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At least 541 records · Page 30

Analyzing the Deployment of Large Amounts of Offshore Wind to Design an Offshore Transmission Grid in the United States: Preprint

This paper revisits the results from the U.S. Department of Energy's '20% Wind Energy By 2030' study, which envisioned that 54 GW of offshore wind would be installed by said year. The analysis is conducted using the Regional Energy Deployment System (ReEDS), a capacity expansion model developed by the National Renewable Energy Laboratory. The model is used to optimize the deployment of the 54 GW of wind capacity along the coasts and lakes of the United States. The graphical representation of the results through maps will be used to provide a qualitative description for planning and designing an offshore grid. ReEDS takes into account many factors in the process of siting offshore wind capacity, such as the quality of the resource, capital and O&M costs, interconnection costs, or variability metrics (wind capacity value, forecast error, expected curtailment). The effect of these metrics in the deployment of offshore wind will be analyzed through examples in the results.

17 WIND ENERGY↗

Interactions of Wind Energy Project Siting, Wind Resource Potential, and the Evolution of the U.S. Power System

The interactions of wind energy project siting, resource potential, and power system evolution are critical to understand given interest in high renewable energy systems, particularly as wind costs have fallen and grid operators implement solutions to manage variable generation. This study applies an integrative approach that combines spatially-explicit resource potential analysis with high spatial resolution U.S. electricity system modeling. Multiple wind supply curves, representing variations in siting regimes that account for interactions with built infrastructure, regulatory, physical, and social land use factors, are evaluated to determine how siting could influence prospective wind development. Different siting regimes lead to variations in future wind capacity, with the greatest impacts observed under scenarios with high demand for clean energy. With the tightest emissions limit modeled, 2050 onshore wind capacity varied by +7% (49 GW) in the least-restrictive siting regime to a decrease of 37% (270 GW) under the most-constrained case. More-stringent siting restrictions lead to higher electricity prices and emissions that should be weighed with local impacts. Under restrictive siting regimes, wind deployment is also sensitive to transmission availability and wind plant design. Overall, the findings highlight the importance of local land use considerations in regional and national power system planning.

17 WIND ENERGY↗

Modeling Framework and Validation of a Smart Grid and Demand Response System for Wind Power Integration

Electricity generation from wind power and other renewable energy sources is increasing, and their variability introduces new challenges to the power system. The emergence of smart grid technologies in recent years has seen a paradigm shift in redefining the electrical system of the future, in which controlled response of the demand side is used to balance fluctuations and intermittencies from the generation side. This paper presents a modeling framework for an integrated electricity system where loads become an additional resource. The agent-based model represents a smart grid power system integrating generators, transmission, distribution, loads and market. The model incorporates generator and load controllers, allowing suppliers and demanders to bid into a Real-Time Pricing (RTP) electricity market. The modeling framework is applied to represent a physical demonstration project conducted on the Olympic Peninsula, Washington, USA, and validation simulations are performed using actual dynamic data. Wind power is then introduced into the power generation mix illustrating the potential of demand response to mitigate the impact of wind power variability, primarily through thermostatically controlled loads. The results also indicate that effective implementation of Demand Response (DR) to assist integration of variable renewable energy resources requires a diversity of loads to ensure functionality of the overall system.

Demand Response↗

An efficient method to identify uncertainties of WRF-Solar variables in forecasting solar irradiance using a tangent linear sensitivity analysis

Uncertainty in predicting solar energy resources introduces major challenges in power system management and necessitates the development of reliable probabilistic solar forecasts. As the first part of the development of probabilistic forecasts based on the Weather Research and Forecasting model with solar extensions (WRF-Solar), this study presents a tangent linear approach to identify input variables responsible for the largest uncertainties in predicting surface solar irradiance and clouds. A tangent linear analysis is capable of efficiently investigating sensitivities of output variables with respect to various input variables of WRF-Solar because this approach avoids the computational burden of perturbing the initial conditions of individual input variables. We develop tangent linear models (TLMs) for six WRF-Solar physics packages that control the formation and dissipation of clouds and solar radiation, and we evaluate the validity of TLMs using a linearity test. The tangent linear sensitivity analysis is conducted under various scenarios based on satellite observations and model simulations to consider realistic input conditions. A simple method is used to quantify the impact of the uncertainty of input variables on the output variables from the TLMs. The results demonstrate that uncertainties in the output variables that are the focus of this study—including global horizontal irradiance, direct normal irradiance, cloud mixing ratio, cloud tendency, cloud fraction, and sensible and latent heat fluxes—are highly sensitive to uncertainties in 14 input variables. This study indicates that the tangent linear method can identify key variables of physics modules in WRF-Solar that can be stochastically perturbed to generate ensemble-based probabilistic forecasts.

