wind energy case study

Case Study: Cape Wind Project

The Cape Wind project's goal is to develop additional sources of wind energy in the Nantucket Sound. Learn why it has faced very strong opposition for more than 10 years from some stakeholders, even after gaining the last of the necessary permits and approval from the federal level in 2010.

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Nantucket Sound is located off the coast of Massachusetts in the Atlantic Ocean. It is defined by Cape Cod in the north, Nantucket Island to the south, and Martha’s Vineyard to the west. Nantucket Sound is about 48 kilometers (30 miles) by 40 kilometers (25 miles) in area. The population of the surrounding areas varies greatly seasonally, as much as tripling in the summer months.

Horseshoe Shoal is a shallow area in Nantucket Sound located 8 kilometers (5 miles) south of Cape Cod. Water depth in Horseshoe Shoal ranges from 15 centimeters (6 inches) to around 18 meters (60 feet). The surrounding islands of Martha’s Vineyard and Nantucket help to buffer Horseshoe Shoal from large waves. The Horseshoe Shoal area is visible from some parts of Cape Cod, Martha’s Vineyard, and Nantucket Island.

The primary industry in the Nantucket Sound area is tourism. The area is known for its mild summer weather, scenic attractions, beautiful beaches, and outdoor recreation opportunities. Fishing is a popular pastime as well as a commercial occupation.

The land areas around Nantucket Sound are largely summer tourist destinations, and a number of celebrities and wealthy families have second homes there. Cape Cod has more than 885 kilometers (550 miles) of coastline, and offers more than 60 public beaches that are popular with tourists. The island of Martha’s Vineyard has a small year-round population, but it is best known as a relaxing summer retreat for the rich and famous. More than half of the homes on the island are only occupied during the summer. The island is not accessible by land, and the cost of living is about 60% higher than on the nearby mainland.

Nantucket Sound is uniquely situated to combine both northern and southern wildlife ranges. Both the cool Labrador Current and the warm Gulf Stream flow through the Sound. Because of this, the Sound is home to a large diversity of marine species, including a number of endangered species. Some endangered species living in the area include humpback whales, North Atlantic right whales, loggerhead turtles, and leatherback turtles.

In November 2001, developers proposed the Cape Wind project, which would locate a large-scale wind farm on Horseshoe Shoal in Nantucket Sound. Cape Wind would be the first offshore wind farm in the United States. The project would include 130 wind turbines spaced over almost 65 square kilometers (25 square miles). Cape Wind would have a maximum electrical output of 468 megawatts, with an average output of 174 megawatts. Electricity from the wind farm would be carried to the mainland through underwater cables.

For over ten years, the project has faced government hurdles, numerous impact studies, and legal opposition from an action group formed to protect the Sound. The project needed both state and federal approval because the turbines would be located in federal waters, while the cables carrying the electricity would travel over Massachusetts land.

Proponents say the wind farm will increase desirable renewable energy capacity, which can help reduce greenhouse gasses affecting global climate change. They also believe the project can help Massachusetts keep up with energy demands. They describe Nantucket Sound as the best available location for the project because of a combination of strong, less turbulent winds, shallow waters, and low wave heights.

While most people agree that the United States should develop additional sources of wind energy , those opposing the Cape Wind project insist that Nantucket Sound is not the place to build such a large project. Opponents argue that the project is too large and will be unsightly, negatively affecting tourism and property values. Opponents have also raised both wildlife and historical conservation issues. A significant unknown issue is the cost of the project, if and by whom the project will be subsidized, and the ultimate cost to the consumer. Opponents argue that the higher-priced electricity from the wind farm will raise prices for electricity in the region. Advocates for the project insist that any increased costs to consumers would be minimal.

The difficulties with getting the project approved have moved into the political arena. Among the opponents of the project were the former Senator Ted Kennedy and former Massachusetts governor Mitt Romney, as well as other politicians from the area. Kennedy cited environmental and economic concerns about the project. Romney pointed to the environment and the legacy of Nantucket as his reasons for opposing the project. Some advocates for the wind farm have suggested that political pressures held up key permits and approvals on both the state and federal levels.

Even after gaining the last of the necessary permits and approval from the federal level in 2010, the Cape Wind project still faced legal challenges from groups ranging from environmental groups to nearby towns to the Wampanoag Tribe.

Stakeholders

Energy Management, Inc.: Energy Management, Inc. is the developer of the Cape Wind project. The company first proposed the project in 2001, and company spokespeople estimate that over $50 million has been spent on the project, even before actual development has begun. After years of investment and delays, Energy Management, Inc. would like to get started installing the turbines and making the system operational.

Electric Utility Companies: In order for the project to be feasible, Cape Wind has to have buyers for the electricity it expects to generate. National Grid agreed to buy half of the wind farm’s electricity and, in 2012, Northeast Utilities and NStar contracted to buy another quarter of the projected supply.

Wampanoag Tribe: The Native American tribe’s ancestors once lived on land now covered by the waters of Nantucket Sound, and the tribe claims the area should be protected as sacred land. They also maintain that the area is in the path of sunrise rituals important to the tribe. The tribe would like to see the Cape Wind project blocked before it disturbs their ancestral lands.

Permanent Residents: Year-round residents of the areas surrounding Nantucket Sound earn most of their living from the tourism industry. Some residents are concerned that the visibility of the wind turbines will negatively affect tourism. Others believe that they will have little, or even a positive, effect on the industry. Residents are also split on costs. Some believe that the wind farm will result in lower electric costs, while others believe it will result in higher costs. A December 2009 poll by the University of Delaware found that 57% of Cape Cod, Martha’s Vineyard, and Nantucket residents supported the Cape Wind project, though public opinion about the project has varied throughout the more than 10-year process.

Vacation Home Owners: Many vacation home owners are concerned about the impact the wind turbines will have on the scenic environment of the Sound, and they seek to preserve the beautiful landscape of the area. They are also concerned that the wind farm will drive property values down. One owner of a vacation home on Martha’s Vineyard even filed suit to stop the project based on the “adverse effects” the project would have on his views and property values. The suit was denied by the State Department of Justice in 2012. Former U.S. Senator Ted Kennedy, whose family property in Hyannis Port would overlook Cape Wind, was vocal in his opposition to the project.

Federal Government: Since taking office, President Obama has been an advocate for renewable energy, including wind energy. The administration has advocated for the use of offshore areas and federal lands for generating renewable energy. In 2010, Interior Secretary Ken Salazar gave the final necessary federal approval to the Cape Wind project.

Wildlife Conservationists: Wildlife conservation groups are split on their opinions of the Cape Wind project. Some wildlife conservation and animal rights groups oppose the project because they fear it will negatively impact endangered species, such as the piping plover, least tern, North Atlantic right whale, and four protected species of sea turtles. They also fear the impact on other wildlife in the area, such as birds using the Atlantic Flyway, of which Horseshoe Shoal is a part. The Humane Society of the United States, the Massachusetts Society for the Prevention of Cruelty to Animals, and the International Marine Mammal Project are among the groups that oppose the project. Among the conservation groups supporting the project is the Massachusetts Audubon Society. Although effects on bird populations are often a concern with wind turbines, the Massachusetts Audubon Society gave their support to the project after reviewing intensive impact studies.

Conflict Mitigation

Throughout the more than ten-year span between the initial proposal and the final federal approvals, numerous compromises and solutions to problems have been incorporated into the Cape Wind project. Extensive environmental impact studies were done in response to concerns raised by conservation groups. Cape Wind developers agreed to mitigation and monitoring suggestions from the Massachusetts Audubon Society to lessen the wind farm’s impact on birds. Similarly, developers worked with state and federal officials to adjust their plans in order to get necessary permits throughout the process. Cape Wind developers also worked with the Department of Justice and the utility companies Northeast Utilities and NStar to develop a contract that would allow Cape Wind to sell electricity to the utility companies while ensuring a relatively stable price for consumers.

Conflict still remains among groups opposed to the project. Many of these conflicts will eventually be worked out in court cases filed to halt the project on the basis of laws such as the Migratory Bird Treaty Act, the Endangered Species Act, and the Outer Continental Shelf Lands Act.

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In the 1980s, the electric power community considered wind energy a mere curiosity. Over the next 40 years, the U.S. Department of Energy’s (DOE) Wind Energy Technologies Office (WETO) worked to establish the electric sector's acceptance of wind energy, enabling it to become a significant contributor to the nation’s energy portfolio. 

WETO, as well as others in the federal government and the private sector, have worked to provide opportunities for personnel at utilities to learn about wind, helping to transform it from a minor contributor to the grid to 10% of U.S. energy generation today.

In 1989, WETO partnered with the Electric Power Research Institute and several U.S. electric utilities to form the Utility Wind Interest Group (UWIG). At the time, wind was considered an unconventional, weather-driven, variable power source. However, over the next decade, UWIG offered utilities a forum to share their information about and experiences with wind power and learn from experts at the forefront of wind energy integration in the electric power industry and the national labs.

By the early 2000s, UWIG had become a go-to resource to identify, quantify, and address technical issues that arose when wind power was integrated into the traditional electric power grid. UWIG also provided an effective avenue for utility industry members to provide feedback to WETO—which provided UWIG with continuous financial and technical support.  

Early Utility Concerns Shift from Wind Energy Costs to Operating Costs 

In the early 2000s, utilities shifted their concerns from wind energy costs to wind power's variability and whether its corresponding uncertainty would increase system operating costs.  

This concern led to one of the first grid integration studies , which UWIG conducted from 2001 through 2003. The study was funded by Xcel Energy with technical support from WETO and examined how Xcel Energy's electric system would respond with a significant amount of wind energy contributing to its electricity-generating mix. Engineers from DOE's National Renewable Energy Laboratory (NREL) and Oak Ridge National Laboratory (ORNL) helped define the study’s methodology and contributed expert technical review.

The study estimated that the financial impact of installed wind energy generation on system operating costs was less than $2 per megawatt-hour of wind energy—well under 10% of the wholesale value of that energy.

These results surprised many in the electric utility industry and helped pave the way for subsequent wind energy expansion in many utility systems. The results encouraged utilities and state governments in Minnesota, Colorado, Nevada, Arizona, Nebraska, Texas, California, and other states to evaluate the feasibility of higher contributions of wind power in their own systems—which included higher levels of wind energy than the UWIG study and increasingly larger geographic areas.  

Regional Analyses Show Systems Can Handle High Wind Energy Penetration 

Results from these early studies concluded that as larger geographical areas were deemed viable for wind energy, the system-operational costs arising from wind energy’s variability decreased—in part due to the naturally occurring geographic diversity of wind.  At any particular moment, different locations in a region experience different winds, leading to some averaging of wind variations over the region. As a result, the variability of energy output decreases as wind power plants cover a larger geographic area. For example, a single wind turbine's output changes in response to local wind variations, but the many turbines in a 100-megawatt (MW) plant each experience different winds at any given moment. This leads to total plant output that is far smoother than that from any individual turbine. Furthermore, several 100 MW plants spread throughout a region will each see different winds, leading to additional averaging and even smoother combined output.

An additional factor contributed to reduced operating costs as the geographic area was expanded to include multiple electric utility service territories. Utility system operators needed to maintain balance between electricity demand and supply at all times, even as demand fluctuates and as unplanned equipment outages occur. Utilities reduce the costs of providing this balance by helping, and being helped by, neighboring utilities. Together, they all share the responsibility for maintaining overall balance throughout their combined, interconnected system. The system benefits—and costs are reduced—because the individual utilities don't all experience the same demand fluctuations or equipment emergencies at the same time, and because no individual utility needs to address imbalances completely by itself. This sharing feature also serves to reduce the impacts of wind variations and the associated costs.

This led to integration studies by independent system operators and regional transmission organizations that examined larger regions of the nation. 

The Western and Eastern Interconnections in North America.

To ensure an organized approach across multiple entities, from 2008 through 2015, WETO funded NREL to define and manage large-area wind integration studies in the following U.S. areas: 

• The Southwest 
• The Western Interconnection (the Western Wind and Solar Integration Study ) 
• The Eastern Interconnection (the Eastern Wind Integration and Transmission Study and the Eastern Renewable Generation Integration Study ).

The multistate Western and Eastern interconnection studies were conducted by experienced electric power planning and analysis experts and used tools and methodology well established in the electric power industry to simulate electric utility operations. To quantify the impacts of large amounts of wind energy and solar power on the grid, the studies examined system production costs (e.g., fuel and operations and maintenance), reliability, transmission congestion and wind curtailment, integration costs, and the response to major system events like regional wind ramps and deep cold events in the Northeast that affect natural gas availability.

