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All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Background Oriented Schlieren (BOS) of a Supersonic Aircraft In Flight

This article describes the development and use of Background Oriented Schlieren on a full-scale supersonic jet in flight. A series of flight tests was performed in October, 2014 and February 2015 using the flora of the desert floor in the Supersonic Flight Corridor on the Edwards Air Force Base as a background. Flight planning was designed based on the camera resolution, the mean size and color of the predominant plants, and the navigation and coordination of two aircraft. Software used to process the image data was improved with additional utilities. The planning proved to be effective and the vast majority of the passes of the target aircraft were successfully recorded. Results were obtained that are the most detailed schlieren imagery of an aircraft in flight to date.

Heineck, James T.↗
NASA NTRS2019

Real-Time Background Oriented Schlieren: Catching Up With Knife Edge Schlieren

Background Oriented Schlieren (BOS) is a widely used technique that provides density gradient information in flow fields of interest, without imposing stringent optical quality requirements on the facility/experiment windows and/or optics used in the BOS setup. Typically, the BOS reference image is acquired before the test begins (flow off) and then the "live" image data are acquired during the actual testing/experiment (flow on). The raw BOS image data, while displayed in real-time as they are acquired from the camera, unfortunately provide little if any visual indication of the density gradients in the flow. Generally, the "live" images must be processed off-line after the testing is completed, providing no indication of the success of the BOS setup and no feedback on the operational success of the test. Advances in computer processing hardware enables the implementation of real-time processing and display of the BOS image data. Two different approaches to implementing the real-time BOS (RT-BOS) processing capability are described herein. First, a traditional multi-core Central Processing Unit (CPU) based approach using scheduled parallel threads is used to build a RT-BOS processing engine. In the second approach, a Graphical Processing Unit (GPU) approach is used to costruct a RT-BOS processing engine. Generally, high core count CPU processors can provide a useful processing rate for RT-BOS. However, the GPU based approach exceeds the processing capability of the CPU approach, at a fraction of the cost. The GPU approach places no restrictions on the Host PC processing capability, except that it be capable of acquiring the BOS image data from the camera in real-time.

Wernet, Mark P.↗
NASA NTRSDate not supplied

Accuracy of Center of Pressure Determination via Motion Capture

BACKGROUND: This study was conducted to support the stability assessment for tasks in lunar gravity and exercises on a Vibration Isolation and Stabilization (VIS) system in microgravity based on the dynamic feasibility criterion of whether the calculated position of the center of pressure (COP) falls within the base of support (BOS) which outlines the subject’s feet. Motion capture data combined with biomechanical modeling and simulation allows the forces and moments between the human and the VIS platform to be computed and the position of the COP as well as the location and shape of the BOS to be determined. The goal of this study was to assess the accuracy of the COP trajectory calculated using motion capture-based data. METHODS AND RESULTS: To obtain the dynamic quantities from which COP is calculated, motion capture data is first collected in the 1g lab environment by recording the trajectories of passive retroreflective markers placed on a subject during exercise or performance of a given task. The OpenSim [1] inverse kinematics (IK) tool is used to fit a scaled subject model to recorded marker trajectories while minimizing marker error to obtain joint angles. Then, a custom OpenSim plugin [2] is used to determine the subject’s time-varying moment of inertia and its time derivative, center of mass (CM) position, velocity, and acceleration, as well as the angular momentum and its time derivative relative to the subject’s CM. Some of these quantities are not needed for modeling tasks performed on a stationary lunar surface but, due to the moving exercise platform, are needed to model VIS response to the subject’s motion. Hand positions, used in calculating a cable force if present, are recorded as well. These quantities are used to calculate the total force (F ⃗^((plate) )) and moment (M ⃗^((plate) )) exerted by the lunar surface or the VIS plate on the subject’s shoe soles. COP is then calculated from the following equations: r_x^((cop) )= M_z^((plate) )/F_y^((plate) ) and r_z^((cop) )= 〖-M〗_x^((plate) )/F_y^((plate) ), where the y axis is normal to the surface. COP accuracy for feasibility assessments is then determined by whether it falls within the BOS, which is also computed by the plugin. To study the accuracy of COP calculated from motion capture, we first investigated whether COP remained within the BOS, as it must, for exercises performed in the 1g lab environment. Standard exercises such as back squat and deadlift were analyzed, as well as more explosive exercises including hang clean and press. Cases in which the COP exited the BOS indicated that COP accuracy required further investigation. In this study, an exercise device with cables was used, so cable force modeling accuracy should also be considered. In a separate study, we collected motion capture and force plate data for twenty-seven motions not involving an exercise device. About a third were genuine countermeasures exercises (e.g., hang clean and press), some were relevant for lunar tasks (e.g., object pick up), and the rest were of a “unit test” nature (e.g., swaying back and forth or side to side). Motion capture-based COP positions were compared with force plate measured COP. We found that while force plate measured COP remained within the BOS, motion capture-based COP was observed to briefly exit the BOS on occasion. Techniques to mitigate IK artifacts and filtering of calculated data could be used to improve the agreement of calculated and measured results, resolving excursions from the BOS within this dataset. The mean error between calculated and measured COP was found to be less than 6 mm. Additionally, we derived and investigated equations for the COP in terms of the cable force, cable location, as well as the human CM position, acceleration, and angular momentum with respect to the CM, and analyzed them for sensitivity to errors in individual quantities. Several were found, but the most significant one was that when the vertical force on the feet approaches zero, indicating a near-detachment or ‘jump off’ condition, errors are amplified. This is consistent with the observation that in the absence of pressure, the concept of the center of pressure would become meaningless.

