text:
June 2019 Issue
Now celebrating 10 years as owner of Bucks Eye Specialists in Yardley, Dr. Sanjay Kamat builds on his commitment to preserving, protecting, and improving patients' vision.
Once we hit adulthood, most of us feel as though the days speed by at a blinding pace. Ten years can pass by almost in a blink. Sanjay Kamat, D.O., knows the feeling. This year, Dr. Kamat is celebrating the 10-year anniversary of owning and operating Bucks Eye Specialists, his Yardley-based ophthalmology practice.
"I can't believe it's been 10 years," says Dr. Kamat. "This milestone has given me an opportunity to look back and contemplate these past 10 years, as well as the path forward. We've worked very hard to establish ourselves here, to help people of all ages see the world around them more clearly, and it's very humbling to see the way that we have been embraced by the community."
At Bucks Eye Specialists, Dr. Kamat treats just about every condition, disease, or disorder associated with the eye: cataracts, glaucoma, and macular degeneration; dry eye; ptosis (drooping of the upper eyelid, which can compromise vision); blepharitis (chronic inflammation of the eyelids); and diabetic retinopathy (damage to retinal blood vessels caused by diabetes).
"If it involves the eye, I've seen it and treated it," says Dr. Kamat, who received his board certification in ophthalmology through the American Osteopathic Colleges of Ophthalmology and Otolaryngology-Head and Neck Surgery (AOCOO-HNS).
Particular areas of specialty include surgery to correct refractive error, such as myopia (nearsightedness), hyperopia (farsightedness), astigmatism, and presbyopia (the inability to see things up close, due to the aging process). He also specializes in "combined procedures," whereby he removes a patient's cataracts while also treating a patient's glaucoma or adding implantable contact lenses, all in one trip to the operating room.
"It's amazing to consider some of the things I can do now," he says. "A decent cataract surgeon will be able to add on ancillary surgery to help people's vision, and that's a real benefit to patient care because you're able to save someone a second trip to the OR."
The 10-year mark in Yardley is of special significance to Dr. Kamat. After all, few people can say they operate a prosperous enterprise that adds value to a community so close to where they came of age.
Dr. Kamat grew up in Bucks County and graduated at the top of his class from Pennsbury High School. He left the Greater Philadelphia Area to attend medical school at Kansas City University of Medicine and Bioscience, and then "came home" for his ophthalmology residency at Philadelphia College of Osteopathic Medicine. He also worked at Albert Einstein Medical Center in Philadelphia, where he gained experience in cataract surgery and oculoplastic trauma.
In 2009, Dr. Kamat took over Bucks Eye Specialists, a practice established by his childhood ophthalmologist, Barry Kutner, M.D. Over the years, Dr. Kamat has taken deliberate steps to grow and fully modernize the practice: converting to electronic medical records; investing in pioneering technology such as Intense Pulsed Light, which is used to treat dry eye; and becoming certified in new, cutting-edge technologies to treat patients with impaired vision.
Dr. Kamat devotes almost 90 percent of his time to direct patient care. In addition, he is a clinical instructor at the Wills Eye Institute in Philadelphia, as well as the ophthalmologist for the Cancer Treatment Centers of America's Northeast Regional Center in Philadelphia. He also devotes his time to being on staff at numerous facilities in the tri-state area, as well as to providing vital care to patients at inner-city clinics.
In other words, Dr. Kamat he has earned his reputation as one of the top ophthalmologists in the Greater Philadelphia Area. In 2017, for example, he was invited to join the medical advisory board of Wills Eye Surgery Center in Warminster. Also, last March the AOCOO-HNS awarded Dr. Kamat with the Governors Achievement Certificate. The AOCOO-HNS Board of Governors bestowed the honor upon him for distinguishing himself through a high degree of accomplishment and meritorious service performed on behalf of the college and its board of examiners.
The honors keep coming. Last month Dr. Kamat crossed the Atlantic Ocean to take a grander, even more visible stage. He served as co-chairman of a two-day event held in Amsterdam, Netherlands, called the 2019 Global Ophthalmology Summit. There, he was the sole American among some of the world's most prominent research scientists, practitioners, and educators, to focus on "exploring the latest advancements in vision science and ophthalmology."
Besides his work as summit co-chairman, he made a formal presentation about one patient who was born with extreme nearsightedness and astigmatism. In it, he offered data about this patient's case, which required "a staged procedure," including the placement of multifocal corrective lenses, to correct the patient's condition.
"I'm honored that they reached out to me and wanted me to be part of the summit," he adds. "I had never been to Amsterdam before this trip, so I was glad to take some extra time to see a part of the world that has so much culture and history."
Overall, from the interactions with fellow practitioners to touring the historic cobblestone streets of Bruges, Belgium, he was "thrilled" with the experience. In fact, hopes to be invited to next year's summit, slated for Rome, Italy.
He considers such trips to be necessary asides, however brief. Even though he and his colleague, Dana Cianni, O.D., were both away at the same time—she was in Iceland with her husband—the practice kept on humming. When a patient came to Bucks Eye Specialists in need of emergency treatment for a retinal issue, Cindy Chhedi, O.D., an optometrist from a sister office in Mount Laurel, N.J., was able to step in and quickly connect the patient with a retina specialist.
"You obviously don't want people to be in need of emergency care, but when they do, you want to be able to help," Dr. Kamat says. "It ended up working out beautifully for the patient; Dr. Chhedi and other members of the team deserve a lot of credit."
Once Dr. Kamat returned home, he jumped right back into the swing of things, treating patients in his Yardley office and in ORs throughout the Greater Philadelphia Area.
"We've been doing very well with premium lenses involving cataract surgery," he says. "In fact, a lot of these people we're treating are coming out of the surgery with 20/20 vision. The technology we're using can change someone's life in significant ways, and that technology is only going to continue to get better and better."
Whether it's adding new products and procedures, new technologies, or new staff, Dr. Kamat is laser focused on providing treatment capable of having a dramatic effect on his patients' eyesight. He'd also like to host an open house, if he can find the time to plan it, in celebration of the 10-year milestone.
"The first 10 years have come with their share of ups and downs, but I have really enjoyed my time here in Yardley," he says. "With everything that's been happening in the past year or so, I feel like we're starting the next 10 years on the right foot."
Bucks Eye Specialists
301 Oxford Valley Road, Suite 801-A
BucksEyeSpecialists.com
Published (and copyrighted) in Suburban Life magazine, June 2019.