These studies concluded that the electricity network could handle high contributions of wind power. In fact, because the designs of wind turbines deployed since the early 2000s included modern controls , such as the ability to provide active power control that can contribute to frequency regulation, their addition could enhance system reliability in some cases.

Wind Energy Becomes Mainstream  

The involvement of utility-industry personnel and use of established power system methodologies and modeling tools for utility-industry analysis made these results highly credible for utilities.  

Over the following years, UWIG expanded to address an ever-increasing scope of issues regarding utility integration and is now called the Energy Systems Integration Group (ESIG)—the nation’s leading forum for discussing the increasingly complex issues of power-system planning and operation with large shares of renewable energy. ESIG focuses on electric-sector technical support for renewable energy integration, DOE’s Grid Solutions program , and enabling technologies such as energy storage.

Additionally, as a follow-up to the regional interconnection studies, in 2020, NREL quantified the costs and benefits of strengthening the connection ( or seam ) between the Eastern and Western Interconnections, including new transmission, to encourage efficient development and utilization of U.S. energy resources.

Connecting U.S. power systems, represented here conceptually, could enhance the ability to harness abundant renewable resources and balance energy loads across the country. WI = Western Interconnection; EI = Eastern Interconnection; ERCOT = Electric Reliability Council of Texas. Per the legend, red dots indicate the top 25 population centers; blue dots indicate hydroelectric facilities; gray shading shows areas with major fossil resource; blue shading shows areas with greatest wind resource; yellow shading shows areas with greatest solar resource; and green shading shows areas with wind and solar resource. The black dashed line divides the EI, WI, and ERCOT.

One of the follow-ups was the 2021 North American Renewable Integration report, a multiyear analysis on how expanding interregional and international transmission can support a reliable future power system. This analysis aimed to inform grid planners, utilities, industry, policymakers, and other stakeholders about challenges and opportunities for continental system integration of large amounts of wind, solar, and hydropower to support a low-carbon future grid.

Now, utilities recognize wind energy as one of the many energy sources contributing to their electric power systems. Wind has joined the energy mainstream, thanks in large part to WETO-funded wind energy integration studies.

Integrating Wind Power into the Electrical Power Network Timeline

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Improving technology to support offshore wind production

Civil Engineering

An Oxford research team has improved engineering design for the ‘monopile’ foundations that support offshore wind turbines – reducing costs to enable the economic scale up of wind energy.

Image: Hornsea One - Offshore Wind Farm. Photo credit: Ørsted

Offshore wind could provide almost “limitless clean energy,” according to Professor Byron Byrne . “The UK is surrounded by sea, where the winds are high and reasonably consistent, so the potential is huge. By increasing the amount of electricity produced by wind power we will reduce our dependence on fossil fuels, cut carbon emissions, and have greater security of supply.”

A current eight-megawatt offshore wind turbine, with a rotor diameter of 170 metres, displaces approximately 12,000 tonnes of CO2 a year from fossil fuel generation and provides electricity to power more than 7,000 homes. These turbines are clustered into farms of 100 or 200 structures, so that they make a meaningful contribution to the UK’s electricity supply. Next generation turbines will be 15 megawatts or more.

New engineering calculations developed by Byrne and colleagues, in collaboration with industry partners and researchers at Imperial College London and University College Dublin, are helping to cut the cost of offshore wind, scale up the size of the wind turbines, and increase confidence in the industry.

The Pile Soil Analysis (PISA) research project, a joint industry project funded through the Carbon Trust Offshore Wind Accelerator and running from 2013-18, has successfully improved the engineering design of offshore wind turbine structures. New methods have been developed to fully optimise the ‘monopile’ foundations, central to the function and stability of turbines – reducing the amount of steel in the foundation by around 30% and extending the sites in which the foundations can be used.

“Monopiles are substantial structures – currently around ten metres in diameter and embedded more than 30 metres into the seafloor,” explains Byrne. “Previously their design was based on methods developed by the offshore oil and gas industry; but the significant differences between a farm of offshore wind turbines and a typical oil and gas platform meant that the traditional techniques do not translate very well.”

“We developed new computational models specific to the design of wind turbines, calibrated to different soil types, which more accurately predict the size of monopiles needed for different locations – leading to more optimised and cost-effective structural designs.”

An extensive process of site testing was central to building industry confidence and encouraging early adoption of the design methods. “We tested the approach at different sites with soil types similar to those found in the North Sea – including a clay in the UK and a dense sand in France – predicting our results and then verifying them through subsequent field testing,” says Byrne.

“Sharing information with our industry partners (11 of Europe’s main offshore wind developers) throughout the research process also helped to build their confidence that our models were as safe and effective as long-established industry design standards.”

The potential impact of the work could be very significant. Use of the new technology has already resulted in direct savings: engineering consultancy Atkins calculated that the technology had significantly reduced the size and depth of embedment of monopiles at one North Sea windfarm compared to traditional design approaches. Ørsted optimised 50% of the foundations at Hornsea 1, previously the world’s largest operating wind farm, and all of the foundations at Hornsea 2, now the world’s largest operating wind farm. The technology has also enabled monopiles, a simple design with a well-established supply chain, to be applied to many more sites than had previously been considered.

“The long-term impact of the work, and the move to scale-up off-shore wind in general, could be transformative,” continues Byrne. “The new technology means industry can use much larger turbines and can more rapidly scale-up design and installation of new sites. The cost of new offshore wind has already dropped dramatically since 2015, being cheaper than nuclear and new gas, with the goal of subsidy free wind power now in sight.”

“The new techniques, and other industry developments, mean the UK can confidently aim to meet the government ambition for 95% of British electricity being low carbon by 2030 – this would be a huge contribution to tackling climate change.”

Oxford team researchers

• Professor Byron Byrne FREng FICE, Professor of Engineering Science and Ørsted / Royal Academy of Engineering Research Chair in Advanced Geotechnical Design (PI)
• Professor Harvey Burd, Associate Professor
• Professor Guy Houlsby FREng FICE, Professor Emeritus, formerly Professor of Civil Engineering
• Professor Chris Martin, Professorial Research Fellow
• Professor Ross McAdam, Associate Professor

In December 2017 the PISA project won the British Geotechnical Association’s Fleming Award. The paper “PISA design model for monopiles for offshore wind turbines: application to a stiff glacial clay till” published in Géotechnique won the British Geotechnical Association Medal for 2020.

The Pile Soil Analysis (PISA) project was a £3.5 million joint industry research project (JIP) led by Ørsted and run through the Carbon Trust’s Offshore Wind Accelerator programme. The Academic Work Group was led by Oxford University and involved Imperial College London and University College Dublin.

Industry partners include: Ørsted, EDF, Equinor, GE Renewable Energy, RWE (formerly E.ON and Innogy), ScottishPower Renewables, SSE, Statkraft, Van Oord and Vattenfall. Funders: Department for Energy and Climate Change, PISA industry partners under the umbrella of the Carbon Trust’s Offshore Wind Accelerator.

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Different models for forecasting wind power generation: case study.

Graphical Abstract

1. Introduction

2. literature review, 2.1. wind power generation potential.

• Optimum constant C p region, where increasing power with increasing wind speed;
• Limited power region, generating a constant power, even in higher winds, by decreasing the C p rotor efficiency; and
• Region of power shutdown, where power generation is decelerated to zero, and wind speed approaches the cut-out limit.

2.2. Types of Wind Energy Forecast

• Ultra-short-term forecast: From a few minutes to 1 h ahead.
• Short-term forecast: From one hour to several hours ahead.
• Medium term forecast: From several hours to one week ahead.
• Long-term forecast: From one week to one year or more ahead.

2.3. Wind Speed Prediction Models

2.4. statistical models and artificial neural networks, 2.5. mixed model or hybrid model.

• Combination of physical and statistical approaches;
• Combination of models for short term and medium term;
• Combination of alternative statistical models; and
• Combination of alternative models of artificial intelligence.

2.6. Methods for the Prediction and Classification of Time Series

• Correlated observations are more difficult to analysis and require specific techniques.
• It is necessary to take into account the temporal order of observations.
• Complicating factors such as presence of trends and seasonal or cyclical variation may be difficult to estimate or remove.
• Model selection can be quite complicated, and the tools can be difficult to interpret.
• It is more difficult to deal with missed observations and discrepant data due to the sequential nature.

2.7. Stationary Time Series

2.8. non-stationary time series, 2.9. box–jenkins models, 2.10. autoregressive models (ar).

• First-order autoregressive model: AR (1); and
• Auto-regressive model of order p: AR (p).

2.11. Moving Average Models (MA)

• First-Order Moving Average Model: MA (1); and
• Moving Average Model of order q: MA (q).

2.12. Autoregressive Moving Average Models

2.13. autoregressive integrated moving average models (arima), 2.14. neural networks, 2.15. use of wavelets, 3. materials and methods, 3.1. database, 3.2. arima model, 3.3. arima + nn1 model, 3.4. arima + nn1 + nn2 model, 3.5. neural networks model, 3.6. forecast of wind speed and generated power, 4. result analysis, 4.1. ultra short term forecast—cpu (minutes), 4.2. forecasted speed at ultra-short term (minutes), 4.3. estimated power at ultra-short-term (minutes), 4.4. short term forecast—(hours), 4.5. wind speed short term forecasting (hours), 4.6. short term (hours) forecasted power in kw, 4.7. medium term forecast (days), 4.8. medium term forecasted speed (days), 4.9. estimated power for medium term (days), 4.10. medium term forecast (weeks), 4.11. predicted wind speed in medium term (weeks), 4.12. estimated power medium term weeks, 4.13. long-term forecast (months), 4.14. long-term (months) forecast speed, 4.15. long-term (months) forecasted power, 4.16. long-term forecast (years), 4.17. long-term forecasted speed, 4.18. long-term (years) power generation forecast, 4.19. average yearly energy predicted for long-term forecast (years), 5. conclusions.

• Accurate and reliable wind speed prediction is vital for wind farm planning and operational planning for electrical networks. To improve the accuracy of wind speed prediction, many forecasting approaches have been proposed; however, these models typically do not account for the importance of data pre-processing and are limited by the use of individual models.
• Achieving accurate forecasts of wind speed and power is still a critical problem. Since wind power is proportional to the wind speed cubed, the wind power potential assessment is summarized as wind speed prediction.
• There are many models and their variants for predicting wind speeds, both simple and hybrid, but none of them cover the full range of forecasting possibilities from ultra-short-term forecasts to several years ahead.
• To forecast the wind speed and the possible power to be generated, four prediction models were used: ARIMA ARIMA + NN1 ARIMA + NN1 + NN2 NEURAL NETWORKS The four types of forecast were made according to the revised literature: Ultra-short-term forecasting Short-term forecasting Medium-term forecasting Long-term forecasting
• Of the models used, the hybrid model of ARIMA + NN1 + NN2 was the one that presented the best results with the smallest errors in the prediction of wind speed in all forecast horizons, as can be seen in the table and graphs presented in this paper. For the prediction for a five-step forward, the best response to the MAE was obtained for the hour horizon with a result of 0.180, and the worst response obtained was for the weeks horizon with a response of 0.292. The best response for the RMSE was obtained for the hour horizon with 0.403, and the worst response was for the weeks horizon with an error of 0.654. For the mean absolute percentage error (MAPE) responses, the best response was obtained for the month’s horizon with 2.329%, and the worst response for the weeks horizon with 3.948%. For prediction of 20 steps forward, the best response to absolute mean error (MAE) was obtained for the hour horizon with a result of 0.189, and the worst response was for the week’s horizon with an error of 0.413. The best response for RMSE was obtained for the hour horizon with 0.843, and the worst response was for the week’s horizon with a response of 1.848. For the mean absolute percentage error (MAPE) responses, the best response was obtained for the hour horizon with 2.571%, and the worst response for the week’s horizon with 5.796%.

Acknowledgments

Author contributions, conflicts of interest.

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Barbosa de Alencar, D.; De Mattos Affonso, C.; Limão de Oliveira, R.C.; Moya Rodríguez, J.L.; Leite, J.C.; Reston Filho, J.C. Different Models for Forecasting Wind Power Generation: Case Study. Energies 2017 , 10 , 1976. https://doi.org/10.3390/en10121976

Barbosa de Alencar D, De Mattos Affonso C, Limão de Oliveira RC, Moya Rodríguez JL, Leite JC, Reston Filho JC. Different Models for Forecasting Wind Power Generation: Case Study. Energies . 2017; 10(12):1976. https://doi.org/10.3390/en10121976

Barbosa de Alencar, David, Carolina De Mattos Affonso, Roberto Célio Limão de Oliveira, Jorge Laureano Moya Rodríguez, Jandecy Cabral Leite, and José Carlos Reston Filho. 2017. "Different Models for Forecasting Wind Power Generation: Case Study" Energies 10, no. 12: 1976. https://doi.org/10.3390/en10121976

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A Wind Energy Case Study: Envision

Imagine a world where every single person has access to clean, secure and affordable energy. With recent technological advancements in the wind energy industry , that picture may not be too far off.  