C A Bell↗
NASA NTRS1978

Cost of photovoltaic energy systems as determined by balance-of-system costs

The effect of the balance-of-system (BOS), i.e., the total system less the modules, on photo-voltaic energy system costs is discussed for multikilowatt, flat-plate systems. Present BOS costs are in the range of 10 to 16 dollars per peak watt (1978 dollars). BOS costs represent approximately 50% of total system cost. The possibility of future BOS cost reduction is examined. It is concluded that, given the nature of BOS costs and the lack of comprehensive national effort focussed on cost reduction, it is unlikely that BOS costs will decline greatly in the next several years. This prognosis is contrasted with the expectations of the Department of Energy National Photovoltaic Program goals and pending legislation in the Congress which require a BOS cost reduction of an order of magnitude or more by the mid-1980s.

Rosenblum, L.↗
NASA NTRSDate not supplied

Recent Improvements and Verification of A Full Body Model in Opensim

BACKGROUND: The dynamic feasibility [1,2] criterion, that the subject’s Center of Pressure (COP) be located within the Base of Support (BOS) which outlines the feet, has aided in assessing the stability of human motion recorded on earth while performing the recorded tasks in lunar gravity or as countermeasures exercises on a vibration isolation and stabilization system in microgravity. The convex hull of the BOS on the platform under the subject’s feet was estimated using virtual markers on the feet of the scaled subject model. The COP was calculated using the ground reaction forces and moments determined from motion capture data with biomechanical modeling tools [3]. Occasionally, large-amplitude oscillatory spikes or “artifacts” were observed in the subject’s linear and angular momentum derivatives, affecting some COP data derived from motion capture. The purpose of this investigation was to assess and improve the accuracy of model scaling and BOS estimation as well as to determine the efficacy of model adjustments in mitigating artifacts influencing motion capture-derived ground reaction force and COP results. METHODS: To aid evaluation of proposed process and model updates, motion capture data were collected for two subjects during unit test and range of motion trials, lunar tasks, and countermeasures exercise motions. Markers were added to the full body Plug-in Gait marker set [4] during data collection. New markers were placed on the front, back, sides, and top of the head to improve scaling using distances between marker pairs. Medial elbow markers were added to stabilize the upper arm during OpenSim Inverse Kinematics (IK) [5]. Finally, markers were added on the outer edge of the heels and on the outside edges of the first and last toes on each foot. These additional foot markers were made available to test new automated foot scaling techniques and to calculate the error between the subject’s estimated and recorded BOS. The modified unscaled OpenSim Full Body Rajagopal Model [6,7] was adjusted using some previously investigated techniques [8] to mitigate rapid shifts in joint angles occurring during IK, as these were found to cause the spike artifacts observed in subsequent stages of analysis. Since OpenSim models use Euler angles and rotation sequences, the arm axes of rotation were adjusted, and the pelvis order of rotation was changed to minimize the likelihood of encountering “gimbal lock” during common human motion. The model clavicle, arm, elbow, wrist, pelvis, and ankle angle limits were adjusted to better accommodate the full human range of motion seen in exercise and lunar data. The shoulder joint center was calculated using a “pivoting” algorithm [9], and both shoulder joint center and upper arm markers were included during IK to provide additional shoulder stability on a case-by-case basis. The quality of IK results was assessed by three criteria: minimizing error between recorded motion capture markers and model markers, checking for reasonable rates of change in joint angles between fames (i.e., no IK artifacts), and ensuring the absence of spikes in the inertial forces and angular momentum derivatives calculated using a custom OpenSim plugin [10]. RESULTS: The additional markers placed on the subject during data collection allowed the head and feet to be scaled more accurately using distances between new marker pairs. Scaling with BOS markers placed on the subject and removing the limit on subtalar angle resulted in more accurate BOS determination. Unrealistically large changes in joint angles between frames could be reduced by including clavicle, sternum, and medial elbow markers during IK. In cases with large arm ranges of motion, results could be further improved by running IK using medial elbow and virtual shoulder joint center markers. Model adjustments significantly improved the IK results affecting COP calculation and increased the accuracy of BOS estimation.

