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NASA NTRS2023

Probabilistic Forecasting of Ground Magnetic Perturbation Spikes at Mid-Latitude Stations

The prediction of large fluctuations in the ground magnetic field (dB/dt) is essential for preventing damage from Geomagnetically Induced Currents. Directly forecasting these fluctuations has proven difficult, but accurately determining the risk of extreme events can allow for the worst of the damage to be prevented. Here we trained Convolutional Neural Network models for eight mid-latitude magnetometers to predict the probability that dB/dt will exceed the 99th percentile threshold 30–60 min in the future. Two model frameworks were compared, a model trained using solar wind data from the Advanced Composition Explorer (ACE) satellite, and another model trained on both ACE and SuperMAG ground magnetometer data. The models were compared to examine if the addition of current ground magnetometer data significantly improved the forecasts of dB/dt in the future prediction window. A bootstrapping method was employed using a random split of the training and validation data to provide a measure of uncertainty in model predictions. The models were evaluated on the ground truth data during eight geomagnetic storms and a suite of evaluation metrics are presented. The models were also compared to a persistence model to ensure that the model using both datasets did not over-rely on dB/dt values in making its predictions. Overall, we find that the models using both the solar wind and ground magnetometer data had better metric scores than the solar wind only and persistence models, and was able to capture more spatially localized variations in the dB/dt threshold crossings.

Michael Coughlan↗

DOE OSTI2018

Balancing Needs Assessment Using Advanced Probabilistic Forecasts

This paper presents a comprehensive approach to predict Balancing Authority (BA) regulation and load following requirements in order to improve BA control performance. In this paper the Pacific Northwest National Laboratory’s (PNNL) “ramp and uncertainty prediction tool (RUT) and day-ahead regulation prediction (DARP) tool” were upgraded to incorporate advanced probabilistic forecast information provided by AWS Truepower. The proposed methodology has been tested and validated using actual California Independent System Operator (CAISO) data. Simulation confirmed that integration probabilistic forecast information can reduce the predicted regulation range by about 12-31%. This means that BAs can procure fewer balancing resources without compromising their reliability and control performance requirements.

Regulation, Solar Generation, Wind Generation, Con↗

DOE OSTI2016

Stochastic Methods Applied to Power System Operations with Renewable Energy: A Review

Renewable energy resources have been rapidly integrated into power systems in many parts of the world, contributing to a cleaner and more sustainable supply of electricity. Wind and solar resources also introduce new challenges for system operations and planning in terms of economics and reliability because of their variability and uncertainty. Operational strategies based on stochastic optimization have been developed recently to address these challenges. In general terms, these stochastic strategies either embed uncertainties into the scheduling formulations (e.g., the unit commitment [UC] problem) in probabilistic forms or develop more appropriate operating reserve strategies to take advantage of advanced forecasting techniques. Other approaches to address uncertainty are also proposed, where operational feasibility is ensured within an uncertainty set of forecasting intervals. In this report, a comprehensive review is conducted to present the state of the art through Spring 2015 in the area of stochastic methods applied to power system operations with high penetration of renewable energy. Chapters 1 and 2 give a brief introduction and overview of power system and electricity market operations, as well as the impact of renewable energy and how this impact is typically considered in modeling tools. Chapter 3 reviews relevant literature on operating reserves and specifically probabilistic methods to estimate the need for system reserve requirements. Chapter 4 looks at stochastic programming formulations of the UC and economic dispatch (ED) problems, highlighting benefits reported in the literature as well as recent industry developments. Chapter 5 briefly introduces alternative formulations of UC under uncertainty, such as robust, chance-constrained, and interval programming. Finally, in Chapter 6, we conclude with the main observations from our review and important directions for future work.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Review of Onsite Temperature and Solar Forecasting Models to Enable Better Building Design and Operations

Advanced building controls and energy optimization for new constructions and retrofits rely on accurate weather data. Traditionally, most studies utilize airport weather information as the decision inputs. However, most buildings are in environments that are quite different than those at the airport miles away. Tree cover, adjacent buildings, and micro-climate effects caused by the larger surrounding area can all yield deviations in air temperature, humidity, solar irradiance, and wind that are large enough to influence design and operation decisions. In order to overcome this challenge, there are many prior studies on developing weather forecasting algorithms from micro-to meso-scales. Additionally, this paper reviews and complies knowledge on common weather data resources, data processing methodologies and forecasting techniques of weather information. Commonly used statistical, machine learning and physical-based models are discussed and presented as two major categories: deterministic forecasting and probabilistic forecasting. Finally, evaluation metrics for forecasting errors are listed and discussed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

