlo (MC) request system that uses SAM to manage MC requests by the physics analysis groups. DAJ significantly simplified SG job submission and was deployed in DZero in an effort to increase the user base of SG. The following year was the advent of SAMGrid job submission to the Open Science Grid (OSG) and LHC Computing Grid (LCG) through a forwarding mechanism. The PI oversaw the integration of these grids into the existing production infrastructure. The PI developed an automatic MC (Automc) request processing system capable of operating without user intervention (other than getting grid credentials), and able to submit to any number of sites on various grids. The system manages production at all but 2 sites. The system was deployed at Fermilab and remains operating there today. The PI's work in distributed computing resulted in several talks at international conferences. UTA, OU, and LU were chosen as the collaborating institutions that form the Southwest Tier 2 Center (SWT2) for ATLAS. During the project period the PI contributed to the online and offline software infrastructure through his work with the Run 2 online group, and played a major role in Monte Carlo production for DZero. During the part of the project period in which the PI served as MC production coordinator MC production increased very significantly. In the first year of the PI's tenure as production coordinator production was 159M events and 6.7~TB of data. During the last year of the project period production was 2,342~M events and 262~TB of data. That is a factor of 15 increase in events and 39 in data volume. The increase occurred with improvements in computer hardware and networks, through the use of grid technology on diverse resources, and through increased automation and efficiency of the production process. LU HEP developed and deployed the automatic MC request processing system in use at FNAL. The complementary strategies of automation and grid production served DZero well. Fermilab has recognized LU HEP's contribution to DZero by allowing the PI to devote full time to research activities by appointing him a guest scientist for the last six years of the project period.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Power Sector Transformation Pathways: Exploring Objectives, Factors, and Technology Innovations to Inform Power Sector Pathway Decisions

The power and heating sectors are responsible for around 30% of global CO2 emissions and this share is likely to grow as countries move towards electrification of the transportation and building sectors. Therefore, enabling forward-thinking, long term strategies in the power sector is a crucial area for international collaboration and support. The rapid transition of power systems toward modern, low-carbon pathways and technologies will be necessary to meet key climate goals while also enabling other critical objectives such as economic development, energy access, and energy system resiliency, among others. Many developed and developing countries are well-poised to champion power sector transformation (PST), however, further support is needed to identify pathways and implement critical near and long-term actions. To address this need, the Low Emission Development Strategies Global Partnership (LEDS GP) together with an expert team including Agora Energiewende, Energy Innovation, European Climate Foundation, Fraunhofer Institute for Systems and Innovation Research , Prayas Energy Group and LEDS Latin America and Caribbean Platform, developed a framework identifying four key pathways that can be integrated and combined to support low-carbon PST. These four pathways are: (1) Distributed Energy Resource Revolution, (2) Bulk Power Transformation, (3) Transmission and Distribution Interactivity, and (4) Distributed Transactional Future. To support exploration of pathways, this study examines PST objectives and factors that may lead countries or jurisdictions to place a greater relative emphasis on certain pathways as well as a framework and complementary tool for considering the emphasis in a hands on manner. The report provides case studies on application of the approach to bring life to the topic. The case studies include Haiti, Kenya, Mexico, Southeast Asia, and the European Union, among others. The report also presents actions to-be-taken in the near-, medium- and long-term to support the realization of pathways and long-term transformation of the power sector. The report, together with a complementary spreadsheet tool developed under the effort, can be used to enable stakeholder engagement and visioning for the power sector over the long-term, taking into account key factors and potential innovations. It can also be used to understand and inform relevant analysis tools and models based on which pathways are emphasized, and to identify key actions in the near- and medium-term to avoid lock-in of carbon-intensive technologies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A Public-Private-Acadmic Partnership to Advance Solar Power Forecasting