C A Bell↗
DOE OSTI2020

ORBIT: Offshore Renewables Balance-of-System and Installation Tool

This report describes the Offshore Renewables Balance-of-system Installation Tool ("ORBIT"), a new model developed by the National Renewable Energy Laboratory (NREL) to evaluate the balance-of-system (BOS) costs associated with offshore wind projects. In the context of wind energy projects BOS costs encompass all expenses required to construct a project other than the capital expenditures (CapEx) of the turbines and towers, including the procurement costs for all other components (such as substructures, cables, and electrical infrastructure), offshore and land-based construction costs, port costs, site surveying fees, permitting fees, and leasing fees are all categorized as BOS costs. BOS costs significantly contribute to the levelized cost of energy (LCOE) for offshore wind, typically comprising over 50\% of the CapEx for a fixed-bottom offshore wind project and 60\% for a floating project. In addition, technology solutions and installation methods vary drastically between projects as they are impacted by factors such as vessel availability, geographic considerations and site geotechnical conditions. These effects require a model with appropriate fidelity to understand how these costs scale as turbine rating increases and the offshore wind supply chain, particularly offshore construction vessels, is expanded. For offshore wind, cost savings attributed to increased turbine rating are primarily realized through BOS procurement and project installation as fewer substructures and less cable are required. BOS costs represent both a modeling challenge, as well as an opportunity, for project developers to optimize solutions to reduce costs. It is critical to understand how these costs are affected by novel technologies, innovative installation processes, and operational constraints in order identify meaningful cost reductions for offshore wind energy.

17 WIND ENERGY↗
NASA NTRS2012

Background Oriented Schlieren Applied to Study Shock Spacing in a Screeching Circular Jet

Background oriented schlieren (BOS) is a recent development of the schlieren and shadowgraph methods. The BOS technique has the ability to provide visualizations of the density gradient in both the axial and radial directions. The resultant magnitude of the density gradients allows for comparison with shadowgraph images. This paper first compares data obtained by the BOS and shadowgraph techniques at identical conditions in a free jet. The patterns and spacing of the shock trains obtained by the two techniques are found to be consistent with one another. This provides confidence in the shock spacing measurement by the BOS technique. Due to its simpler setup, BOS is then applied to investigate the shock spacing associated with the screech phenomenon, especially during stage jumps. Screech frequencies from a 37.6 mm convergent nozzle, as a function of jet Mach number (M(sub j)), are shown to exhibit various stages. As many as eight stages are identified with the present nozzle over the range 1.0 < M(sub j) <1.7. BOS images are acquired at various screech conditions and the shock spacing is examined as a function of M(sub j).