14 SOLAR ENERGY↗

Computational analysis of storage synthesis in developing Brassica napus L. (oilseed rape) embryos: Flux variability analysis in relation to 13C-metabolic flux analysis

Plant oils are an important renewable resource, and seed oil content is a key agronomical trait that is in part controlled by the metabolic processes within developing seeds. A large-scale model of cellular metabolism in developing embryos of Brassica napus (bna572) was used to predict biomass formation and to analyze metabolic steady states by flux variability analysis under different physiological conditions. Predicted flux patterns are highly correlated with results from prior 13C metabolic flux analysis of B. napus developing embryos. Minor differences from the experimental results arose because bna572 always selected only one sugar and one nitrogen source from the available alternatives, and failed to predict the use of the oxidative pentose phosphate pathway. Flux variability, indicative of alternative optimal solutions, revealed alternative pathways that can provide pyruvate and NADPH to plastidic fatty acid synthesis. The nutritional values of different medium substrates were compared based on the overall carbon conversion efficiency (CCE) for the biosynthesis of biomass. Although bna572 has a functional nitrogen assimilation pathway via glutamate synthase, the simulations predict an unexpected role of glycine decarboxylase operating in the direction of NH4+ assimilation. Analysis of the light-dependent improvement of carbon economy predicted two metabolic phases. At very low light levels small reductions in CO2 efflux can be attributed to enzymes of the tricarboxylic acid cycle (oxoglutarate dehydrogenase, isocitrate dehydrogenase) and glycine decarboxylase. At higher light levels relevant to the 13C flux studies, ribulose-1,5-bisphosphate carboxylase activity is predicted to account fully for the light-dependent changes in carbon balance.

09 BIOMASS FUELS↗

A review of tidal energy—Resource, feedbacks, and environmental interactions

The ocean contains a variety of renewable energy resources, little of which has been exploited. Here, we review both tidal range and tidal stream energy, with a focus on the resource, feedbacks, and environmental interactions. The review covers a wide range of timescales of relevance to tidal energy, from fortnightly (spring-neap) and semi-diurnal variability, down to array, and device-scale turbulence. When simulating the regional tidal energy resource, and to assess environmental impacts, it is necessary to account for feedbacks between the tidal array and the resource itself. We critically review various methods for simulating energy extraction, from insights gained through theoretical studies of “tidal fences” in idealized channels, to realistic three-dimensional model studies with complex geometry and arrays of turbines represented by momentum sinks and additional turbulence due to the presence of rotors and support structures. We discuss how variability can be reduced by developing multiple (aggregated) sites with a consideration of the enhanced phase diversity offered by exploiting less energetic tidal currents. This leads to future research questions that have not yet been explored in depth at first-generation tidal sites in relatively sheltered channels (e.g., the interaction of waves with currents). Such enhanced understanding of real sea conditions, including the effects of wind and waves, leads to our other identified primary future research direction—reduced uncertainties in turbulence predictions, including the development of realistic models that simulate the interaction between ambient turbulence and the turbulence resulting from multiple wakes, and changes to system-wide hydrodynamics, water quality, and sedimentation.