The National Center for Atmospheric Research (NCAR) is pleased to have led a partnership to advance the state-of-the-science of solar power forecasting by designing, developing, building, deploying, testing, and assessing the SunCast™ Solar Power Forecasting System. The project has included cutting edge research, testing in several geographically- and climatologically-diverse high penetration solar utilities and Independent System Operators (ISOs), and wide dissemination of the research results to raise the bar on solar power forecasting technology. The partners include three other national laboratories, six universities, and industry partners. This public-private-academic team has worked in concert to perform use-inspired research to advance solar power forecasting through cutting-edge research to advance both the necessary forecasting technologies and the metrics for evaluating them. The project has culminated in a year-long, full-scale demonstration of provide irradiance and power forecasts to utilities and ISOs to use in their operations. The project focused on providing elements of a value chain, beginning with the weather that causes a deviation from clear sky irradiance and progresses through monitoring and observations, modeling, forecasting, dissemination and communication of the forecasts, interpretation of the forecast, and through decision-making, which produces outcomes that have an economic value. The system has been evaluated using metrics developed specifically for this project, which has provided rich information on model and system performance. Research was accomplished on the very short range (0-6 hours) Nowcasting system as well as on the longer term (6-72 hour) forecasting system. The shortest range forecasts are based on observations in the field. The shortest range system, built by Brookhaven National Laboratory (BNL) and based on Total Sky Imagers (TSIs) is TSICast, which operates on the shortest time scale with a latency of only a few minutes and forecasts that currently go out to about 15 min. This project has facilitated research in improving the hardware and software so that the new high definition cameras deployed at multiple nearby locations allow discernment of the clouds at varying levels and advection according to the winds observed at those levels. Improvements over “smart persistence” are about 29% for even these very short forecasts. StatCast is based on pyranometer data measured at the site as well as concurrent meteorological observations and forecasts. StatCast is based on regime-dependent artificial intelligence forecasting techniques and has been shown to improve on “smart persistence” forecasts by 15-50%. A second category of short-range forecasting systems employ satellite imagery and use that information to discern clouds and their motion, allowing them to project the clouds, and the resulting blockage of irradiance, in time. CIRACast (the system produced by the Cooperative Institute for Atmospheric Research [CIRA] at Colorado State University) was already one of the more advanced cloud motion systems, which is the reason that team was brought to this project. During the project timeframe, the CIRA team was able to advance cloud shadowing, parallax removal, and implementation of better advecting winds at different altitudes. CIRACast shows generally a 25-40% improvement over Smart Persistence between sunrise and approximately 1600 UTC (Coordinated Universal Time) . A second satellite-based system, MADCast (Multi-sensor Advective Diffusive foreCast system), assimilates data from multiple satellite imagers and profilers to assimilate a fully three-dimensional picture of the cloud into the dynamic core of WRF. During 2015, MADCast (provided at least 70% improvement over Smart Persistence, with most of that skill being derived during partly cloudy conditions. That allows advection of the clouds via the Weather Research and Forecasting (WRF) model dynamics directly. After WRF-Solar™ showed initial success, it was also deployed in nowcasting mode with coarser runs out to 6 hours made hourly. It provided improvements on the order of 50-60% over Smart Persistence for forecasts up to 1600 UTC. The advantages of WRF-Solar-Nowcasting and MADCast were then blended to develop the new MAD-WRF model that incorporates the most important features of each of those models, both assimilating satellite cloud fields and using WRF-So far physics to develop and dissipate clouds. MAE improvements for MAD-WRF for forecasts from 3-6 hours are improved over WRF-Solar-Now by 20%. While all the Nowcasting system components by themselves provide improvement over Smart Persistence, the largest benefit is derived when they are smartly blended together by the Nowcasting Integrator to produce an integrated forecast. The development of WRF-Solar™ under this project has provided the first numerical weather prediction (NWP) model specifically designed to meet the needs of irradiance forecasting. The first augmentation improved the solar tracking algorithm to account for deviations associated with the eccentricity of the Earth’s orbit and the obliquity of the Earth. Second, WRF-Solar™ added the direct normal irradiance (DNI) and diffuse (DIF) components from the radiation parameterization to the model output. Third, efficient parameterizations were implemented to either interpolate the irradiance in between calls to the expensive radiative transfer parameterization, or to use a fast radiative transfer code that avoids computing three-dimensional heating rates but provides the surface irradiance. Fourth, a new parameterization was developed to improve the representation of absorption and scattering of radiation by aerosols (aerosol direct effect). A fifth advance is that the aerosols now interact with the cloud microphysics, altering the cloud evolution and radiative properties, an effect that has been traditionally only implemented in atmospheric computationally costly chemistry models. A sixth development accounts for the feedbacks that sub-grid scale clouds produce in shortwave irradiance as implemented in a shallow cumulus parameterization Finally, WRF-Solar™ also allows assimilation of infrared irradiances from satellites to determine the three dimensional cloud field, allowing for an improved initialization of the cloud field that increases the performance of short-range forecasts. We find that WRF-Solar™ can improve clear sky irradiance prediction by 15-80% over a standard version of WRF, depending on location and cloud conditions. In a formal comparison to the NAM baseline, WRF-Solar™ showed improvements in the Day-Ahead forecast of 22-42%. The SunCast™ system requires substantial software engineering to blend all of the new model components as well as existing publically available NWP model runs. To do this we use an expert system for the Nowcasting blender and the Dynamic Integrated foreCast (DICast®) system for the NWP models. These two systems are then blended, we use an empirical power conversion method to convert the irradiance predictions to power, then apply an analog ensemble (AnEn) approach to further tune the forecast as well as to estimate its uncertainty. The AnEn module decreased RMSE (root mean squared error) by 17% over the blended SunCast™ power forecasts and provided skill in the probabilistic forecast with a Brier Skill Score of 0.55. In addition, we have also developed a Gridded Atmospheric Forecast System (GRAFS) in parallel, leveraging cost share funds. An economic evaluation based on Production Cost Modeling in the Public Service Company of Colorado showed that the observed 50% improvement in forecast accuracy will save their customers $819,200 with the projected MW deployment for 2024. Using econometrics, NCAR has scaled this savings to a national level and shown that an annual expected savings for this 50% forecast error reduction ranges from $11M in 2015 to $43M expected in 2040 with increased solar deployment. This amounts to a $455M discounted savings over the 26 year period of analysis.

14 SOLAR ENERGY↗