The global wind turbines market registered a market value of $44.74 billion in 2017 and is expected to grow to $47.83 billion in 2022, according to Global Data . This is largely due to the increased activity within the Asia Pacific (APAC) and Europe & Middle East regions. In the U.S. alone, wind energy is set to grow 36 percent, with a 69 percent drop in costs between 2009 and 2018. 

These global investments in wind power are spurring the industry on to rapid growth. Wind farms are helping power markets around the world prioritize self-sufficiency, energy security and the need to address issues surrounding climate change. 

Increased global investments in smart energy solutions , such as wind turbines, make sense. Smart wind turbines are one of the most effective technologies used to generate renewable power, producing more energy while reducing maintenance costs. In fact, some new wind turbines feature exclusive technology that includes sensor-enabled controls to optimize their performance and energy generation in harmony with the environment.  

Envision , a smart energy solutions company headquartered in Shanghai, is at the forefront of this industry innovation.  

“We are creating wind turbines with a brain,” explained Lei Zhang, founder and CEO of Envision Group. Using hundreds of sensors, advanced control algorithms and AI predictions, Envision’s technology lets wind turbines accurately perceive their own status and environmental conditions to ensure maximum power generation and longer service life. This software-defined turbine approach surpasses the technological limitations of traditional wind turbines while boosting wind power generation efficiency by 15 percent.

Envision & Jabil

Empowering wind energy innovations  .

In bridging the gap between digital and physical energy systems, Envision is driving a global transition to smart, clean and abundant energy. As a result, wind farm operators benefit from greater visibility and control over environmental and other external factors that can impact turbine performance. But this innovation doesn’t happen in a vacuum. 

“In the wind business, it’s all about quality, reliability and cost-efficiency,” said Kane Xu, Global VP, Envision, India. “When you think about turbines sitting in rural areas—on mountaintops or in the ocean—there must be a quality system in place that enables you to achieve the highest levels of performance.” 

To usher in a new era of renewable energy, Envision sought a partner to support the company’s go-to-market strategy at unprecedented speed and scale. That’s when Envision turned to Jabil .  

For engineering and production at such a high scale, it is essential for companies to have a New Product Introduction (NPI) system in place to increase work efficiencies. The implementation of NPI management systems helps companies manage employees’ work progress and the manufacturing process flow. Envision had many moving parts in designing wind turbines and creating a seamless supply chain strategy. But with Jabil’s help, Envision launched its own NPI management system with full power production testing, value engineering and complete supplier management.

Unlocking Innovation through Collaboration 

By 2030, wind energy will account for nearly 15 percent of global electricity generated, according to Frost and Sullivan . As the wind energy economy becomes stronger, markets are beginning to emerge across the world, specifically in Mexico, Brazil, Russia and India. Due to a decline in wind energy costs and the minimal risk for developers, India is the most ideal country for expansions . Since the country is the second largest territory for Envision, aggressive expansion plans drove the strategy to align localized supply chain and manufacturing resources. 

In its desire to expand to other regions, the Envision team quickly realized the importance of a localized supply chain strategy. The close collaboration with Jabil and a shared culture of innovation resulted in the decision to open a new India-based manufacturing facility dedicated to Envision.  

In only five months – a record-breaking speed in the manufacturing world – Jabil stood up an entire factory with the ability to produce up to 300 wind turbines annually. “For Jabil’s industrial and process engineering teams, building this capability at this large a scale and this fast is something we hadn’t done before,” said Scott Gebicke, global head of Jabil’s energy, industrial and building group. “We did it together with Envision.” 

Additionally, the opportunity to handle manufacturing and assembly in India led to additional cost efficiencies, enabling Envision to reduce the cost of making wind turbines by up to 30 percent. “The team did a great job to ramp the new factory from producing zero to 50 wind turbines in just three months,” Zhang said. 

The future of wind energy is strong. In addition to onshore wind farms, there’s also a massive opportunity for offshore wind farms , and the potential for power generation on the open seas is even greater than on land, where uneven geography slows the wind. From massive wind farms spanning across the great plains to mini-wind turbines used to power a single home, the wind power industry will only gain momentum. Smart energy solutions will soon become the norm and retaining energy will become easier and safer for the environment.

Envision Case Study

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Denmark Wind: Case Study

Kieran O'Day

Denmark produces more renewable energy per capita than any other country in the world.  In 2014, Denmark produced nearly 40% of its energy from wind power alone. This case study will examine Denmark’s path to renewable energy, and plans for the future, and how wind power can be implemented in other places in the world (Ropenus).

Denmark’s path to renewable energy is driven by political, economic, and consumer components.  In the 1970s, Denmark was nearly completely dependant on fossil fuels. Oil crises in 1973 and 1979 resulted in the creation of the “Sketch for an Energy Plan in Denmark” and “Energy for the future: alternative Energy Plan.” These plans were developed by independent groups of experts, and detailed plans for nuclear energy with wind power as a possible alternative (Shukla).  The anti-nuclear energy movement in 1978 pushed down public opinion of nuclear energy, and promoted the development of wind energy. Two marches during the movement had turnouts of over 50,000 activists (Buns). The movement was successful in Denmark because of nonviolent protests, international scale, use of scientific evidence, and non-partisan political dialogue (Buns).

By the mid 1970s, Denmark established a tax on energy consumption, which was used in research and development of renewable energy. By the mid 1980s, wind turbines with capacities as large as 55 kW were being sold to groups of consumers to provide individual energy needs to their community (Shukla). These local wind cooperatives were encouraged by taxes on oil and coal and government subsidies for building local turbines. In 1985 ambitious goals for wind energy and more subsidies were implemented by the Danish government in order to support local wind energy industry, and encourage the growth of wind energy (Shukla).

In the 1990s, the Danish government continued to increase development of wind energy. National planning procedures were created and used locally to find new sites suitable for wind turbine development. Public hearings before any application to build a turbine encouraged public acceptance of their creation. In addition, the government provided financial support to all wind projects in the country, in the form of tax refunds on energy and carbon taxes. By 1996, over 2100 wind power cooperatives including more than 100000 families existed (Shukla).

From “Offshore Wind”

1991 saw the installation of the first offshore wind farm in the world in Denmark(“Offshore Wind Energy”).  In 1998, 5 more offshore wind farms were planned by the Danish government (Shukla). Offshore wind has several advantages over onshore wind power.  For one thing, winds at sea are much more predictable, steady, and blow with more  force than those on land. Offshore turbines can also be bigger than those on land, resulting in an increase in energy produced. Because of this, with wind speeds even just two mph stronger, offshore turbines can produce as much as 50% more power than onshore turbines (“Offshore Wind Energy”).  Though offshore farms cannot be financed locally and transportation costs may be higher, their larger scales make them a sound investment for the future (Roberts).

Development of wind energy has continued through the 2000s, and Denmark has more plans for the future.  The “Energy Strategy 2050” is a cross-sector energy strategy that sets a number of goals for Denmark’s future. Goals include “a coal phase-out in power stations and oil stations by 2030,” “100 percent renewable energy sources by 2050,” 100 percent renewables in electricity and heat by 2035” and several more (Ropenus).  The strategy also plans for the unknown and includes flexibility to respond to different trends in the future. “The Green Agreement of 2012 supports the Energy Strategy with intermediate goals for 2020 including reductions in CO 2 , energy consumption, and an increase in the renewable energy share in electricity production (Ropenus).

From (Ropenus)

Several factors contributed to wind energy’s success in Denmark.  The cooperation across scales between local, corporate and government was key. Often it was the government’s role to provide funding for green initiatives, such as local wind cooperatives or large industrial wind farms. This funding was generally supplied by the consumers of electricity with electricity taxes, which also encourage limited electricity usage. This cooperation was only possible because of Denmark’s efforts to limit disconnects.  All legislation on wind energy was transparent, and local meetings were held before any wind power was installed. Additionally, “the Danish Energy Agency serves as a one-stop-shop authority; its functions include granting licenses for preliminary investigations, licenses for establishment and licenses for electricity production” (Ropenus). Because of this efficiency, legislation time was cut down, and the convenience of starting a project was greatly increased. Perhaps the most important driver of success was the comprehensive and concrete goals that Denmark set. Throughout the process, plans for the future were clear and available for the public to see.  These goals made the project attractive and possible.

From this case study, it is important to think how similar success could be met in other parts of the world. The US has already made quite a bit of progress with wind energy, but more progress could and should be made.  From Denmark, we can see the success of local wind cooperatives, and subsidies for wind development from the government. Offshore wind may also be an important factor, since about 50% of the American population live in coastal areas (“Offshore Wind Energy”). No matter what the solution, it is clear that more comprehensive goals for green energy must be set and worked towards. Additionally, legislative and regulatory processes should be more transparent to the public, and disconnects created by slow bureaucracy must be eliminated.  

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Predicting turbine failure to power reliability, revenue

Wind power producer benefits from prognostic asset management solution.

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The global wind industry is seeing strong year-over-year growth, up 53% from 2019 for a record 93 GW of new capacity in 2020. 1 As wind power production increases, so too does demand for optimising operation and asset management to ensure a wind project’s profitability.

This wind power case study features prognostic asset management for wind turbines at one of Europe’s market leaders in both onshore and offshore wind power generation.

With our Lumada APM , the power producer with around 50 wind farms operating across five countries was able to do the following:

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Wind energy case studies

What does a wind farm development mean for the surrounding community? The businesses in nearby towns, the contractors who work on the wind farm in a huge variety of roles, and the farmers who own the land?

These case studies explore the opportunities and benefits created by wind farm to local businesses and economies.

Business and community opportunities

A new wind farm can become a catalyst for business and community renewal, as the people involved with Te Uku wind farm, near Raglan, are finding out.

You never know where wind will take you

To the casual observer, a wind farm may look simple and elegant on the hillside. But there is a wide range of work that needs to be done on site to maximise its electricity production. And this work is creating business and career opportunities for many Kiwis.

Improving electricity supply

Most people will simply flick a switch and expect a light to shine or a kettle to boil. While it is easy to use electricity, ensuring electricity is available whenever and wherever it is wanted is anything but. New Zealand's wind farms are helping to improve electricity supply by improving the robustness of networks and supplying local generation.

Farming the wind

For many farmers harnessing the wind enables them to improve the viability and productivity of their farms. Wind turbines provide an additional source of income, and the roads required for building and operating wind turbines enable farmers to improve their farming operations.

Local economic benefits

The wind farms in the Manawatu do more than supply New Zealanders with renewable electricity. Their construction and ongoing operation creates jobs and provides opportunities for many New Zealand companies. This case study looks at the economic activity created by the construction and operation of Stage 3 of Tararua wind farm - a 93 megawatt development in the Manawatu.

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Unlocking the Power Potential of Offshore Wind Farms

Hopkins and Portland State researchers combine computational methods and experimental techniques.

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A collaboration between researchers from Johns Hopkins   Whiting School of Engineering   (WSE) and   Portland State University   (PSU) aims to help unlock the vast potential of floating offshore windfarms in the United States by improving understanding of wind-wave-turbine interactions, which if not accounted for properly, can greatly reduce the power output of a group of wind turbines.

The project combines developing a new computational method for enhancing the accuracy of Large Eddy Simulations (LES) – a mathematical computer model that depicts the wind field within floating offshore windfarms, with advanced experimental techniques using a state-of-the-art wind tunnel/wave tank facility at PSU. By integrating both computational and experimental methods, which are usually used separately in offshore wind research, the team aims to develop more accurate tools for the design and optimization of wind farms in the deep ocean.

“One of the challenges to floating offshore windfarms is we don’t have test beds. You can’t go out to sea, build a test windfarm, and see how it performs. It’s just too expensive,” said project Co-Principal Investigator   Dennice Gayme , a professor of mechanical engineering at the Whiting School of Engineering and member of the   Ralph O’Connor Sustainable Energy Institute   (ROSEI) leadership council. “Most studies focus on LES simulations or lab experiments and don’t look at how to bridge the gap between the two, which is key to developing a complete understanding of the system.”

The JHU-PSU team’s project is the first to receive funding through the   U.S. National Science Foundation   (NSF) and the   Department of Energy’s   (DOE)   Wind Energy Technologies Office   (WETO)’s partnership in wind energy.