Environmental impacts↗

On the Use of the Beta Distribution in Probabilistic Resource Assessments

The triangular distribution is a popular choice when it comes to modeling bounded continuous random variables. Its wide acceptance derives mostly from its simple analytic properties and the ease with which modelers can specify its three parameters through the extremes and the mode. On the negative side, hardly any real process follows a triangular distribution, which from the outset puts at a disadvantage any model employing triangular distributions. At a time when numerical techniques such as the Monte Carlo method are displacing analytic approaches in stochastic resource assessments, easy specification remains the most attractive characteristic of the triangular distribution. The beta distribution is another continuous distribution defined within a finite interval offering wider flexibility in style of variation, thus allowing consideration of models in which the random variables closely follow the observed or expected styles of variation. Despite its more complex definition, generation of values following a beta distribution is as straightforward as generating values following a triangular distribution, leaving the selection of parameters as the main impediment to practically considering beta distributions. This contribution intends to promote the acceptance of the beta distribution by explaining its properties and offering several suggestions to facilitate the specification of its two shape parameters. In general, given the same distributional parameters, use of the beta distributions in stochastic modeling may yield significantly different results, yet better estimates, than the triangular distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DRIPS: Dynamic Rebalancing of Pipelined Streaming Applications on CGRAs

Coarse-grained reconfigurable arrays (CGRAs) provide higher flexibility than application-specific integrated circuits (ASICs) and higher efficiency than fine-grained reconfigurable devices such as Field Programmable Gate Arrays (FPGAs). However, CGRAs are generally designed to support offloading of a single kernel. While their design, based on communicating functional units, appears to naturally suit data streaming applications composed of multiple cooperating kernels, current approaches only statically partition the resources across application kernels. However, emerging streaming applications at the edge (scientific instruments, sensor networks, network processing) perform much more than digital signal processing and often are data and input dependent. This leads to extremely variable kernel execution times, severely impacting the throughput of the entire pipeline if resources are only statically allocated. Therefore, in this paper, we propose DRIPS — a coarse-grained, dynamically, and partially reconfigurable array for data-dependent streaming applications. We present a unified compiler framework to facilitate the mapping of a given streaming application onto the DRIPS CGRA architecture. The experimental results show that DRIPS achieves an average throughput improvement of 1.46$\times$ across a set of representative applications over a statically partitioned solution. The additional area overhead to enable dynamic rebalancing consumes 16.34% of the entire area for a 5x5 CGRA prototype.

Tan, Cheng↗

On the Inclusion of Energy-Shifting Demand Response in Production Cost Models: Methodology and a Case Study

In the context of future power system requirements for additional flexibility, demand response (DR) is an attractive potential resource. Its proponents widely laud its prospective benefits, which include enabling higher penetrations of variable renewable generation at lower cost than alternative storage technologies, and improving economic efficiency. In practice, DR from the commercial and residential sectors is largely an emerging, not a mature, resource, and its actual costs and benefits need to be studied to determine promising combinations of physical DR resource, enabling controls and communications, power system characteristics, regulatory environments, market structures, and business models. The work described in this report focuses on the enablement of such analysis from the production cost modeling perspective. In particular, we contribute a bottom-up methodology for modeling load-shifting DR in production cost models. The resulting model is sufficiently detailed to reflect the physical characteristics and constraints of the underlying flexible load, and includes the possibility of capturing diurnal and seasonal variations in the resource. Nonetheless, the model is of low complexity and thus suitable for inclusion in conventional unit commitment and market clearing algorithms. The ability to simulate DR as an operational resource on a power system over a year facilitates an assessment of its time-varying value to the power system.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Wind and Weather Variability within the Californian Offshore Wind Energy Areas

Weather variability over the Northeast Pacific (NEP) region and its influence on wind resources within the Californian offshore wind energy areas (WEAs) at Humboldt and Morro Bay are characterized using 20-years reanalysis model and satellite data. The hub-height (180 m) winds at both locations are predominantly northwesterly driven by the NEP high pressure system, with strong coastal gradients in surface pressure, fluxes, planetary boundary layer (PBL) depths and cloudiness. These sharp coastal gradients and strong annual cycles of temperature and moisture advections pose potential challenges in accurately modeling the local wind resource. Hub-height wind speeds and power capacity factors significantly vary for different regimes of PBL depths, surface fluxes and rain area fractions. This highlights the importance of studying the physical mechanisms driving these weather regimes, hence our analysis of how large-scale NEP weather variability drives the local meteorology at the WEAs. Furthermore, at both WEAs, PBL tops and cloud boundaries intersect the rotor layer (80-280 m) more than 30% and 20% of the time, respectively. While PBL depths significantly modulates hub-height winds and power, cloud boundaries do not have a similar impact, likely due to reanalysis errors in simulating cloud boundaries accurately. These findings underscore the challenges in deploying tall wind turbines in shallow cloudy boundary layers, where the interaction between clouds, precipitation, and atmospheric layers can impact turbine efficiency. As turbines grow taller and are deployed in more complex meteorological conditions, understanding these interactions is crucial for improving wind power forecasting and optimizing energy production in coastal regions.