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Q: Hiding a row if text box is hidden I have a report that lists parts required for a job, and then within each part it has rows that show locations and quantities of parts on-hand.  The main list has a header (part number, description, quantity) which is only shown once at the top because it is not within the grouping.  However, the second header (on-hand quantity, location) is within the grouping so it repeats.  I would like it to only show once.
I have tried using the hide duplicates property for the header text boxes, but this still leaves blank rows.  I have also tried setting the row visibility using a comparison between ReportItem!lblOnHand.Value and Previous(ReportItem!lblOnHand.Value) but this gives me an aggregate error.
This is what the report is displaying now:

A: You need to set the row visibility rather than the individual text boxes. Right-click the row header to access the setting..

You should (untested) be able to use the same logic as you have now. If this does not work then you will need to test if the group is the first group and use that in the expression, something like...
=Fields!Partnumber.Value <> FIRST(Fields!Partnumber.Value, "myGroupOrDatasetNameHere")

The above would hide thew row if the part number in the current context is not the same as the first part number in the group or dataset name specified.

redpajama_set_name: RedPajamaStackExchange


text:
Quamrul Hassan (, 1921-1988) était un artiste bengali. Hassan est souvent appelé Potua au Bangladesh, un mot habituellement associé aux artistes folkloriques, en raison de son style terre à terre mais très moderne dans la nature car il a toujours ajouté le cubisme à ses œuvres d'art. En plus de son héritage artistique, deux des œuvres d'Hassan font maintenant partie de l'histoire politique du Bangladesh. La première est une restitution monstrueuse de Yahya Khan, le président pakistanais qui a ordonné le génocide au Bangladesh. Le second était juste avant sa mort, se moquant du dictateur bangladais de l'époque, Hossain Mohammad Ershad. Cette esquisse était intitulée « Desh aaj bisshobeheheyar khoppre » (Notre terre est maintenant entre les mains du champion de l'impudeur).