“This proposal is exciting because it’s incredibly well-rounded and brings together a pair of universities that have a history of excellence in wind energy research,” said Ben Hallissy, a technology manager with WETO. “It uses a combination of modeling advancements and scaled experimental results to answer some fundamental questions; for example, how do we better predict the interaction of the wind, waves, and turbines, and how do we learn as much as possible from cost-effective small-scale experiments in the laboratory before scaling up and putting turbines in the ocean?”

Ron Joslin, the program director for the   NSF fluid dynamics program , added “NSF and DOE often have complementary roles in fostering US research and innovation, and together we move discoveries from the academic lab to commercial implementation. NSF has partnered with WETO to co-fund groundbreaking research in wind renewable energy to increase the U.S. capacity for renewable energy. This partnership gives us greater flexibility to award new projects with the funds available at each agency.”

Unlike traditional offshore wind turbines that are attached directly to the ocean floor, floating windfarms stand on buoyant structures that are anchored to the ocean bed by mooring lines. This allows placement in deep ocean waters, where about two-thirds of U.S. offshore wind energy potential exists,   according to WETO .

But turbines on platforms that move with the water make it difficult to design windfarms in a way that maximizes their energy potential. Computationally, a major challenge to creating LES for effective windfarm design is accurately reflecting wind flow over always-moving waves with multiple wavelengths and complicated shapes.

Project Principal Investigator   Charles Meneveau , a professor of mechanical engineering at WSE and an associate researcher with ROSEI, explains two conventional methods for representing wind flow over moving water. The classic method assigns a general “roughness length” number to it, allowing for quicker but less precise simulations. The other method uses a computational grid that adapts to the wave. This approach offers greater accuracy but is quite difficult and time-consuming to create, making it impractical for most common use.

In this work, Meneveau and Gayme propose an intermediate approach, combining a less precise grid that doesn’t follow the waves, with a variable forcing term that represents the pressure force along the water’s surface.

“We can get accurate results using this model by combining the better features of both the faster less accurate method, as well as the slower more exact one,” Meneveau said. “Our model reflects different moving waves with peaks and troughs but does so quickly and accurately. It can also factor in a moving platform with a turbine on top of it. It works quickly but provides the critical details.”

The experimental aspects of the project will be led by   Raúl Bayoán Cal , a professor of mechanical and materials engineering at PSU. His lab facility features a test length that is five meters long, with a wave tank with multiple small turbines floating on the water surface. Most groups studying wind turbines are limited to testing a single turbine at a time, making it more challenging to see how the turbines interact with each other.

“What we have is much smaller than an actual floating wind farm, but our platform enables the measurement of many different factors simultaneously, including dynamics of turbines, power extracted from turbines, motion of the waves, and the flow behind the turbines,” Cal said. “We can also recreate various environments where the wind and waves are forced in different ways, meaning my group can study a multitude of conditions that are observed in offshore wind farms, helping us prepare a wind farm for a given scenario.”

Before joining the faculty at PSU, in the late 2000s, Cal was a postdoctoral fellow advised by Meneveau at Hopkins, leading to this and many other collaborations between the two groups, including one of the first scaled windfarm experiments to ever happen in a wind tunnel.

“A big reason that you don’t see collaborations between groups that work in the computational and lab spaces is relationships. Knowing how myself, Charles, and Dennice all work has played a big part in us partnering,” Cal said. “When working with both computational and experiments, the questions need to be really defined and within that we can say ‘What are the computational elements that can be exploited in a lab experiment and vice versa.’ It’s easier to find answers to those questions when you have a history with your partners.”

The project is jointly supported by NSF and DOE through awards to Johns Hopkins University   (#2401013 ) and Portland State University   (#2401014 ).

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As the world races to decarbonize power systems to mitigate climate change, the body of research analyzing paths to zero emissions electricity grids has substantially grown. Although studies typically include commercially available technologies, few of them consider offshore wind and wave energy as contenders in future zero-emissions grids. Here, we model with high geographic resolution both offshore wind and wave energy as independent technologies with the possibility of collocation in a power system capacity expansion model of the Western Interconnection with zero emissions by 2050. In this work, we identify cost targets for offshore wind and wave energy to become cost effective, calculate a 17% reduction in total installed capacity by 2050 when offshore wind and wave energy are fully deployed, and show how curtailment, generation, and transmission change as offshore wind and wave energy deployment increase.

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Introduction.

Power systems around the world are changing drastically as countries race to decarbonize in an effort to curb climate change. Traditional fossil fuel generators must be replaced with a diverse mix of renewable energy and other distributed energy resources to reduce carbon emissions while also maintaining grid stability and serving society’s increasing demand for power. However, it remains as an open research question what the optimal mix of technologies is for decarbonizing power sectors in different regions across the globe.

Several studies 1 , 2 , 3 , 4 , 5 , 6 utilize different types of capacity expansion models to understand what future cost-optimal low-carbon electricity mixes may look like for the U.S. A few of these studies 1 , 2 , 3 provide analyses that seek to understand the role specific technologies may have in a future cost-optimal, low-carbon U.S. grid. For example, the authors of ref.  1 investigate the impact that integrating bioenergy with carbon capture and sequestration (BECCS) with significant renewable deployment may have on enabling a carbon-negative power system in western North America by 2050. Similarly, the authors of ref. 2 investigate the role of firm low-carbon resources, such as nuclear, reservoir hydropower, geothermal, bioenergy, and natural gas, with carbon capture in reducing the cost of a decarbonized power grid. The authors of ref. 3 investigate how concentrated solar power with thermal energy storage (CSP+TES) competes with short-duration storage. Although refs.  1 , 2 , 3 , 4 do consider some promising technologies, they omit other emerging technologies that may be available in the future for commercial deployment, such as offshore wind and wave energy.

The study presented in this manuscript focuses on the Western Interconnection of the U.S. Many states 7 , 8 , 9 , 10 , 11 that constitute the Western Interconnection have pledged to achieve clean energy goals by 2030–2050. In light of these ambitious targets, wave energy and offshore wind energy, two co-existing abundant resources on the West Coast of the U.S., arise as clean energy sources to be considered in the transition towards carbon-free generation portfolios of the Western Interconnection.

The resource potential for both offshore wind and wave energy is tremendous along the West Coast of the U.S. (California, Oregon, Washington) 12 , 13 , 14 . In the U.S. West Coast, the offshore wind energy potential is 800 TWh/yr 14 and the wave energy potential is 240 TWh/yr 15 , together demonstrating ~1.2 times the 2021 annual electricity demand in the Western Interconnection 16 . Despite this potential, there are no offshore wind turbines off the coast of the Western U.S. There are only two commercial offshore wind farms off the coast of the Eastern U.S. (a 5-turbine farm and a 12-turbine farm), as well as two demonstration offshore wind turbines off the coast of Virginia. There are no commercially operating wave energy farms on either coast 17 .

Sharing the same hostile marine environment, similar obstacles have prevented cost parity with other technologies in the grid and hindered the growth of both of these technologies. Some of these obstacles include high maintenance costs due to intense ocean conditions, environmental disruption concerns, permitting challenges due to marine zoning laws, and visual impact concerns for near-shore deployment 18 . Current offshore wind and wave energy technologies are not cost-competitive with fossil fuel technologies, onshore wind energy, or solar energy either historically or with projections into 2030 17 , 19 , 20 , 21 . However, as we move towards a decarbonized energy future, we would benefit by considering a diverse portfolio of renewable energy sources. The technical benefits of integrating offshore wind and wave energy, coupled with cost reductions that would take place from deploying them, may make them contenders in the future.

Wave energy has several attributes that are advantageous. For example, wave energy is predictable up to 3 days in advance and is more consistent than most other renewable alternatives 22 . In some regions, when compared to wind energy, wave energy has less visual impact and higher energy density, as well as more continuous and predictable power output 23 . Furthermore, integrating wave energy with other renewable technologies can be complementary in nature. For example, ref.  23 studies how wave energy has decoupled weather patterns to solar, depending on the local conditions. Hence, coupling these technologies can have balancing effects. For the U.S. West Coast, wave energy is expected to have approximately four times more energy availability during winter months than summer months, as demonstrated by the PacWave test site off the coast of Newport, OR 24 . Deploying wave energy on offshore wind farms could also have similar power output smoothing effects, especially in areas with low correlations between wind and wave conditions or with a lag between the two power sources, as the authors of ref. 23 discuss. Additionally, coupling wave energy with offshore wind could provide enhanced energy yield and better predictability. One study showed that combined wind-wave farms in California would have fewer than 100 h of no power output per year, compared to >1000 h for offshore wind or more than 200 h for wave farms alone 25 . Other advantages that combined wind-wave farms have over traditional offshore wind farms include more efficient utilization of offshore site areas, shared project development costs between the two technologies, shared underwater transmission costs, shared substructure foundations, and reduced environmental impacts 26 , 27 .

Offshore wind also has several technical and social benefits. The most attractive attribute of offshore wind is the higher capacity factors it yields compared to land-based wind 28 . Additionally, offshore wind tends to have a higher public acceptance than land-based wind and other land-based renewable technologies because the public does not experience significant visual impacts, noise production, or shadow casting from wind turbines if they are placed sufficiently far from the shore 28 .

Few studies consider the role and system-wide impacts that wave and offshore wind technologies may have on the grid when they are deployed. The work in ref. 23 analyzes the value and effects that wave energy combined with offshore wind energy can have on southern Sweden’s electricity grid. However, since the work conducts the analysis with a production cost model, it does not consider the investment costs of generating units or transmission infrastructure. The authors of ref. 29 analyze the effects of wave energy on the Southwest United Kingdom grid, but it focuses only on the effects of considering multiple wave energy sites on the quality of power output in terms of reduced intermittency of supply and step changes in generated power. The scope of ref. 30 is limited to studying the impact of one particular wave energy test site off the coast of Oregon, U.S., on the local grid in terms of steady-state, dynamic, and transient characteristics.

Several studies 31 , 32 , 33 , 34 analyze the impacts of integrating specifically offshore wind farms into the power grid, but they are limited to analyzing only the effects caused by offshore wind integration on voltage and frequency stability and wholesale prices in the electricity market, or their results do not stem from an optimization framework or the use of a real grid (stylized small power networks). A recent study analyzes the role of offshore wind in decarbonizing the U.S. using a capacity expansion model and various scenarios centered around policy and demand, technology cost and availability, transmission, and sitting constraints for various generation options 35 . Although this study is thorough in reviewing factors that shape offshore wind deployment and how those factors affect the role that offshore wind plays in achieving various levels of grid decarbonization, it does not include wave energy or explore the interplay between offshore wind and wave energy with the potential for collocation.

Despite the large body of work analyzing the potential electricity generation mixes for a future decarbonized U.S. grid and the several studies investigating certain impacts of integrating offshore wind and/or wave energy, the literature falls short of including both fixed-bottom and floating offshore wind and wave energy in the mix of candidate renewable technologies and understanding the technical implications of their relative deployment. To address this gap, this paper investigates the system-wide impacts of integrating various amounts of offshore wind (both fixed-bottom and floating) and wave energy into a carbon-free electricity mix using. For this, we use a least-cost capacity planning model with high spatial resolution, detailed power systems modeling, and a wide variety of candidate technologies.

We model the Western Interconnection with a 2050 zero-emissions future using SWITCH 36 , a long-term capacity expansion model that has been used in numerous studies of low- or zero-emissions electricity grids 1 , 37 , 38 , 39 . Our model also contains 7000+ candidate plants that the model may choose to build. These plants are distributed across 50 load zones that cover the Western Electricity Coordinating Council (WECC) and are connected by 126 aggregated transmission lines. Additionally, the model simultaneously optimizes investment and dispatch decisions to minimize the total system cost and meet each load zone’s power demand while considering the transmission network. Dispatch decisions are made at consecutive four-hour intervals for two representative days per month for investment periods 2020, 2030, 2040, and 2050. The year 2050 is when WECC-wide carbon emissions from electricity generation are required to reach zero in all scenarios. Since we seek to understand how integrating offshore wind and wave energy affects the cost-optimal zero-emissions system, the results presented in this paper focus on the year 2050. Results for investment periods 2020–2040 are presented in section  3 of the Supplementary Information.