A Bayesian Approach for Estimating Uncertainty in Stochastic Economic Dispatch considering Wind Power Penetration

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To estimate the uncertainty in this stochastic economic dispatch problem for forecasting purposes, the conventional Monte-Carlo method is prohibitively time-consuming for practical applications. To overcome this problem, here we propose a novel Gaussian-process-emulator-based approach to quantify the uncertainty in the stochastic economic dispatch considering wind power penetration. Facing high-dimensional real-world data representing the correlated uncertainties from wind generation, a manifold-learning-based Isomap algorithm is proposed to efficiently represent the low-dimensional hidden probabilistic structure of the data. In this low-dimensional latent space, with Latin hypercube sampling as the computer experimental design, a Gaussian-process emulator is used, for the first time, to serve as a nonparametric, surrogate model for the original complicated stochastic economic dispatch model. This reduced-order representative allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus test system reveal the impressive performance of the proposed method.

17 WIND ENERGY↗

DOE OSTI2023

Data-Driven Transition Path Analysis Yields a Statistical Understanding of Sudden Stratospheric Warming Events in an Idealized Model

Abstract Atmospheric regime transitions are highly impactful as drivers of extreme weather events, but pose two formidable modeling challenges: predicting the next event (weather forecasting) and characterizing the statistics of events of a given severity (the risk climatology). Each event has a different duration and spatial structure, making it hard to define an objective “average event.” We argue here that transition path theory (TPT), a stochastic process framework, is an appropriate tool for the task. We demonstrate TPT’s capacities on a wave–mean flow model of sudden stratospheric warmings (SSWs) developed by Holton and Mass, which is idealized enough for transparent TPT analysis but complex enough to demonstrate computational scalability. Whereas a recent article (Finkel et al. 2021) studied near-term SSW predictability, the present article uses TPT to link predictability to long-term SSW frequency. This requires not only forecasting forward in time from an initial condition, but also backward in time to assess the probability of the initial conditions themselves. TPT enables one to condition the dynamics on the regime transition occurring, and thus visualize its physical drivers with a vector field called the reactive current . The reactive current shows that before an SSW, dissipation and stochastic forcing drive a slow decay of vortex strength at lower altitudes. The response of upper-level winds is late and sudden, occurring only after the transition is almost complete from a probabilistic point of view. This case study demonstrates that TPT quantities, visualized in a space of physically meaningful variables, can help one understand the dynamics of regime transitions.

Meteorology & Atmospheric Sciences↗

DOE OSTI2016

Distributed Resource Energy Analysis and Management System (DREAMS) Development for Real-time Grid Operations

This project supports development of the next generation, integrated energy management infrastructure (EMS) able to incorporate advance visualization of behind-the-meter distributed resource information and probabilistic renewable energy generation forecasts to inform real-time operational decisions. The project involves end-users and active feedback from an Utility Advisory Team (UAT) to help inform how information can be used to enhance operational functions (e.g. unit commitment, load forecasting, Automatic Generation Control (AGC) reserve monitoring, ramp alerts) within two major EMS platforms. Objectives include: Engaging utility operations personnel to develop user input on displays, set expectations, test and review; Developing ease of use and timeliness metrics for measuring enhancements; Developing prototype integrated capabilities within two operational EMS environments; Demonstrating an integrated decision analysis platform with real-time wind and solar forecasting information and timely distributed resource information; Seamlessly integrating new 4-dimensional information into operations without increasing workload and complexities; Developing sufficient analytics to inform and confidently transform and adopt new operating practices and procedures; Disseminating project lessons learned through industry sponsored workshops and conferences;Building on collaborative utility-vendor partnership and industry capabilities

14 SOLAR ENERGY↗

DOE OSTI2020

Assessment of wind power scenario creation methods for stochastic power systems operations

Probabilistic scenarios of renewable energy production, such as wind, have been gaining popularity for use in stochastic variants of power systems operations scheduling problems, allowing for optimal decision-making under uncertainty. The quality of the scenarios has a direct impact on the value of the resulting decisions, but until now, methods for creating scenarios have not been compared under realistic operational conditions. Here, we compare the quality of scenario sets created using three different methods, based on a simulated re-enactment of stochastic day-ahead unit commitment and subsequent dispatch for a realistic test system. We create scenarios using a dataset of forecasted and actual wind power values, scaled to evaluate the effects of increasing wind penetration levels. We show that the choice of scenario set can significantly impact system operating cost, renewable energy use, and the ability of the system to meet demand. This result has implications for the ability of system operators to efficiently integrate renewable production into their day-ahead planning, highlighting the need for the use of performance-based assessments for scenario evaluation.