17 WIND ENERGY↗

Photovoltaic Analysis and Response Support (PARS) Platform for Solar Situational Awareness and Resiliency Services

The project's primary objective is to develop a digital-twin based Photovoltaic (PV) Analysis and Response Support (PARS) platform, which aims to provide real-time situational awareness and optimal response plans. This platform is designed to enhance the performance of hybrid PV systems, making them competitive with or even superior to conventional generation resources. The PARS platform enabled the project team to develop and evaluate an extensive suite of grid support functionalities for the hybrid PV systems to enhance grid performance, across key areas including visibility, dispatchability, security, resilience, and reliability. Given the global push toward achieving 100% clean energy by 2035, there is a significant increase in the integration of inverter-based resources (IBRs) throughout the energy grid. Effectively managing the inherent variability and uncertainty associated with IBRs is crucial for ensuring cost-effectiveness, reliability, and security in both the main grid and islanded microgrids. Constrained to a limited array of IEEE test systems or standard feeder models, traditional IBR modeling struggles to assimilate new field data, accurately reflect system dynamics, and adapt to the evolving energy landscape. In our project, we embraced a Digital Twin (DT) strategy for crafting the PARS platform. A digital twin acts as a precise virtual counterpart of a physical system, built on historical data and continuously honed with real-time insights. This enables the high-fidelity DT to accurately mirror current system operations and forecast future scenarios. Consequently, the PARS platform becomes an ideal environment for testing and refining monitoring, control, power, and energy management algorithms designed to boost hybrid PV system performance. The defining feature of the PARS platform, distinguishing it from other advanced simulation tools, is its exceptional adaptability. This is achieved by employing actual network topologies and utilizing real-time field data for fine-tuning and calibration, ensuring a close emulation of real-world conditions. The project deliverables include: 1) High-fidelity IBR models and tools for real-time parameterization, utilizing real-time field measurements to refine IBR models for enhanced accuracy and performance; 2) Grid-forming and Grid-following capabilities to deliver resilience services, including blackstart, voltage and frequency support, cold-load pick-up, power reserves, and three-phase load balancing across grid-connected and microgrid settings; 3) Machine learning-based forecasting tools and methods for generating synthetic data and topologies, creating diverse and realistic simulation environments for evaluating varied operational scenarios; 4) Advanced microgrid power and energy management algorithms for optimizing the integration and operation of PV, storage, and demand response resources within both feeder and community scales. The power grid data sets are provided by four utility companies in North Carolina and the New York Power Administration. Acting as industry advisors, our industry partners communicated stakeholder needs and regulatory standards to the research teams, aiding technology transfer by incorporating the developed methodologies into their daily operations. This collaboration ensures that the PARS platform, functioning as a power system digital twin, enhances our understanding of IBR dynamic behaviors and enables the development and evaluation of IBR control functions that match or exceed the capabilities of conventional synchronous generators.

14 SOLAR ENERGY↗

Intra-Hour Dispatch and Automatic Generator Control Demonstration with Solar Forecasting - Final Report

In this project we address multiple resource integration challenges associated with increasing levels of solar penetration that arise from the variability and uncertainty in solar irradiance. We will model the SMUD service region as its own balancing region, and develop an integrated, real-time operational tool that takes solar-load forecast uncertainties into consideration and commits optimal energy resources and reserves for intra-hour and intra-day decisions. The primary objectives of this effort are to reduce power system operation cost by committing appropriate amount of energy resources and reserves, as well as to provide operators a prediction of the generation fleet’s behavior in real time for realistic PV penetration scenarios. The proposed methodology includes the following steps: clustering analysis on the expected solar variability per region for the SMUD system, Day-ahead (DA) and real-time (RT) load forecasts for the entire service areas, 1-year of intra-hour CPR forecasts for cluster centers, 1-year of smart re-forecasting CPR forecasts in real-time for determination of irreducible errors, and uncertainty quantification for integrated solar-load for both distributed and central stations (selected locations within service region) PV generation.