We design five different cost targets for wave energy. The most conservative cost target corresponds to a 50% cost reduction by the year 2050. The other four cost targets, in order from more conservative to more optimistic, are such that the 2050 overnight and operation and maintenance (O&M) wave energy costs reach parity with the National Renewable Energy (NREL) 2022 Annual Technology Baseline (ATB) 40 : (2) land-based wind 2020 costs, (3) land-based wind projected 2050 costs, (4) utility-scale photovoltaic (PV) energy 2020 costs, and (5) utility-scale PV energy projected 2050 costs, assuming a linear projection between the wave energy 2020 and 2050 costs. Similarly, we design five offshore wind overnight and O&M cost targets. The three core cost targets follow the NREL 2022 ATB conservative, moderate, and advanced cost projections for fixed and floating offshore wind energy. We also designed an additional very conservative and very advanced offshore wind cost target.

We combine the five wave energy cost targets and five offshore wind cost targets into 25 (5 × 5) scenarios that pair each wave energy cost target with each offshore wind energy cost target to evaluate how the relative cost assumptions affect the optimal zero-emissions 2050 energy mix. Figure  1 summarizes the scenario number assigned to each combination of offshore wind and wave energy cost targets.

The row labels describe which technology wave energy is assumed to reach cost parity by 2050 in each of the 25 scenarios designed for this study. Note that a 50% cost reduction for wave energy corresponds to $ 1732.50/kW overnight cost and $ 52.70/kW-yr O& m cost for wave energy in 2050. The column labels describe which offshore wind NREL 2022 ATB scenario is assumed for the cost of offshore wind energy in each of the 25 scenarios designed for this study. *Derived by offsetting an NREL 2022 ATB projection.

The simultaneous decrease in costs of offshore wind and wave energy technologies captured by the scenarios reflects a positive feedback loop in research and deployment for offshore energy technologies. If more offshore wind gets deployed over time, economies of scale and built infrastructure could positively affect further cost declines for offshore wind, and at the same time, it could lower entry barriers for other offshore technologies, such as wave energy. On the other hand, the scenarios that represent offshore wind and/or wave energy becoming significantly less expensive by 2050 while the other technology remains expensive capture the possibility that one technology may be substantially more invested in as we transition to renewable energy while the other is left behind.

The purpose of these scenarios is not to predict cost targets or likely trends for offshore wind and wave energy overnight and O&M costs in coming years, but rather they serve to answer What if? questions related to offshore wind and wave energy becoming cost-competitive with other renewable resources to varying degrees.

The main contributions of this work are the following: (1) modeling offshore wind and wave energy as independent technologies with the possibility of collocation in a power system capacity expansion model of the Western Interconnection, (2) identifying, cost targets for offshore wind and wave energy to become cost-effective in a zero-emissions grid, (3) observing a 17% of reduction in total installed capacity by 2050 when offshore wind and wave energy are fully deployed, and (4) quantifying how lower wave energy cost targets result in lower total transmission expansion, and on the other hand, lower offshore wind cost targets result in higher transmission expansion. We find that if wave energy reaches cost parity with land-based wind by 2050 and offshore wind energy aligns with the advanced offshore wind NREL 2022 ATB scenario, then wave energy and offshore wind energy can reach about 6% and 9% deployment in a cost-optimal zero-emissions Western Interconnection, respectively.

Total installed capacity of the zero-carbon grid decreases

In general, as offshore wind and wave energy 2050 cost targets decrease, and consequently their deployment in the grid in 2050 increases, the total installed zero-emissions generation capacity in the Western Interconnection decreases (Fig.  2 a). The overall installed capacity decreases by a maximum of 133 GW between scenario 1 (most expensive offshore wind and wave energy cost targets) and scenario 24 (very advanced offshore wind energy cost target and wave energy cost parity with land-based wind in 2050). This corresponds to a 17% decrease in total installed capacity in the grid, which is mostly driven by decreased cost targets of offshore wind energy, and, thus, increased deployment of offshore wind energy, as seen in Fig.  2 a. When wave energy cost target decreases from the most conservative to the most optimistic wave energy cost target, we see a maximum decrease in total installed capacity of 3%.

Scenario numbers are displayed at the top of each bar. a Total 2050 installed zero-emissions generation capacity (GW) in the Western Interconnection in each scenario. Total installed capacity decreases with decreasing offshore wind energy cost targets and mostly decreases with decreasing wave energy cost targets until offshore wind energy costs decline beyond the NREL ATB moderate scenario. b 2050 solar energy installed capacity (GW) in each scenario. Solar energy installed capacity decreases with decreasing offshore wind and wave energy cost targets. c 2050 energy storage installed capacity (GW) in each scenario. Energy storage installed capacity decreases with decreasing offshore wind and wave energy cost targets. d 2050 total land-based transmission capacity (GW) in the Western Interconnection for each scenario. Transmission capacity decreases with decreasing wave energy cost targets and increases with decreasing offshore wind energy cost targets. Note that the x and y axes are flipped in plot ( d ). This is done so that the trend is fully visible. Source data are provided as a Source Data file.

The significant reduction in installed capacity across the scenarios implies that offshore wind and wave energy may play a key role in limiting the overbuilding of the grid to ensure demands are met in the future 2050 zero-emissions grid, even if they make up a relatively small portion of the total electricity mix. One of the factors that partially contributes to this reduction in total installed capacity is related to installed solar energy capacity: as more offshore wind and wave energy are deployed across the scenarios, the amount of solar capacity that needs to be installed in the zero-emissions Western Interconnection in 2050 decreases, as seen in Fig.  2 b, although solar consistently remains the dominant source of energy for electricity generation. We observe a difference of 132 GW of solar installed between scenarios 1 and 25, which is a ~39% decrease. As a reminder, scenario 25 assumes wave energy reaches cost parity with utility PV energy in 2050, and offshore wind energy costs align with the very advanced NREL 2022 ATB scenario (which is an offset of NREL’s advanced scenario). Hence, if offshore wind and wave energy costs decline dramatically in the coming decades, these technologies have the potential to significantly reduce how much installed solar energy is required in the future zero-emissions grid.

Less deployment of solar energy consequently reduces mid-day over-generation and hence reduces reliance on energy storage. We observe that lower offshore wind and wave energy costs lead to lower storage capacity installed in the Western Interconnection in 2050. This effect is most dramatically seen with more rapidly declining offshore wind costs (Fig.  2 c). We observe a maximum difference of 60 GW of storage installed (37% decrease) across scenarios. This decrease corresponds to a decline from 44% to 32% in terms of the share of total installed capacity made up by energy storage.

While solar energy remains the dominant technology across all scenarios, the reduction of solar energy and storage charging peaks in the grid achieved by increased deployment of offshore wind and wave energy may be beneficial, as the mid-day peak and nighttime lull of solar energy combined with peak electricity demand in the evenings causes the duck curve, which is known to cause utility challenges 41 . The daily dispatch profile on a peak-demand day in 2050 reveals that increased deployment of wave energy and (especially) offshore wind energy reduces the solar energy and storage charging peaks in the grid. As offshore wind and wave energy cost targets decline, we observe a maximum decrease of 26% in the solar generation peak on a peak-demand day in 2050. Contrary to solar energy, offshore wind, and wave energy are dispatched at an almost consistent level throughout the day, only decreasing when solar is in excess. Hence, the more consistent generation profiles of wave energy and offshore wind may be useful for serving the grid’s base load and reducing the duck curve effect in a highly renewable grid.

As expected, lower cost targets of offshore wind energy result in more offshore wind installed capacity, as seen in Fig.  3 a. We observe a maximum increase in installed capacity of offshore wind from 2 GW to 59 GW, which corresponds to an increase from 0.3% to 9% of the total installed capacity. Similarly, the amount of wave energy capacity installed in the Western Interconnection in each scenario increases as the cost targets of wave energy decrease, as seen in Fig.  3 b. We observe a maximum increase in the installed capacity of wave energy from 3.7 GW to 40 GW, which corresponds to an increase from 0.6% to 5.5% of the total installed capacity. The 40 GW of wave energy installed corresponds to 93% of the maximum amount of wave energy that could be installed in the 101 new wave energy candidate projects added to SWITCH WECC for this study. Hence, at the wave energy overnight and O&M cost targets of $ 618/kW and $ 13.25/kW, respectively, which corresponds to parity with utility PV in 2050, SWITCH nearly maxes out the amount of available wave energy capacity (as allotted by the candidate projects in study) on the U.S. West Coast.

2050 offshore wind energy ( a ) and wave energy ( b ) capacity installed (GW) in each scenario. Scenario numbers are displayed at the top of each bar. Offshore wind energy installed capacity increases as offshore wind energy cost targets decline and as wave energy cost targets rise. Wave energy installed capacity increases as wave energy cost targets decline and as offshore wind energy cost targets rise. *Note that the x and y axes are flipped in the plot on the left. This is done so that the trend is fully visible. Source data are provided as a Source Data file.

Refer to Tables  3 – 10 of the Supplementary Information for detailed numerical results related to 2050 total installed capacity and installed capacity of individual technologies across the scenarios. Refer to Fig.  11 of the Supplementary Information for a graph of the 2050 peak-demand day dispatch profiles for the four edge-case scenarios.

Highly intermittent sources in coastal zones are needed less

Because offshore wind and wave energy farms deliver generated power to substations located along the U.S. West Coast, the generation profiles of coastal load zones (20 zones) are most affected by the deployment of these technologies. These impacts are significant to the whole system because the total electricity demand across the coastal load zones makes up almost 42% of the entire demand in the Western Interconnection in 2050. Figure  4 shows the daily dispatch profile that represents the dispatch specifically in coastal load zones on the peak day in December, 2050 in the four edge-case scenarios (with either highest or lowest cost target for offshore wind and/or wave energy). Similar to the total grid daily dispatch profiles, the daily dispatch profiles in the coastal load zones reveal that offshore wind and wave energy have almost constant generation throughout the day. This further suggests that they are well-suited technologies for serving the base and that they may contribute to less reliance on storage since less power is generated excessively during times of the day when it is not needed. Note that the load is the same in all scenarios, but that scenario 25 (least expensive offshore wind and wave energy cost targets) shows a notably smaller solar peak than scenario 1 (most expensive offshore wind and wave energy cost targets) (Fig.  4) . Coastal load zones exhibit a maximum decrease of 24% in the solar peak on a peak-demand day in 2050. This indicates that the relatively constant nature of offshore wind and wave energy generation reduces the amount of generation needed from more intermittent sources. For reference, the scenario 25 overnight cost targets of fixed-bottom and floating offshore wind and wave energy in 2050 are $ 1382/kW, $ 2296/kW, and $ 618/kW, respectively, while solar energy’s 2050 overnight cost is assumed to be $ 703/kW. Notice that although the overnight cost of solar energy is significantly lower than that of offshore wind, we still observe a decline in the solar energy generation peak when offshore wind is most deployed. Coastal load zones in scenario 25 also have visibly fewer daily imports from other load zones and more daily exports to other load zones than in scenario 1, which implies that these zones are becoming less reliant on other zones to serve their local loads as more offshore wind and wave energy are deployed.

The daily dispatch profiles show relatively constant offshore wind (blue) and wave power (magenta) generation, decreased dispatch of solar energy (yellow) and energy storage (light green) with increased dispatch of offshore wind (blue) and wave energy (magenta), and decreased imports from other load zones (dark pink) and increased exports to other load zones (light pink) with increased dispatch of offshore wind and wave energy. Source data are provided as a Source Data file.

Figure  5 shows the monthly dispatch profiles in 2050 for coastal load zones for the edge-case scenarios. Between scenario 1 and scenario 25 (most and least expensive offshore wind and wave energy cost targets, respectively), there is a 31% decrease in annual (2050) energy imports (from other load zones) and a 58% increase in annual energy exports (to other load zones) in coastal load zones. We also observe this trend when only offshore wind or wave energy become dramatically cheaper while the other technology remains expensive.

The monthly dispatch profiles show decreased dispatch of solar energy (yellow) and energy storage (light green) with increased dispatch of offshore wind (blue) and wave energy (magenta), as well as decreased imports from other load zones and increased exports to other load zones (shades of pink) with increased dispatch of offshore wind (blue) and wave energy (magenta). Source data are provided as a Source Data file.

These results reveal that wave energy and offshore wind deployment influence increases in energy exports from coastal load zones to other load zones and decreases in energy imports from other load zones to coastal load zones. Hence, if these technologies are deployed substantially, they may play a role in helping coastal regions to become more self-sufficient and also become larger generation centers for supporting inland regions.

We can observe the increase in offshore wind and wave energy generation along the U.S. West coast with decreasing cost targets when comparing the dispatch portfolio map of scenario 1 to the dispatch portfolio map of scenario 25 (Fig.  6 ). The decline in solar energy and energy storage dispatch along the coast is also visible.