Hassan a enseigné à Rafiqun Nabi.

Références

Liens externes

Naissance en février 1921
Naissance à Calcutta
Décès en mai 1988
Décès à Dacca
Universitaire bangladais
Étudiant de l'université de Calcutta
Dessinateur de drapeau
Peintre bangladais
Décès à 67 ans

redpajama_set_name: RedPajamaWikipedia


Kitchеn cabinets hаve manу purposes. Not only do theу hоld аppliаnces, diѕheѕ, and food, thеу alѕо brіng the essential style to thе kіtсhen. Buying kitсhen cаbinets can bе еxpеnsivе and dіffісult, but understanding thе different cabinet оptiоns on thе market and fіndіng reputable kitchen cabinеt distributors will be able to gеt a beautiful kitchеn without breakіng the bank.
Shakеr, flat panels, and raised panеls. Pocket and swіng dооrs. Eсo-friendly cabinеt options. These are all basiс thіngs that buyеrѕ nееd to know before finalizing on thе kitchen cabinets. Thеѕе tеrms mау sound complicated, but thеу arе nоt as intricаte as buyerѕ may thіnk.
Door ѕtyleѕ іnclude shaker, flat, and inѕеt. Chooѕing thе рerfect kind іѕ impоrtant sіnce it соuld be thе biggеѕt kitchеn exрense. Shаker cabinets are thе most cоmmоn door ѕtylе. It is a fivе piеcе flat panel thаt hаѕ a frаmе made frоm four pіeces and a sіnglе flat сenter panel fоr thе fifth рiece.
Flat panel doors arе simple and stylish and do nоt hаve any expensive details. Theу contain hаrd lines and a minimalist fоrm thаt makes it perfect fоr contemporаry and mоdеrn kitchens. Flat panel cabinets wоrk beѕt in mоdern kitchеns. Hardware needs to match thіs ѕtylе. Clean and simple рullѕ lооk cоntempоrary and wоrk well wіth thiѕ cаbinet ѕtyle.
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The cabinets do nоt havе to bе trаditionаl wood. Getting glass doorѕ arе a great way to open up thе kіtchen to light and spaсe. Glass doorѕ have somе negativeѕ аѕ well. Theу arе easily fingerprinted so requіre morе frеquеnt cleaning. Thе interior cabinets also nееd to bе organized аt all times fоr аesthetic purposes.
Stаndаrd cabinet doorѕ swing, but there arе alѕo flip up doors, corner drawers, and pocket doors, can makе cabinets more functional. Flіp up dооrs use a hydraulic meсhanism to rаise thе cabinet door up instead of oрening them sidewаys. They are grеat for specialty arеaѕ.
Pocket doors are uѕеd to hіde thе heavіly usеd task and prep arеas in thе kitсhen. Corner drawers are a twist on thе cоrner cabinet thаt pulls out from thе сornеr. They arе fully accessible thаt allow the difficult cоrner cabіnet to be opened easily.
Oрen shelving is a grеаt іdea to make a kіtchen morе modern. It іѕ a simple and clean stоrage style thаt wоrkѕ well wіth anу hоme. They еxhіbіt thе feel of a lived-in workаblе space. It mаkeѕ the kitchеn thе heart of the homе no mаtter what ѕtyle thе kitсhеn is.
Adding molding to thе сabinet is an eaѕy waу to make any kind of cаbinet lооk custom. Adding сrown moldіng to an exiѕting kitchen or edge molding to nеw cabinets will help the kitсhen lооk morе elegant and rich. It is a great addіtіоn to do аftеr buying new cabinets fоr thе kіtсhen.
Decorative supports, аprons, and corbels arе great extrа features to аdd to cabinеts. Theу arе nоt standard on moѕt сabinets, but arе a great рroject to аdd on to the kitchen аftеr installation of thе new cabinet. Decorаtive ѕuррortѕ put an аrtful emphaѕiѕ on uррer cabinets. Thе ѕupportѕ wеrе originally designed to hеlp suppоrt cabіnets, but now thеу оnlу ѕеrvе аѕ dеcor.
Related Posts of "Brushed Nickel Kitchen Cabinet Knobs"