17 WIND ENERGY↗

DOE OSTI2014

Incorporating Forecast Uncertainty in Utility Control Center

Uncertainties in forecasting the output of intermittent resources such as wind and solar generation, as well as system loads are not adequately reflected in existing industry-grade tools used for transmission system management, generation commitment, dispatch and market operation. There are other sources of uncertainty such as uninstructed deviations of conventional generators from their dispatch set points, generator forced outages and failures to start up, load drops, losses of major transmission facilities and frequency variation. These uncertainties can cause deviations from the system balance, which sometimes require inefficient and costly last minute solutions in the near real-time timeframe. This Chapter considers sources of uncertainty and variability, overall system uncertainty model, a possible plan for transition from deterministic to probabilistic methods in planning and operations, and two examples of uncertainty-based fools for grid operations.This chapter is based on work conducted at the Pacific Northwest National Laboratory (PNNL)

wind generation, solar generation, Energy managmen↗

NASA NTRS2018

NASA's GMAO Atmospheric Motion Vectors Simulator: Description and Application to the MISTiC Winds Concept

An atmospheric wind vectors (AMVs) simulator was developed by NASA's GMAO to simulate observations from future satellite constellation concepts. The synthetic AMVs can then be used in OSSEs to estimate and quantify the potential added value of new observations to the present Earth observing system and, ultimately, the expected impact on the current weather forecasting skill. The GMAO AMV simulator is a tunable and flexible computer code that is able to simulate AMVs expected to be derived from different instruments and satellite orbit configurations. As a case study and example of the usefulness of this tool, the GMAO AMV simulator was used to simulate AMVs envisioned to be provided by the MISTiC Winds, a NASA mission concept consisting of a constellation of satellites equipped with infrared spectral midwave spectrometers, expected to provide high spatial and temporal resolution temperature and humidity soundings of the troposphere that can be used to derive AMVs from the tracking of clouds and water vapor features. The GMAO AMV simulator identifies trackable clouds and water vapor features in the G5NR and employs a probabilistic function to draw a subset of the identified trackable features. Before the simulator is applied to the MISTiC Winds concept, the simulator was calibrated to yield realistic observations counts and spatial distributions and validated considering as a proxy instrument to the MISTiC Winds the Himawari-8 Advanced Imager (AHI). The simulated AHI AMVs showed a close match with the real AHI AMVs in terms of observation counts and spatial distributions, showing that the GMAO AMVs simulator synthesizes AMVs observations with enough quality and realism to produce a response from the DAS equivalent to the one produced with real observations. When applied to the MISTiC Winds scanning points, it can be expected that the MISTiC Winds will be able to collect approximately 60,000 wind observations every 6 hours, if considering a constellation composed of 12 satellites (4 orbital planes). In addition, one of the main expected impacts of the MISTiC Winds concept is the ability to derive water vapor feature tracking AMVs below 500-400 hPa, an unique feature among the water vapor AMVs derived from the current Earth observing system.

Carvalho, David↗

NASA NTRS2018

NASA's GMAO Atmospheric Motion Vectors Simulator: Description and Application to the MISTiC Winds Concept

Carvalho, David↗

DOE OSTI2016

Impact of Uncertainty from Load-Based Reserves and Renewables on Dispatch Costs and Emissions

Aggregations of controllable loads are considered to be a fast-responding, cost-efficient, and environmental-friendly candidate for power system ancillary services. Unlike conventional service providers, the potential capacity from the aggregation is highly affected by factors like ambient conditions and load usage patterns. Previous work modeled aggregations of controllable loads (such as air conditioners) as thermal batteries, which are capable of providing reserves but with uncertain capacity. A stochastic optimal power flow problem was formulated to manage this uncertainty, as well as uncertainty in renewable generation. In this paper, we explore how the types and levels of uncertainty, generation reserve costs, and controllable load capacity affect the dispatch solution, operational costs, and CO2 emissions. We also compare the results of two methods for solving the stochastic optimization problem, namely the probabilistically robust method and analytical reformulation assuming Gaussian distributions. Case studies are conducted on a modified IEEE 9-bus system with renewables, controllable loads, and congestion. We find that different types and levels of uncertainty have significant impacts on dispatch and emissions. More controllable loads and less conservative solution methodologies lead to lower costs and emissions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2014