Scenario 1 (left) and scenario 25 (right) (most and least expensive offshore wind and wave energy cost targets, respectively) annual generation breakdown and transmission lines for each load zone in 2050. Between scenarios 1 and 25, coastal load zones show an increase in the share of electricity generation from offshore wind and wave energy, as well as less generation from solar energy and energy storage. Source data are provided as a Source Data file.

California, which has the highest load, generation, and offshore wind and wave energy installed capacity when compared to the other coastal states, has an increased ratio of generation to load as offshore wind and wave energy are increasingly deployed. We observe the ratio of generation to load in California increase from 0.87 to 0.94. Washington (ratio increases from 0.78 to 0.84) and Oregon (ratio increases from 1.04 to 1.63) exhibit a similar pattern. This provides further evidence that when coastal states integrate more offshore wind and wave energy into their electricity generation mixes, they are able to meet more of their state’s demand and thus are more self-sufficient (i.e., less reliant on energy imports from other states).

Refer to Table  11 of the Supplementary Information to see the ratio of generation to load in California in 2050 overall 25 scenarios.

Renewable energy curtailment increases

The constant nature of offshore wind and wave energy generation observed in Fig.  4 is an advantage that these technologies have over their renewable counterparts. Consequently, as offshore wind and wave energy are increasingly deployed, and hence more of the demand in coastal load zones is being met locally, there is more curtailment of land-based wind energy and solar energy in the year 2050. Figure  7 shows that as offshore wind and wave energy cost targets decrease, total curtailment in the grid increases by a maximum of 49 TWh (48% increase). This increase in curtailment corresponds to an increase of 3.4% in terms of percent of total available renewable electricity that is curtailed. More than half of that increase in renewable curtailment is attributed to increased curtailment of land-based wind energy and solar energy.

Energy curtailment increases with increasing offshore wind and wave energy cost targets. Scenario numbers are displayed at the top of each bar. *Note that the x axis and y axis are flipped with respect to plots a to c in Fig.  2 . This is done so that the trend is fully visible. Source data are provided as a Source Data file.

Refer to Table  12 of the Supplementary Information for detailed numerical results related to curtailment in 2050.

More offshore wind energy leads to more built transmission

We observe that lower wave energy cost targets lead to less installed land-based transmission in 2050, and lower offshore wind energy costs lead to more installed land-based transmission (Fig.  2 d). Note that the cost of underwater transmission for the offshore wind and wave energy deployments is captured in the connection cost of each project, but the analysis in this section focuses on installed capacity of land-based transmission only. All subsequent discussions of transmission are referring to land-based transmission. Across the scenarios where wave energy cost targets are decreasing, the amount of installed transmission decreases by a maximum of 21.8 GW (15% decrease). Across the scenarios where offshore wind energy cost targets are decreasing, the amount of installed transmission increases by a maximum of 80 GW (92% increase). The increase in transmission associated with increasing amounts of offshore wind energy installed can be explained by the new transmission required to transport power produced in offshore wind farms throughout the main grid. If significant amounts of offshore wind generation cause the coastal load zones to become larger generation centers, then increased transmission capacity will be needed to move power from the coasts inland, as observed in Fig.  6 .

The decrease in installed transmission with lower wave energy costs becomes more prevalent once offshore wind energy cost targets reach the moderate NREL ATB scenario or lower targets. This trend is explained by the decreased offshore wind energy capacity as wave energy cost targets decrease. This relationship between installed capacity of offshore wind energy and installed transmission capacity can be observed by comparing Figs.  3 a and 2 d. This suggests that offshore wind energy is the main diver for increased installed transmission, and that installing a more even mix of offshore wind and wave energy, rather than installing a significant amount offshore wind energy and a small amount of wave energy, can help decrease the amount of new transmission required.

Refer to Table  13 of the Supplementary Information for detailed numerical results related to 2050 installed transmission capacity across the scenarios.

Lower cost targets lead to more collocation

Finally, we observe that lower offshore wind and wave energy costs lead to more collocated offshore wind and wave energy farms (Fig.  8 ). Scenario 1 (most expensive offshore wind and wave energy cost targets) has no collocated offshore wind and wave energy farms in 2050. However, as offshore wind and wave energy costs decline, we see the number of collocated sites increase to a maximum of 28 (out of 101 total possible sites for collocation), which corresponds to 23% of the installed offshore wind and/or wave energy farms exhibiting collocation.

In general, the number of sites chosen for collocation increases with decreasing offshore wind and wave energy cost targets. Scenario numbers are displayed at the top of each bar. Source data are provided as a Source Data file.

This increase in the number (and percent) of collocated sites as offshore wind and wave energy become increasingly more cost competitive with other renewable resources shows that the optimization model favors the collocation of these technologies as they are increasingly deployed for electricity generation. Although, not captured in our model, this tendency would be even stronger as we would expect to observe reduced costs associated with collocated offshore wind and wave energy as they would share land-based infrastructure.

Refer to Tables  14 – 17 of the Supplementary Information for detailed numerical results related to collocation of offshore wind and wave energy across the scenarios.

Total system cost decreases by up to 4%

We observe that as offshore wind and wave energy become increasingly cost competitive with other renewable technologies, and consequently become increasingly deployed in the grid, the total Western Interconnection System cost in net present value (NPV), with 2018 as the dollar base year and summed across all four investment periods, decreases by a maximum of 4%.

There are several factors that contribute to this decline in addition to decreasing offshore wind and wave energy costs targets. Firstly, 2050 incurred fuel costs decline slightly across the scenarios (maximum decrease of 0.9%). The main contributing factor to this decline in fuel costs is a 7.8% decrease in biomass generation in the year 2050. Second, incurred energy storage fixed costs decline by a maximum of 50%. This is a direct result of the significant decrease in installed energy storage that is observed with increased penetration of offshore wind and wave energy. Third, incurred O&M and fixed costs of electricity generators slightly decline (maximum decrease of 1.4% and 2.3%, respectively). This is likely a consequence of the over 17% reduction of installed capacity in the grid, as well as the lower investment and O&M costs assumed for offshore wind and wave energy. In contrast, we observe a maximum increase of 28% in transmission fixed costs, which is a direct result of the increase in transmission capacity observed with decreasing offshore wind costs. However, decreased wave energy cost targets consistently cause decreased transmission costs. This is due to the reduced transmission required when more wave energy is deployed, as explained in the section titled, “More Offshore Wind Energy Leads to More Built Transmission.”

Refer to Table  18 of the Supplementary Information for detailed numerical results related to system cost components across the scenarios.

As we have seen, even relatively small percentages of offshore wind and wave energy penetrations in a 2050 zero-emissions electricity mix have significant implications on the grid. One of the most remarkable consequences of deploying offshore wind and wave energy we observe in this study is the large (133 GW, or 17.3%) reduction between the scenarios in total installed generation capacity in a 2050 zero-emissions Western Interconnection. This decrease in installed capacity is tied to less installed capacity of renewable resources with intermittent diurnal generation patterns, such as solar energy, and consequently less energy storage. This implies that these technologies will play a key role in limiting the upsizing of generation capacity in the grid, therefore limiting costs, as we move away from fossil fuels. The results show that for offshore wind and wave energy to induce >10% reduction in the 2050 total system installed capacity, offshore wind energy costs would have to decline to those of the NREL 2022 ATB advanced scenario, and wave energy costs would need to decline by at least 50%. The U.S. Office of Energy Efficiency and Renewable Energy has even more ambitious cost targets for floating offshore wind turbines over the next decade: The Floating Offshore Wind Energy Shot Initiative seeks to lower LCOE costs of offshore wind turbines by more than 70%, to $ 45/MWh by 2035 42 . This is $ 7/MWh less than what the NREL 2022 ATB advanced scenario assumes floating offshore wind will cost by 2035. According to NREL, for the ATB advanced scenario to manifest, turbine sizes would need to increase at a rate that is considerably higher than in recent years 40 . Offshore wind energy innovation that leads to cost reductions also includes significant changes to the manufacturing, installation, operation, and performance of wind farms 40 . Wave energy would need to experience similar innovations to achieve these cost reduction targets, and the supply chain and manufacturing infrastructure to support the deployment of Wave Energy Converters (WECs) would need to be established. Fortunately, as offshore wind energy becomes increasingly deployed, it is likely that the infrastructure built to enable its adoption will positively influence wave energy cost reductions since the two technologies share the same ocean environment and require similar infrastructure.

While offshore wind and wave energy have faced many cost challenges associated with the hostility of ocean environments, their costs are expected to decline as supply chain infrastructure becomes more developed, designs become more efficient and refined, and markets adapt to compensate offshore wind and wave energy developers appropriately for the ancillary services that these technologies may provide to the grid (such as base-load support, reactive power support, etc.). Wave energy in particular has a long way to go when it comes to reducing costs by designing standardized WECs that can be manufactured with streamlined techniques, a problem further complicated by the fact the optimal WEC design can vary depending on the dominant wave frequency at a given site 23 . Standardization may still take place to create main categories of commonly used WEC designs which can be refined individually and deployed in areas with corresponding ocean conditions. Hence, there is still significant room for improvement of these technologies and the physical, economic, regulatory, and political infrastructure to support them.

Because the benefits that offshore wind and wave energy may provide for the future zero-emissions grid are so significant, we recommend that policy makers design incentives to stimulate investment, research, and development of these technologies that will drive their overnight and O&M costs sufficiently down to ensure that they become cost competitive with other renewable resources. For wave energy to reach cost parity with land-based wind by 2050, its overnight and O&M costs would need to decline by ~80% and 70%, respectively, over the next three decades. For offshore wind energy to align with the NREL 2022 ATB advanced scenario costs by 2050, fixed-bottom and floating offshore wind energy overnight and O&M costs would need to decline by ~43% over the next three decades. Although these declines seem drastic, solar and land-based wind energy have demonstrated momentous cost declines in the past decade. Solar energy costs have decreased 80% and land-based wind energy costs have decreased almost 40% since 2010 43 . Hence, significant drops in renewable energy costs are not unprecedented.

Additionally, the results of this study show that reduced offshore wind and wave energy costs result in increased collocation of the technologies in an optimal grid. Research suggests that through collocation, grid infrastructure, O&M, and licensing expenses could all be shared (which is not captured in this study). For instance 44 , shows that two-thirds of offshore wind farm project development costs can be shared with wave energy deployments. However, the research on assessing collocation potential for offshore wind and wave energy in the Pacific Ocean is severely limited. Capacity expansion planners and offshore wind and wave energy developers should consider co-design and the potential for collocation of these technologies to avoid costly and inefficient integration in the future. Hence, if we are to utilize the synergistic benefits of offshore wind and wave energy in the most efficient way, there should be significant funding for research surrounding collocation of these technologies in the coming years.

First, we identify sites with high potential of offshore wind and wave energy along the coast of the Western Interconnection. We next model candidate generation projects at these sites, (i) filtering out sites that are in marine protected areas (MPAs) with strict classifications 45 , military danger zones and restricted military activity areas 46 , and (ii) calculating the hourly capacity factors for each candidate project for one year of data. Finally, we use SWITCH, a power system capacity expansion model, to study the role and impacts of these offshore wind and wave energy candidate projects under 25 scenarios with different cost targets.

A more detailed overview of the methodology for this study is summarized in Fig.  9 .

Overview of methodology used for this study.

Data acquisition and processing

The sites of industry interest represent high-potential wave farm sites along the U.S. West Coast. They are calculated as the result of a scoring framework developed by CalWave. Each site considered by CalWave receives a score between 0 and 100, based on a weighted sum of the following six quantitative parameters: wave energy resource density, distance to shore, water depth, wind resource, bathymetry, and local population density 47 . The parameters are weighted based on CalWave’s assessment of their relative importance to the development of utility-scale wave energy infrastructure. CalWave uses NREL’s report on Marine Hydrokinetic Energy Site Identification and Ranking 48 as a guideline for their own ranking framework. The parameters that CalWave considers which coincide with NREL’s report are wave resource density and water depth. Some differences between the parameters considered by CalWave and NREL are as follows:

While NREL considers market size and distance to transmission connection, CalWave considers local population density and distance to shore

NREL considers energy price and shipping cost, but CalWave does not

CalWave considers bathymetry and wind resource, while NREL does not

NREL assigns equal ranking to each of the parameters considered, while CalWave assigns different weights to each parameter empirically based on their experience as a wave energy developer and input from wave energy industry and academic ocean energy experts. The parameters in order of assigned weight from highest weight to lowest weight is as follows:

Wave resource

Distance to shore

Water depth

Wind resource

Local population density

It is important to mention that the CalWave scoring framework does not use costs and existing infrastructure as compared to the report from NREL 48 because it intentionally encourages the development of wave energy infrastructure in the locations most technically suitable. The sites that rank as the top 100 sites according to CalWave’s proprietary framework are identified as the industry sites of interest for the U.S. West Coast. Figure  10 shows each site of interest represented by the latitudinal and longitudinal coordinates of its center (blue points).