Clem, Michelle M.↗
NASA NTRS2016

Background-Oriented Schlieren used in a hypersonic inlet test at NASA GRC

Background Oriented Schlieren (BOS) is a derivative of the classical schlieren technology, which is used to visualize density gradients, such as shock wave structures in a wind tunnel. Changes in refractive index resulting from density gradients cause light rays to bend, resulting in apparent motion of a random background pattern. The apparent motion of the pattern is determined using cross-correlation algorithms (between no-flow and with-flow image pairs) producing a schlieren-like image. One advantage of BOS is its simplified setup which enables a larger field-of-view (FOV) than traditional schlieren systems. In the present study, BOS was implemented into the Combined Cycle Engine Large-Scale Inlet Mode Transition Experiment (CCE LIMX) in the 10x10 Supersonic Wind Tunnel at NASA Glenn Research Center. The model hardware for the CCE LIMX accommodates a fully integrated turbine based combined cycle propulsion system. To date, inlet mode transition between turbine and ramjet operation has been successfully demonstrated. High-speed BOS was used to visualize the behavior of the flow structures shock waves during unsteady inlet unstarts, a phenomenon known as buzz. Transient video images of inlet buzz were recorded for both the ramjet flow path (high speed inlet) and turbine flow path (low speed inlet). To understand the stability limits of the inlet, operation was pushed to the point of unstart and buzz. BOS was implemented in order to view both inlets simultaneously, since the required FOV was beyond the capability of the current traditional schlieren system. An example of BOS data (Images 1-6) capturing inlet buzz are presented.

Background-oriented schlieren↗
DOE OSTI2021

Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks

Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions using multiple camera BOS projections, and is particularly useful for instantaneous flow visualizations of complex fluid dynamics problems. We propose a new method based on physics-informed neural networks (PINNs) to infer the full continuous three-dimensional (3-D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging. The PINNs seamlessly integrate the underlying physics of the observed fluid flow and the visualization data, hence enabling the inference of latent quantities using limited experimental data. In this hidden fluid mechanics paradigm, we train the neural network by minimizing a loss function composed of a data mismatch term and residual terms associated with the coupled Navier–Stokes and heat transfer equations. We first quantify the accuracy of the proposed method based on a two-dimensional synthetic data set for buoyancy-driven flow, and subsequently apply it to the Tomo-BOS data set, where we are able to infer the instantaneous velocity and pressure fields of the flow over an espresso cup based only on the temperature field provided by the Tomo-BOS imaging. Moreover, we conduct an independent PIV experiment to validate the PINN inference for the unsteady velocity field at a centre plane. To explain the observed flow physics, we also perform systematic PINN simulations at different Reynolds and Richardson numbers and quantify the variations in velocity and pressure fields. Furthermore, the results in this paper indicate that the proposed deep learning technique can become a promising direction in experimental fluid mechanics.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Twenty-Five Years of Background-Oriented Schlieren: Advances and Novel Applications

Since its introduction in the year 2000, background-oriented schlieren (BOS) has become acornerstone technique for visualizing variable-density flows. In this review, we provide a rigorousexamination of the optical principles underpinning BOS and related refractive-index-basedtechniques, complemented by an appendix linking schlieren imaging to Maxwell’s equations.The core sections delve into the practical aspects of BOS, with detailed discussions on imageprocessing algorithms and critical considerations for experimental setups. We then explorerecent advancements and innovations, including extensions of BOS with tomography, dataassimilation, and event-based imaging. Finally, we present notable applications of BOS inchallenging and unconventional environments, showcasing the method’s versatility and offerinspiration for future research directions.

Background-Oriented Schlieren↗
NASA NTRSDate not supplied

Considerations for High-Speed Background-Oriented Schlieren Visualization Capability for Ground Test Facilities

Since its introduction in the year 2000, background-oriented schlieren (BOS) has become a cornerstone technique for visualizing variable-density flows. In this review, we provide a rigorous examination of the optical principles underpinning BOS and related refractive-index-based techniques, complemented by an appendix linking schlieren imaging to Maxwell’s equations. The core sections delve into the practical aspects of BOS, with detailed discussions on image processing algorithms and critical considerations for experimental setups. We then explore recent advancements and innovations, including extensions of BOS with tomography, data assimilation, and event-based imaging. Finally, we present notable applications of BOS in challenging and unconventional environments, showcasing the method’s versatility and offer inspiration for future research directions.

Brett Bathel↗
DOE OSTI2021

Scaling trends for balance-of-system costs at land-based wind power plants: Opportunities for innovations in foundation and erection

Wind power plant sizes, hub heights, and turbine ratings have increased since 2008 to optimize the cost and performance of wind power; however, the limits of these economies of scale remain unclear. Here, we explore how the costs incurred to install turbines at a wind power plant—the balance-of-system (BOS) costs—scale with turbine rating, hub height, and plant size. We also investigate how these changes in BOS costs influence the levelized cost of energy (LCOE). We show that increasing the plant size from 150 to 400 MW could reduce the BOS costs by 21%. We also show that if the foundation costs decreased by 50%, building a wind power plant with 5-MW turbines (having rotor diameters of 166 m and hub heights of 120 m) could decrease the LCOE by 5%. These results could help inform future BOS cost-reduction opportunities and thereby reduce future capital costs for land-based wind power.