14 SOLAR ENERGY↗

The Use of Statistically Based Rolling Supply Curves for Electricity Market Analysis: A Preliminary Look

In light of the changing electricity resource mixes across the United States, an important question in electricity modeling is how additions and retirements of generation, including additions in variable renewable energy (VRE) generation could impact markets by changing hourly wholesale energy prices. Instead of using resource-intensive production cost models (PCMs) or building and using simple generator supply curves, this analysis uses a 'top-down' approach based on regression analysis of hourly historical energy and load data to estimate the impact of supply changes on wholesale electricity prices, provided the changes are not so substantial that they fundamentally alter the market and dispatch-order driven behavior of non-retiring units. The rolling supply curve (RSC) method used in this report estimates the shape of the supply curve that fits historical hourly price and load data for given time intervals, such as two-weeks, and then repeats this on a rolling basis through the year. These supply curves can then be modified on an hourly basis to reflect the impact of generation retirements or additions, including VRE and then reapplied to the same load data to estimate the change in hourly electricity price. The choice of duration over which these RSCs are estimated has a significant impact on goodness of fit. For example, in PJM in 2015, moving from fitting one curve per year to 26 rolling two-week supply curves improves the standard error of the regression from 16 dollars/MWh to 6 dollars/MWh and the R-squared of the estimate from 0.48 to 0.76. We illustrate the potential use and value of the RSC method by estimating wholesale price effects under various generator retirement and addition scenarios, and we discuss potential limits of the technique, some of which are inherent. The ability to do this type of analysis is important to a wide range of market participants and other stakeholders, and it may have a role in complementing use of or providing calibrating insights to PCMs.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Development of an Improved Methodology to Assess Potential Unconventional Gas Resources

Considering the important role played today by unconventional gas resources in North America and their enormous potential for the future around the world, it is vital to both policy makers and industry that the volumes of these resources and the impact of technology on these resources be assessed. To provide for optimal decision making regarding energy policy, research funding, and resource development, it is necessary to reliably quantify the uncertainty in these resource assessments. Since the 1970s, studies to assess potential unconventional gas resources have been conducted by various private and governmental agencies, the most rigorous of which was by the United States Geological Survey (USGS). The USGS employed a cell-based, probabilistic methodology which used analytical equations to calculate distributions of the resources assessed. USGS assessments have generally produced distributions for potential unconventional gas resources that, in our judgment, are unrealistically narrow for what are essentially undiscovered, untested resources. In this article, we present an improved methodology to assess potential unconventional gas resources. Our methodology is a stochastic approach that includes Monte Carlo simulation and correlation between input variables. Application of the improved methodology to the Uinta-Piceance province of Utah and Colorado with USGS data validates the means and standard deviations of resource distributions produced by the USGS methodology, but reveals that these distributions are not right skewed, as expected for a natural resource. Our investigation indicates that the unrealistic shape and width of the gas resource distributions are caused by the use of narrow triangular input parameter distributions. The stochastic methodology proposed here is more versatile and robust than the USGS analytic methodology. Adoption of the methodology, along with a careful examination and revision of input distributions, should allow a more realistic assessment of the uncertainty surrounding potential unconventional gas resources.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Dataset for Biorefinery-specific feedstock price variability, Part 1: Corn stover

This dataset was utilized in a report to highlight parameters that affect near-term sustainable supply of corn stover and forest resources at $56 and $74 per dry ton delivered. While the report focus is restricted to 2018, the modeling runs are available from 2016-2022. In the 2016 Billion-ton Report (BT16), two stover cases were presented. In this dataset, we vary technical levels of those assumptions to measure stover supply response and to evaluate the major determinants of stover supply. In each of these cases, the supply is modeled first at the farmgate at prices up to $80 per dry ton for five deterministic scenarios. Building on this dataset, a supplementary dataset of delivered supply was modeled for 800k dry ton per year capacity facilities in two facility siting approaches. Results were summarized across delivered supply curves for twelve scenarios. The resulting supply curves are highly elastic, resulting in a range of potential supplies across scenarios at specified prices. Interactive visualization of these data allows exploration into any specified nth plant supply sensitivity to key variables and spatial distribution of stover resources. The analysis is economic supply risk and doesn’t account for disruptions from competing demands, namely livestock feed and bedding markets. Scenario ending in _BC3080 is a reference scenario consistent with BT16 Basecase (BC1), but with corn stover price isolation. Scenario ending in _OHB080 includes high operational efficiency constraints for corn stover. Scenario ending in _OLB080 includes low operational efficiency constraints for corn stover. Scenario ending in _PLB080 includes low opportunity cost. Scenario ending in _PHB080 includes high opportunity cost. No Land Rental costs are applied to these scenarios. All scenarios were under an exogenous price simulation using POLYSYS (v2017).