Fresh off the heels of Beyoncé's legendary, record-breaking performance at Coachella, one California-based church is getting in formation by honoring the superstar singer and philanthropist with her own designated mass service. Grace Cathedral recently announced that its contemporary worship service, the Vine, will host Beyoncé Mass on Wednesday, April 25, to highlight the "Halo" singer's music, specifically as it relates to Black female spirituality.
The Beyoncé Mass is part of a three-part series to be held at the Nob Hill church called "Speaking Truth: The Power of Story in Community." The series was created with the intention of lifting up the voices of those largely marginalized and oppressed by the Church, particularly women, skeptics and communities of color.
On the surface, including an artist who is, arguably, more famous for her secular music than she is from her humble beginnings singing in the choir in Houston, seems odd for Grace Cathedral. However, upon delving deeper into the artistry of the 36-year-old musical icon, the deliberate imagery of spiritual deities sprinkled in her televised performances and interspersing of religious odes at her concerts have always been present throughout the course of Beyoncé's 20-year career.
There was her awe-inspiring Grammy performance in 2017, where she embodied African goddess Oshun, as well as her recent rendition of the African-American hymnal, "Lift Every Voice and Sing" at #Beychella. Not to mention, her pregnancy photos and the captivating portrait of her newborn twins posted on Instagram in July 2017 drew comparisons to the Black Madonna and challenged the traditional acceptance of the white Virgin Mary.
The Beyoncé Mass is just one of many programs and services Grace Cathedral has implemented to elevate the conversation surrounding Black women, immigrants and the LGBTQ community.
"I am committed to leading a community that is not afraid to engage hard conversations about what it means to walk with God in a world still beset by structural injustice," Reverend Harmon tells ESSENCE.


Matteo Renzi. Flickr/Palazzo Chigi. Some rights reserved.
Whatever the result of the January 25 elections the surge in support for Syriza will force open divisions within Italy's social democratic government. The country's premier Matteo Renzi has been frequently compared to Tsipras – as another young and nominally 'left' leader – but key differences, particularly regarding state investment and job creation, will now take centre-stage. In reality the two have been in conflict for some time, with the former accusing the Greek party of "living in the past" and the latter of dealing in "Merkel's medicine".
This is no mere bickering but a significant battle in the fate of a left that has failed to distinguish itself from the neoliberal consensus. If Syriza do win next week, Renzi will be placed under pressure from all sides. Many members of the Partito Democratico have been dissatisfied with his leadership (particularly the controversial Jobs Act) and some have given explicit support to Tsipras's program.
Added to this, the electoral list L'altra Europa con Tsipras, which won Syriza an Italian seat in last year's European elections, demonstrated that much of the PD's base – and especially young supporters – are critical of Renzi's relationship with the Troika.
This puts the Italian Premier in an impossible position. If Renzi supports Syriza in Europe he will anger the EU elite and supposedly jeopardise the neoliberal recovery plan. If, however, he explicitly criticizes them, his own party is likely to fracture and the plan will be compromised at a domestic level.
Most likely he will attempt to avoid the issue altogether, as he has to this point. If Syriza win enough votes to govern with confidence, however, this will not be an option.
There is another factor in the Greco-Italian relationship that makes these questions particularly important. The Italian economy is one of the largest and most fragile in Europe (a combination which led Mario Monti to label it in 2012 as 'the detonator of the Eurozone'). In the recent ECB stress test nine of the country's banks failed.
The message is clear. Despite claims to the contrary by Italian Economy Minister Pier Carlo Padoan, any major instability, such as that which would apparently arise in the case of a major Syriza victory, would trigger a chain reaction among these very banks.
This is a doomsday scenario, say some, but the threat of contagion will determine how the Italian dialogue plays out in the next months. It is unlikely to work in Tsipras's favour.