17 WIND ENERGY↗
DOE OSTI2025

Nature of innovations affecting photovoltaic system costs

Innovations improve technology costs through various kinds of engineering advancements, including changes to materials choices and device or process designs. Understanding how these innovations relate to cost change can reveal aspects of the process of technology evolution, yet developing such understanding is often not possible with a strictly quantitative approach due to data limitations. In this paper we develop a hybrid quantitative-qualitative framework for relating specific innovations to cost change by using the variables in a quantitative technology cost change model as an organizing principle. We demonstrate this framework by applying it to the cost decline in photovoltaic (PV) systems over the last five decades. This framework generates new understanding of a set of innovations that contributed to PV modules’ sustained cost decline and the more modest trends observed in balance-of-system (BOS) costs. The results show the great diversity of innovations that affected PV costs, drawing on wide-ranging fields of expertise within scientific research and practice. We find that there are differences in the characteristics of innovations that reduced the cost of PV modules compared to innovations influencing BOS costs. Numerous module innovations reduced costs by advancing manufacturing tools and processes that improved material quality. Many BOS innovations reduced costs through a combination of component design changes, integration, automation, digitalization, and standardization. Overall, most innovations in our sample affected PV hardware. However, some also target ‘soft technologies’ such as task durations through innovations like fast-track permitting, which require improved collaboration and process streamlining. This framework also provides insight into the nature of knowledge spillovers between technologies. Both module and BOS hardware innovations show the benefits of PV’s position within an ‘ecosystem’ of continuously advancing technologies in many industries, in particular semiconductors and electronics, and also point to the importance of public institutions for accelerating testing, permitting, and training.

14 SOLAR ENERGY↗
NASA NTRS2018

Simultaneous Conventional and Plenoptic Background Oriented Schlieren Imaging

Plenoptic Background Oriented Schlieren (BOS) is an emerging schlieren technique that is capable of providing 3D qualitative and quantitative information about density gradients present in a wide range of fluid dynamics problems. In this work, the fundamental concepts of plenoptic BOS are reviewed before discussing an open-air experiment with a buoyant plume where both conventional BOS and plenoptic BOS measurements were acquired simultaneously. Both cameras had the same field-of-view for all experiments, and three different focal plane arrangements were explored: (1) the focal plane was set to the background positions and the plume varied between 11 different positions relative to this focal plane, (2) the focal plane was set to 635- millimeters in front of the background position, and (3) the nominal focal plane varied while the position of the plume remained fixed. Such discussion will provide insight on how the two techniques compare, and what additional work is required to better understand the results provided by these two imaging systems.

Klemkowsky, Jenna N.↗
DOE OSTI2020

Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments

Here, we theoretically analyze the effect of density/refractive index gradients on the measurement precision of background-oriented schlieren (BOS) experiments by deriving the Cramer–Rao lower bound (CRLB) for the 2D centroid estimation process. A model is derived for the diffraction limited image of a dot viewed through a medium containing density gradients that includes the effect of the experimental parameters such as the magnification and f-number. It is shown using the model that nonlinearities in the density gradient field lead to blurring of the dot image. This blurring amplifies the effect of image noise on the centroid estimation process, leading to an increase in the CRLB and a decrease in the measurement precision. The ratio of position uncertainties of a dot in the reference and gradient images is shown to be a function of the ratio of the dot diameters and dot intensities. We termed this parameter the amplification ratio (A F ), and a methodology for reporting position uncertainties in tracking-based BOS measurements is proposed. The theoretical predictions of the dot position estimation variance from the CRLB are compared to ray tracing simulations, and agreement is obtained. The uncertainty amplification is also demonstrated on experimental BOS images of flow induced by a spark discharge, where it is seen that regions of high amplification ratio correspond to regions of density gradients. This analysis elucidates the dependence of the position uncertainty on density and refractive index gradient-induced distortion parameters, provides a methodology for accounting its effect on uncertainty quantification and provides a framework for optimizing experiment design.

42 ENGINEERING↗
DOE OSTI2020

Uncertainty-based weighted least squares density integration for background-oriented schlieren

We propose an improved density integration methodology for Background-Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. Here, the method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge shows a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.