The Radiation, Interplanetary Shocks, and Coronal Sources (RISCS) Toolset

We outline a plan to develop a physics based predictive toolset RISCS to describe the interplanetary energetic particle and radiation environment throughout the inner heliosphere, including at the Earth. To forecast and "nowcast" the radiation environment requires the fusing of three components: 1) the ability to provide probabilities for incipient solar activity; 2) the use of these probabilities and daily coronal and solar wind observations to model the 3D spatial and temporal heliosphere, including magnetic field structure and transients, within 10 AU; and 3) the ability to model the acceleration and transport of energetic particles based on current and anticipated coronal and heliospheric conditions. We describe how to address 1) - 3) based on our existing, well developed, and validated codes and models. The goal of RISCS toolset is to provide an operational forecast and "nowcast" capability that will a) predict solar energetic particle (SEP) intensities; b) spectra for protons and heavy ions; c) predict maximum energies and their duration; d) SEP composition; e) cosmic ray intensities, and f) plasma parameters, including shock arrival times, strength and obliquity at any given heliospheric location and time. The toolset would have a 72 hour predicative capability, with associated probabilistic bounds, that would be updated hourly thereafter to improve the predicted event(s) and reduce the associated probability bounds. The RISCS toolset would be highly adaptable and portable, capable of running on a variety of platforms to accommodate various operational needs and requirements.

Zank, G. P.↗

NASA NTRS2014

Development and Transition of the Radiation, Interplanetary Shocks, and Coronal Sources (RISCS) Toolset

We outline a plan to develop and transition a physics based predictive toolset called The Radiation, Interplanetary Shocks, and Coronal Sources (RISCS) to describe the interplanetary energetic particle and radiation environment throughout the inner heliosphere, including at the Earth. To forecast and "nowcast" the radiation environment requires the fusing of three components: 1) the ability to provide probabilities for incipient solar activity; 2) the use of these probabilities and daily coronal and solar wind observations to model the 3D spatial and temporal heliosphere, including magnetic field structure and transients, within 10 Astronomical Units; and 3) the ability to model the acceleration and transport of energetic particles based on current and anticipated coronal and heliospheric conditions. We describe how to address 1) - 3) based on our existing, well developed, and validated codes and models. The goal of RISCS toolset is to provide an operational forecast and "nowcast" capability that will a) predict solar energetic particle (SEP) intensities; b) spectra for protons and heavy ions; c) predict maximum energies and their duration; d) SEP composition; e) cosmic ray intensities, and f) plasma parameters, including shock arrival times, strength and obliquity at any given heliospheric location and time. The toolset would have a 72 hour predicative capability, with associated probabilistic bounds, that would be updated hourly thereafter to improve the predicted event(s) and reduce the associated probability bounds. The RISCS toolset would be highly adaptable and portable, capable of running on a variety of platforms to accommodate various operational needs and requirements. The described transition plan is based on a well established approach developed in the Earth Science discipline that ensures that the customer has a tool that meets their needs

Spann, James F.↗

DOE OSTI2023

Causes and evolution of winter polynyas north of Greenland

During the 42-year period (1979–2020) of satellite measurements, four major winter (December–March) polynyas have been observed north of Greenland: one in December 1986 and three in the last decade, i.e., February of 2011, 2017, and 2018. The 2018 polynya was unparalleled in its magnitude and duration compared to the three previous events. Given the apparent recent increase in the occurrence of these extreme events, this study aims to examine their evolution and causality, in terms of forced versus natural variability. The limited weather station and remotely sensed sea ice data are analyzed combining with output from the fully coupled Regional Arctic System Model (RASM), including one hindcast and two ensemble simulations. We found that neither the accompanying anomalous warm surface air intrusion nor the ocean below had an impact (i.e., no significant ice melting) on the evolution of the observed winter open-water episodes in the region. Instead, the extreme atmospheric wind forcing resulted in greater sea ice deformation and transport offshore, accounting for the majority of sea ice loss in all four polynyas. Our analysis suggests that strong southerly winds (i.e., northward wind with speeds greater than 10 m s –1 ) blowing persistently over the study region for at least 2 d or more were required over the study region to mechanically redistribute some of the thickest Arctic sea ice out of the region and thus to create open-water areas (i.e., a latent heat polynya). To assess the role of internal variability versus external forcing of such events, we carried out and examined results from the two RASM ensembles dynamically downscaled with output from the Community Earth System Model (CESM) Decadal Prediction Large Ensemble (DPLE) simulations. Out of 100 winters in each of the two ensembles (initialized 30 years apart: one in December 1985 and another in December 2015), 17 and 16 winter polynyas were produced north of Greenland, respectively. The frequency of polynya occurrence had no apparent sensitivity to the initial sea ice thickness in the study area pointing to internal variability of atmospheric forcing as a dominant cause of winter polynyas north of Greenland. We assert that dynamical downscaling using a high-resolution regional climate model offers a robust tool for process-level examination in space and time, synthesis with limited observations, and probabilistic forecasts of Arctic events, such as the ones being investigated here and elsewhere.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

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↗