Agricultural residues, biomass resources, 2018, bi↗

Seasonal forecasting skill for the High Mountain Asia region in the Goddard Earth Observing System

Seasonal variability of the global hydrologic cycle directly impacts human activities, including hazard assessment and mitigation, agricultural decisions, and water resources management. This is particularly true across the High Mountain Asia (HMA) region, where availability of water resources can change depending on local seasonality of the hydrologic cycle. Forecasting the atmospheric states and surface conditions, including hydrometeorologically relevant variables, at subseasonal-to-seasonal (S2S) lead times of weeks to months is an area of active research and development. NASA's Goddard Earth Observing System (GEOS) S2S prediction system has been developed with this research goal in mind. Here, we benchmark the forecast skill of GEOS-S2S (version 2) hydrometeorological forecasts at 1–3-month lead times in the HMA region, including a portion of the Indian subcontinent, during the retrospective forecast period, 1981–2016. To assess forecast skill, we evaluate 2 m air temperature, total precipitation, fractional snow cover, snow water equivalent, surface soil moisture, and terrestrial water storage forecasts against the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) and independent reanalysis data, satellite observations, and data fusion products. Anomaly correlation is highest when the forecasts are evaluated against MERRA-2 and particularly in variables with long memory in the climate system, likely due to the similar initial conditions and model architecture used in GEOS-S2S and MERRA-2. When compared to MERRA-2, results for the 1-month forecast skill range from an anomaly correlation of R anom =0.18 for precipitation to R anom =0.62 for soil moisture. Anomaly correlations are consistently lower when forecasts are evaluated against independent observations; results for the 1-month forecast skill range from R anom =0.13 for snow water equivalent to R anom =0.24 for fractional snow cover. We find that, generally, hydrometeorological forecast skill is dependent on the forecast lead time, the memory of the variable within the physical system, and the validation dataset used. Overall, these results benchmark the GEOS-S2S system's ability to forecast HMA hydrometeorology.

54 ENVIRONMENTAL SCIENCES↗

Dimension-adaptive machine learning-based quantum state reconstruction

Here, we introduce an approach for performing quantum state reconstruction on systems of n qubits using a machine learning-based reconstruction system trained exclusively on m qubits, where m ≥ n. This approach removes the necessity of exactly matching the dimensionality of a system under consideration with the dimension of a model used for training. We demonstrate our technique by performing quantum state reconstruction on randomly sampled systems of one, two, and three qubits using machine learning-based methods trained exclusively on systems containing at least one additional qubit. The reconstruction time required for machine learning-based methods scales significantly more favorably than the training time; hence this technique can offer an overall saving of resources by leveraging a single neural network for dimension-variable state reconstruction, obviating the need to train dedicated machine learning systems for each Hilbert space.

42 ENGINEERING↗

State-Level Trends in Renewable Energy Procurement via Solar Installation versus Green Electricity

In recent years, options for procuring renewable energy have increased, ranging from rooftop solar installation to utility green pricing to Community Choice Aggregation. These options vary in terms of costs and benefits to the consumer as well as grid integration implications. However, little is known regarding how the presence of a wide range of voluntary utility-scale renewable procurement options as well as their growth could affect adoption of distributed residential solar. To examine this relationship, we fit a two-stage least squares random effects regression model on panel data from 2016 to 2019 for all fifty US states plus the District of Columbia, controlling for variables that measure state-level policies, economic factors, and resource availability. Although there was no evidence of a strong relationship between demand for utility-scale and distributed options across all states, the state-level correlations suggest a wide variation between states including a positive, zero or negative relationship between utility-scale and distributed generation.

consumer demand↗