42 ENGINEERING↗
DOE OSTI2020

Modeling Photovoltaics Innovation and Deployment Dynamics

PV’s historically rapid cost reduction is exceptional among technologies. Further cost reductions could play a major role in increasing deployment in the future. To enable such cost reductions, new modeling frameworks are needed to understand the determinants of innovation in PV. In this project, we study the mechanisms driving PV module and system cost reductions, delving deeply into the specific technological innovations that have occurred in the past and the policies that encouraged them, and also opportunities for future cost reduction and widespread deployment. The project contributes new fundamental insight on the determinants of technological innovation by developing novel methods and insights that are generalizable and can therefore be applied to other technologies. The results will allow policy makers, engineers, and other stakeholders to better prioritize their efforts and investments in the future. The project is organized around four journal articles as described below. The first article [1] identifies ‘low-level’ (e.g. conversion efficiency improvement) and ‘high- level’ (e.g. R&D efforts) mechanisms of cost reduction in PV systems (Tasks 1-4). This work builds on a previous DOE grant, where we developed a framework for technological innovation leading to PV module cost reduction [2]. We advance a method to disentangle the contributions of physical (‘hardware’) and non-physical (‘soft technology’) changes. Our results uncover reasons behind the relatively slow evolution of soft technology and can inform new innovation approaches to these technologies. The second article [3] identifies specific engineering or institutional innovations that enabled the low-level mechanisms of cost reduction in PV module and balance-of-systems (BOS) (Tasks 5, 9, 10). We identify 85 innovations and connect them to the cost variables they affected. By developing an innovations typology, this study shows the differences between the types of innovations affecting PV modules and BOS components. Finally, by analyzing the industry origins of innovations, this study also finds that PV was well-positioned within an ecosystem of continuously advancing technologies. The third article [4] studies prospective cost reduction opportunities (Task 10). We explore how design approaches that emphasize standardization and automation, such as plug-and-play PV systems, can create cost reduction opportunities by reducing interactions and speeding up activities with high process costs. We show that this can lead to cost reduction in cost components with the most untapped opportunity for improvement such as installation labor, overhead, electrical BOS, and customer acquisition. The fourth article [5] analyzes how various policies supporting PV deployment and R&D contributed to PV’s cost improvement by enabling high-level mechanisms, specific innovations, and ultimately low-level mechanisms of cost reduction (Tasks 8, 13, 14). We investigate examples from different countries and connect these policies to quantifiable cost change mechanisms. Our study sheds light on the roles that different nations played over time, through a diverse set of policy approaches.

14 SOLAR ENERGY↗
DOE OSTI2021

U.S. Solar Photovoltaic System and Energy Storage Cost Benchmarks: Q1 2021

Based on our bottom-up modeling, the Q1 2021 PV and energy storage cost benchmarks are: $\$2.65$ per watt DC (WDC) (or $\$3.05$/WAC) for residential PV systems, 1.56/WDC (or $\$1.79$/WAC) for commercial rooftop PV systems, $\$1.64$/WDC (or $\$1.88$/WAC) for commercial ground-mount PV systems, $\$0.83$/WDC (or $\$1.13$/WAC) for fixed-tilt utility-scale PV systems, $\$0.89$/WDC (or $\$1.20$/WAC) for one-axis-tracking utility-scale PV systems, $\$30,326$-$\$33,618$ for a 7.15-kWDC residential PV system with 5 kW/12.5 kWh nameplate of storage, $\$2.04$ - $\$2.10$ million for a 1-MWDC commercial ground-mount PV system colocated with 600 kW/2.4 MWhusable of storage, $\$166$ - $\$167$ million for a 100-MWDC one-axis tracker PV system colocated with 60 MW/240 MWhusable of storage. Between 2020 and 2021, there were 3.3% ($\$0.0$9/W), 10.7% ($\$0.19$/W), and 12.3% ($\$0.13$/W) reductions (in 2020 USD) in the residential, commercial rooftop, and utility-scale (one-axis) PV system cost benchmarks respectively. Balance of system (BOS) costs have either increased or remained flat across sectors, year-on-year, unlike in previous benchmark reports, which generally have reported declining BOS costs. The increase in BOS cost has been offset by a 17% reduction in module cost. Overall, modeled PV installed costs across the three sectors have declined compared to our Q1 2020 system costs.

14 SOLAR ENERGY↗