The sites of industry interest appearing in this figure have been filtered to exclude sites in MPAs and military danger zones. All candidate project areas and BOEM call areas may have offshore wind energy, wave energy, or both technologies installed. Source data are provided as a Source Data file.

When developing candidate projects for offshore wind and wave energy, we first filter the sites of industry interest to ensure that no site overlaps with MPAs that have the 3 strictest classifications 45 : No Take, No Impact, No Access. No Take zones “prohibit the extraction or significant destruction of natural and cultural resources,” No Impact zones “prohibit all activities that could harm the site’s resources or disrupt the ecological and cultural services they provide,” and No Access zones “restrict all human access in order to prevent potential ecological disturbance” 45 . Additionally, the sites are filtered to ensure that no site overlaps with military danger zones and restricted military activity areas. No United Nations Educational, Scientific and Cultural Organization (UNESCO) World Heritage Marine Sites (WHMSs) overlap with any of the sites of industry interest 49 . Four sites of industry interest overlap with these restricted zones, thus they are removed from consideration for candidate project locations.

Sites with an ocean depth 60 m or shallower are classified as fixed-bottom offshore wind resources, and sites with an ocean depth deeper than 60 m are classified as floating offshore wind resources 40 . It is important to make this distinction because fixed-bottom and floating offshore wind farms have different cost targets and technical characteristics. In order to give each site an area in which arrays of wind turbines and WECs can be installed, rectangular polygons are drawn around each site of industry interest using QGIS. Figure  10 shows these candidate project areas along the U.S. West Coast. Each polygon is designed such that no site areas overlap, no MPAs of restricted classification or military activity zones are encroached on, and each area falls exclusively in shallow (≤60-m depth) or deep (>60-m depth) water. The polygons are drawn such that their length is parallel to the coastline since waves tend to form parallel to the coastline. Some polygons in Fig.  10 are so small that they may not appear visible, but note that all industry sites of interest are given a corresponding candidate project area. Some sites that are very close to the coast have limited areas that they could encompass because of nearby land in the east direction and deep water in the west direction.

Five U.S. West Coast offshore wind Call Areas 50 , 51 (Coos Bay, Brookings, Humboldt, Morro Bay, and Diablo Canyon) are added to the list of candidate projects, bringing the total number of candidate project areas to 101. Call Areas are potential commercial offshore wind development areas identified by the Bureau of Ocean Energy Management (BOEM) for public comment during the Call for Information and Nomination stage 50 . The offshore wind Call Areas are important to include as candidate project areas for this study so that the potential for offshore wind, wave energy, and collocated offshore wind and wave energy may also be evaluated for these federally identified sites from a grid capacity expansion planning perspective, in addition to the wave energy sites of industry interest. The largest candidate project area (pink polygons in Fig.  10) is designed to be no larger than the largest offshore wind Call Area.

We do not enforce a maximum water depth on the offshore wind and wave energy candidate projects because it is uncertain what water depths will be possible to install marine energy devices in the year 2050 due to technological advancements over the coming decades. Furthermore, the BOEM Offshore Wind Call Areas are between 200 m and 1300 m deep. Less than 5% of the candidate project areas have any portions of their areas beyond the 1300 m depth contour.

Refer to section  1 of the Supplementary Information for more details related to the methodology for candidate project design. There we include the names and coordinates of the sites removed from consideration (Supplementary Table  1) and details regarding what characteristics were considered during the sites of interest filtering process.

Wave energy availability can be measured using the significant wave height ( H s ) and energy period ( T e ) of a wave. These metrics serve as input data for determining how much power a WEC can generate. We use all 699,903 coordinates available along the U.S. West Coast from the U.S. Department of Energy (DOE) Water Power Technology Office’s (WPTO) U.S. Wave dataset 52 . This dataset is the highest spatial resolution publicly available long-term (1979-2010) wave hindcast dataset 52 . It has an unstructured grid spatial resolution that ranges from 200 meters (in shallow water) to 10 kilometers (in deep water) 52 . The 699,903 available data points are generated from the SWAN and WaveWatch III models, which have been validated using publicly available spectral data from buoys 53 .

We overlay these coordinates with the candidate project areas (Fig.  10) in QGIS to identify 89,650 overlapping coordinates. We use 3-hour time resolution time series of wave characteristics for the year 2006 corresponding to every ten (to reduce download time) of the 89,650 coordinates from 52 . A total of 8811 coordinates are downloaded, and each coordinate has a time series that includes timestamps, significant wave height values in meters, energy period values in seconds, and latitude/longitude coordinates associated with the locations for which data is extracted. We linearly interpolate to convert the time resolution of the dataset from 3-hour to 1-hour resolution. Due to the high spatial resolution of the 3-hour dataset, the linearly interpolated data is used to develop the wave characteristic time series used in this study. We assign a time series to each wave energy candidate project by taking the average time series of the WPTO coordinates within each project area.

The capacity factor, C F , is defined as the ratio between the available generating power, P g , and the rated power capacity, P r , as shown in Eq. ( 1 ).

Since the capacity factor of a WEC is subject to the availability of the primary resource (e.g., wave energy), the capacity factor changes according to the wave characteristics at the location where the WEC is installed at a given time.

In this study, we choose the Reference Model 6 (RM6) Oscillating WEC as the representative WEC 54 . Its rated power capacity is 350.5 kW and its power matrix can be downloaded from NREL’s Marine Energy Atlas 55 . The power matrix reveals the available generating power of the WEC as a function of the significant wave height (meters) and the energy period (seconds).

We use the wave height and energy period data from the linearly interpolated 1-hour time resolution time series, the RM6 power matrix, and Eq. ( 1 ) to calculate hourly capacity factors corresponding to the WPTO coordinates. We calculate an average hourly time series for the year 2006 corresponding to each candidate project area by averaging the time series of all of the WPTO coordinates that fall within each area. We do not consider the wake effects of WECs because there is limited information on this topic, and wake effects can vary largely from one WEC design to another.

In order to determine the maximum possible installed wave energy capacity at each site, we assume the packing density of the WECs to be 1.0515 MW/km 2 . To derive this value, we consider the array layout design provided by the RM6 report 54 . We calculate the packing density as follows ( 2 ):

Refer to section  1 of the Supplementary Information to see the details of two error analyses related to the wave energy capacity factor time series used in this study:

To justify taking every 10 of the overlapping points

To verify that linear interpolation from 3-hour to 1-hour resolution for the wave energy capacity factor time series does not introduce substantial error

We choose the 2020 ATB Reference 15 Wind Turbine and its corresponding power curve as the representative wind turbine and power curve for this study 56 . This is the same turbine used by NREL to develop the moderate-cost target for offshore wind in the 2022 ATB 40 . It has a rated power of 15 MW, a height of 150 meters, and a rotor diameter of 240 meters 56 . Similarly to the wave energy data, we extract the coordinates of the NREL Offshore NW Pacific Dataset 57 for 160-meter height, and we overlay the coordinates with the candidate project areas shown in Fig.  10 to determine which coordinates overlap. We download hourly time series data of wind characteristics for all coordinates that lie within the areas. The NREL Offshore NW Pacific Dataset is a 21-year wind resource dataset with a 5-minute time resolution created using the Weather Research and Forecasting numerical weather prediction model 57 .

We design 101 offshore wind candidate projects to occupy the same areas as the wave energy candidate projects to allow the potential for collocation of these technologies. We create an interpolation function using the power curve of the turbine while considering the turbine’s operating limits to determine the power generated by the turbine at any given wind speed in m/s. We assign a time series to each offshore wind candidate project by taking the average time series of the NREL coordinates within each project area. A total of 9207 coordinates lie within the project areas. We separate them based on which project area they fall within and use them to calculate an average time series for each area. We compute the hourly offshore wind energy capacity factors as the ratio between the available generating power and the rated power capacity of the turbine (Eq. ( 1 )).

In order to determine the maximum possible installed offshore wind energy capacity at each site, we assume the packing density of the offshore wind turbines to be 4.3 MW/km 2 . This value is based on the average theoretical capacity density of the Morro Bay Wind Energy Area 58 , which is a current offshore wind leasing area on the U.S. West Coast. There is no standard for offshore wind turbine spacing because packing density can vary based on site-specific conditions or farm designs. Thus, for simplicity, we assume the same packing density for all fixed-bottom and floating turbines. Furthermore, we do not consider wake effects of offshore wind turbines given that this is a variable dependant on specific farm array design that can be minimized by developers through strategic design.

SWITCH model

SWITCH 36 is a linear programming electricity capacity expansion model that finds the least-cost generation portfolio and transmission infrastructure subject to electricity demand and operational constraints. SWITCH is able to model multiple investment periods (periods of one or more years where investment decisions are made), e.g., sets of decades, and multiple time series (chronological sequences of grouped timepoints where operational decisions are made) with different time resolution for each investment period.

The objective function minimized corresponds to the total power system cost, i.e., investment and operational costs of generation and transmission. The decision variables of the optimization problem can be summarized in the following sets: capacity investment decisions for each potential new generation project in each period, capacity investment decisions for each potential new or existing transmission line between any load areas in each period, hourly dispatch decisions for each existing and new generator installed for each period, and decisions on hourly transmitted energy through the existing and new transmission lines.

The main constraints in the optimization problem are: power balance in each zone where power generators, storage technologies, demand and transmission lines are connected, electricity dispatch of the generation technologies limited by their corresponding power capacities, energy flows across the transmission lines limited by their corresponding power capacities, electricity dispatch of renewable energy generators also limited by geolocated hourly capacity factor time series, generation from each hydropower plant limited by historical monthly availability (minimum, average and maximum generation), biomass and geothermal deployment limited by the resource availability, respect yearly maintenance time for each generation technology, policy constraints as carbon cap, carbon tax, Renewable Portfolio Standards, among others. For its detailed mathematical description, refer to section  6 of the Supplementary Information.

Many research groups have further developed different versions of the SWITCH model to analyze decarbonization pathways in different regions 1 , 37 , 38 , 39 , 59 , 60 , 61 , 62 , 63 , 64 . We use the SWITCH WECC 65 model which represents the Western Interconnection by dividing it into 50 geographical zones. The time resolution can vary from hourly to sampled hours that represent typical days during the years being optimized. These modeling virtues of the SWITCH WECC model allow a more realistic study of the expansion and operation of large regional electrical grids with the presence of renewable intermittent resources.

As mentioned previously, investment decisions are made in periods 2020, 2030, 2040, and 2050 which result in a zero-carbon grid by 2050. Our analysis in the Results section focuses on results in 2050. As a reminder, we represent each period as ten-year periods by sampling every month in 2020, 2030, 2040, and 2050, two days per month (median and peak load days) and every four hours per day (12 months × 2 days/month × 6 hour/day = 144 hours). Peak days have a weight of one and median days of n −1 where n is the number of days of that month, and this represents a full month.

The use of a four-hour interval instead of the typical hourly dispatch is part of the reason high geographic resolution could be achieved. Additionally, the reduced complexity from using a four-hour time interval allows us to spend more computational effort on having a high geographical resolution for potential sites and having 2030, 2040, and 2050 investment decisions to better understand the transition. A faster run time from sampling hours also allowed us to create many scenarios to evaluate the relative deployment of offshore wind and wave energy.

We model the transmission system of the Western Interconnection using Ventyx geolocated aggregated transmission line data 66 and the thermal limits from the Federal Energy Regulatory Commission 67 . In total, we consider 105 existing transmission lines connecting load zones of the Western Interconnection. SWITCH can decide to build more transmission lines or expand the capacity of existing ones if it is optimal. The model considers transmission line derating and losses.

The electricity demand profiles come from historical hourly loads from 2006 68 , 69 (and ITRON consulting group). These profiles are projected for future years. The model includes geolocated hourly capacity factor time series for over 7000 potential new locations for solar and land-based wind power, as well as potential new locations for other renewable energy technologies (geothermal and biomass). New power plants for nuclear energy, hydropower, and geothermal energy are also included as candidate projects, as well as battery energy storage and pumped hydro storage. We calculate hourly existing and potential new land-based wind farm power output from the 3TIER Western Wind and Solar Integration Study wind speed dataset 70 , 71 using idealized turbine power output curves on interpolated wind speed values. For existing and potential new solar power plants, we simulate the hourly capacity factors of each project over the course of the year 2006 using the System Advisor Model from NREL 72 . The optimization can then choose from over 7000 potential new geolocated generators in the Western Interconnection. Fuel price projections for each load area are from the U.S. Energy Information Administration 73 . Capital costs and O&M costs are from NREL ATB 2020 74 . The historical pool of exiting power plants in the Western Interconnection is from the U.S. Energy Information Administration (EIA-860, EIA-923, 2020 release 75 ).

Scenarios description

We seek to evaluate the role that offshore wind and wave energy may play in decarbonizing the Western Interconnection by the year 2050. Because the objective function in SWITCH minimizes system cost, we expect deployment of offshore wind and wave energy to vary with cost. Therefore, we design twenty-five scenarios with different offshore wind and wave energy 2050 cost targets. All costs are reported in 2018 U.S. dollars (USD), which is the base year we use in SWITCH WECC. The 2020 wave energy overnight and O&M costs for all scenarios are $ 3465/kW and $ 105.4/kW, respectively. We compute these values by dividing the estimated RM6 WEC overnight and O&M costs for 10-unit deployment by 10 54 . This division by 10 is justified by the economies of scale of the candidate projects designed for this study: the reported costs assume a 10-unit deployment while the designed wave energy candidate projects may have several hundreds of WECs deployed in each site area (based on the packing density assumed and the size of the candidate project areas). The RM6 report 54 demonstrates how lower costs are associated with larger-scale WEC farms. These assumed 2020 wave energy costs align with the lower-end of a range provided by leading wave energy developers as an approximation of the current capital expenditure and operating expenditure costs of wave energy 76 .

As a reminder, there are five different cost targets for wave energy, with the most conservative cost target corresponding to a 50% cost reduction by the year 2050 and the most optimistic cost target corresponding to parity between the 2050 overnight and O&M wave energy costs and the NREL 2022 ATB 40 utility-scale PV energy projected 2050 costs (Fig.  1) . As mentioned previously, we assume a linear projection between the wave energy 2020 and 2050 costs. Although we could use learning coefficients to model the decline in wave energy costs between 2020 and 2050, formulating accurate cost projections (or learning/experience curves) is not within the scope of this work, but it may be considered in future work. Additionally, the study in 77 uses a two-stage Monte Carlo simulation to forecast the levelized cost of electricity (LCOE) for wave energy and finds that the cost reductions are nearly linear. Thus, we assume a linear trend for its simplicity.

Similarly, we design five offshore wind overnight and O&M cost targets based on the NREL 2022 ATB cost projections for fixed and floating offshore wind energy (Fig.  1) . We use Wind Resource Class 3 for fixed-bottom turbines, and Wind Resource Class 12 for fixed-bottom turbines. According to NREL, Class 3 and Class 12 are the most representative of near-term U.S. fixed-bottom and mid-term U.S. floating offshore wind projects, respectively 40 . We design an additional very conservative offshore wind cost target such that $ 488.39/kW is added to the overnight costs and $ 15.90/kW-yr is added to the O&M costs of the NREL 2022 ATB conservative projection for fixed-bottom offshore wind turbines (after converting to 2018 dollars). For floating offshore wind turbines, we add $ 720.55/kW to the overnight costs and $ 14.98/kW-yr to the O&M costs (after converting to 2018 dollars) to generate a very conservative scenario. Similarly, we design an additional very advanced offshore wind cost target such that $ 488.39/kW is subtracted from the overnight costs and $ 15.90/kW-yr is subtracted from the O&M costs of the NREL 2022 ATB advanced fixed offshore wind projection (after converting to 2018 dollars). For floating offshore wind turbines, we subtract $ 720.55/kW from the overnight costs and $ 14.98/kW-yr from the O&M costs of the NREL 2022 ATB advanced floating offshore wind projection (after converting to 2018 dollars). The offsets of $ 488.39/kW, $ 15.90/kW-yr, $ 720.55/kW, and $ 14.98/kW-yr are chosen because they equal the average difference between the NREL 2022 ATB moderate and advanced scenario overnight and O&M costs and the moderate and conservative scenario overnight and O&M costs for fixed and floating offshore wind turbines, respectively.

As mentioned previously, the five wave energy cost targets and five offshore wind cost targets are combined into 25 (5 × 5) scenarios, as shown in Fig.  1 . Refer to Figs.  4 – 5 of the Supplementary Information for alternate visualizations of the cost target scenarios.

All offshore wind and wave energy candidate projects assume an interconnection cost of $ 487,000/MW of capacity installed. This is the average interconnection cost for an offshore wind project with a commercial operation date of 2023 in 2018 dollars from ref.  78 .

Limitations

Since the optimization model chooses to collocate more offshore wind and wave energy projects as their costs decrease, we infer that pairing the technologies could be valuable in a zero-emissions grid due to the shared land-based infrastructure cost savings that are achieved when the technologies are collocated. One limitation of this study is that it does not capture the cost benefits associated with shared underwater transmission infrastructure in collocated offshore wind and wave energy farms. Future work is planned to additionally capture this benefit of collocation in the model, as well as to distinguish connection costs across offshore energy sites according to each site’s bathymetry.

Another limitation is that existing underwater pipelines and cables, existing shipping routes, and archeological sites other than those included in UNESCO’s WHMSs are not considered in the process of filtering sites of industry interest. We also do not consider the proximity of each site to residential areas on land. We believe that the potential impact from not including these parameters when filtering the industry sites of interested is limited but of local relevance. The main difference in the study if these parameters were able to be included would likely be the shapes of the individual candidate project areas (if they are modified to avoid additional ocean zones). Although this may slightly alter the capacity factor time series of certain candidate project areas, we believe it is unlikely that it would substantially change the system-wide trends we observe when integrating various amounts of wave and offshore wind energy into the Western Interconnection. One aspect that could have a larger impact is if more areas are classified as not suitable for economic activity due to ecological considerations. In that case, our study can show how to prioritize deployment if less offshore energy installed capacity can be deployed.

Furthermore, our study does not enforce a maximum water depth on the sites of industry interest, because it is unclear what the limit of water depth for floating offshore wind turbines will be in the year 2050. Although only 5 of the 101 candidate project areas have any portions of their areas beyond 1500 meters of depth, these sites may be challenging to develop due to their extreme bathymetric conditions and significant distances from shore. Hence, the inclusion of these 5 sites without adding a cost multiplier to account for their innate deployment challenges slightly diminishes the realisticness of the model. However, since less than 5% of the sites exhibit very deep water, we believe the impact is minimal.

Lastly, the temporal resolution of our study (2 representative days per month, every 4-hours) may not fully capture the unique power output qualities of offshore wind and/or wave energy in the model. Although the simplified temporal resolution allows us to run a larger set of scenarios with very high spatial resolution, it diminishes the amount of information that the model draws from the capacity factor time series for each marine generator. We believe that a higher temporal resolution would lead to the same trends observed in this study, with slight variations in the numerical results. In our previous study that uses SWITCH to evaluate the impact of using various time sampling resolutions on the utilization of long-duration storage (LDS) 79 , we find that although the utilization of LDS is affected by the time sampling resolution used, the overall installed capacity mix does not vary largely between the different time sampling resolution scenarios. Our near-term future work includes an analysis of the interaction between offshore wind and wave energy and LDS, and we intend to run scenarios with various temporal resolutions, including a scenario with hourly resolution overall 365 days.

Reporting summary

Further information on research design is available in the  Nature Portfolio Reporting Summary linked to this article.

Data availability

The SWITCH 2.0 output data generated in this study has been deposited in the dataset supporting “Offshore Wind and Wave Energy Can Reduce Total Installed Capacity Required in Zero Emissions Grids” Figshare database under ref.  80 . The results data generated in this study are provided in the  Supplementary Information /Source Data file.  Source data are provided with this paper.

Code availability

The SWITCH WECC model (version v2.0.0) is open source and published on GitHub ( https://github.com/REAM-lab/switch ). The source code for the SWITCH 2.0 model used in this study has also been deposited in Zenodo under [ https://doi.org/10.5281/zenodo.11116972 ] 65 .

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Acknowledgements

The authors would like to thank the U.S. Department of Energy for their funding through the Water Power Technologies Office (award number DE-EE0009443) (D.A.S., P.H.G., and D.M.K.). We acknowledge the support of Marcus Lehmann from CalWave for his contributions to the grant proposal writing. We acknowledge the early involvement in the project of Shiny Choudhury for downloading preliminary 14 coordinates with time series to calculate wave energy capacity factors and test preliminary SWITCH WECC toy runs for the 2022 Q1 U.S. Department of Energy quarterly report. We would like to thank Sarah Kurtz for her support and feedback on the newly imported offshore wind and wave energy candidate projects by N.G. and P.S.P. We would also like to thank Matthias Fripp, Josiah Johnston, Rodrigo Henriquez-Auba, Benjamin Maluenda, Ana Mileva and Jimmy Nelson for their prior contributions and developments of the SWITCH model. Special thanks go to Matthias Fripp and Rodrigo Henriquez-Auba for their courtesy of sharing the mathematical formulation Latex files of their  Supplementary Information for us to continue expanding upon. This material is based upon work supported by the U.S. National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-2038238 (N.G.). Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the U.S. National Science Foundation.

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Contributions

N.G. extracted 8811 coordinates with time series from NREL’s WPTO West Coast sites to calculate hourly capacity factors for the 101 sites of industry interest selected by R.D. P.S.T., and N.G. collaborated on data extraction, cleaning, and calculations of hourly capacity factors. P.S.P. extracted coordinates with time series for offshore wind sites (collocated) from NREL Offshore NW Pacific Dataset and calculated hourly capacity factors. N.G. and P.H.G. designed cost scenarios for this study. N.G. and P.H.G. imported new data sets to the database and created new scenarios. N.G. and P.S.T. ran SWITCH WECC under all scenarios, analyzed output data, created figures, tables, and wrote the manuscript with the guidance of P.H.G. R.W. supported N.G. in the creation of figures and tables for the  Supplementary Information . B.M. provided technical support and resources to calculate hourly capacity factors for wave energy sites. SWITCH WECC development: (since 2020) M.S., (since 2020) P.S.P., (since 2020) J.S., and (since 2016) P.H.G. have been developing SWITCH WECC to this stage. P.H.G. and D.A.S. conceptualized the study. P.H.G., D.A.S., and D.A.K. acquired funds. P.H.G. supervised and advised the direction of this study, how to present findings, and edited the manuscript. N.G., P.S.T., B.M., J.S., R.W., D.M.K., D.A.S., and P.H.G. reviewed and edited the manuscript.

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Correspondence to Natalia Gonzalez or Patricia Hidalgo-Gonzalez .

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Competing interests.

Ryan Davidson is an employee at CalWave, a wave energy company, however the WEC we use in our study (RM6 from the National Renewable Energy Laboratory) has no similarities with the private designs at CalWave. Ryan Davidson’s expertize supports the methodology and choice of sites of industry interest for this study. The remaining authors declare no competing interests.

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Gonzalez, N., Serna-Torre, P., Sánchez-Pérez, P.A. et al. Offshore wind and wave energy can reduce total installed capacity required in zero-emissions grids. Nat Commun 15 , 6826 (2024). https://doi.org/10.1038/s41467-024-50040-6

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A modified grey wolf optimizer for wind farm layout optimization problem

• Original Article
• Published: 17 August 2024

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• Shitu Singh 1 &
• Jagdish Chand Bansal   ORCID: orcid.org/0000-0003-3352-6597 1  

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The optimal solution to the wind farm layout optimization problem helps in maximizing the total energy output from the given wind farm. Meta-heuristic algorithms are one of the famous methods for achieving this objective. In this paper, we focus on developing an efficient meta-heuristic based on the grey wolf optimizer for solving the wind farm layout optimization problem. The proposed algorithm is called enhanced chaotic grey wolf optimizer and it is introduced after validating it on a well-known benchmark set of 23 numerical optimization problems. By confirming its efficiency through these benchmarks, it is utilized for wind farm layout optimization. The proposed algorithm is comprised of four search strategies including a modified GWO search mechanism, modified control parameter, chaotic search, and adaptive re-initialization of poor solutions during the search. Two case studies of the wind farm layout optimization problem are considered for numerical experiments. Results are analyzed and compared with other state-of-the-art algorithms. The comparison indicates the efficiency of the proposed algorithm for solving numerical and wind farm layout optimization problems.

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This research work was supported by Institutional funds from the South Asian University, New Delhi.

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Singh, S., Bansal, J.C. A modified grey wolf optimizer for wind farm layout optimization problem. Int J Syst Assur Eng Manag (2024). https://doi.org/10.1007/s13198-024-02462-0

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