Remote Teams rely on Gmelius to bring their teams closer. Communication and collaboration is top priority when distance separates your team.
With email assignment, you get the opportunity to delegate an email to your assistant without forwarding it.


AXIS FA3105-L is a compact eyeball sensor unit with built in IR illumination (15 m / 49 ft range of reach) for use with AXIS FA Main Unit. It has 103º horizontal field of view and 1080p HDTV resolution with Forensic WDR (wide dynamic range) that is optimized for low light and motion. The unit comes with a mounting bracket and an 8 m (26 ft.) cable for connection to the main unit.


text:
History of WMF
2019 Renewal Form
Affiliated Membership
World Missions Reports
Missions Gallery
Convo 2019
Executive Blog
Brian & Pam Sharp
Brian and Pam Sharp met at and are graduates of Oral Roberts University, Tulsa, Oklahoma. Brian later went on to get his M.Div. degree from Perkins School of Theology SMU, Dallas. They have been in ministry for 35 years, first as youth ministers then as pastors. They are the founding pastors of Grace Christian Fellowship in Poplar Bluff, Missouri, the church they now pastor, and are in their 21st year there. They love missions having been to Mexico, Ecuador, Brazil, Zimbabwe, and the Democratic Republic of the Congo. They have been members of WMF since 1993. Brian and Pam are currently serving as President and Ladies President respectively.
Don & Sheila Kimball
Prior to Don serving on the Executive Board, he served 15 years on the Central Ordination Council. In addition Don as continually served as Stat Director for CT, RI, and ME since 1998 to the present. Sheila served 14 years on the ACT's Board (Anointed Children & Teens) and is currently serving on the Ladies Executive Board and Intercessory Prayer Coordinator for WMF. Don & Sheila also served as Host and Hostess of Convocation for over 10 years. They have established a ministry called "Let the Church Rise" and feel called to minister to ministers individually and corporately and to minister to congregations in the Word, song and in prayer. Sheila also continues to serve as the CT State Coordinator for the National Day of Prayer since 2009. Don & Sheila are serving as First Vice-Presidents.
Phil & Jan Ellsworth
Phil and Jan Ellsworth have been a part of WMF since 1981. In 1980, they pioneered Grace Christian Fellowship Church in Shawnee, KS and Phil still serves there as Senior Pastor. High school sweethearts, they have been married over 35 years, have three wonderful children, and often teach together on Effective Biblical Parenting. Phil has served WMF as the Kansas State Director and on the Advisory Board. He has a degree in Business Mgmt., is a graduate of RHEMA Bible Training Center and holds a Master's Degree from Liberty University. Jan has taught numerous women's groups and, in the Christian School they opened in 2001. Phil and Jan are currently serving as Vice Presidents.
Darrell & Tiffany Sutton
Darrell Sutton and his wife Tiffany oversee multiple fellowships in the Heartland, but reside in Red Cloud, Nebraska where they pastor Revival Tabernacle in the Great Plains. The two of them travel throughout the United States holding revivals and ministering together at various camp meetings: with Tiffany supplying ministry through song. Deeply involved in urban, rural and foreign missions, they labor to support the greater body of Christ, thereby increasing the Church's fruitfulness and effectiveness. Darrell also is the host of Bible Prophecy Unraveled on the LeSea Broadcasting Network. They have been members of World Ministry Fellowship since 2001. Darrell is now the International Missions Director for World Ministry Fellowship and is also serving as Secretary of the Executive Board.
Jim & Lisa McCool
H.J. "Jim" McCool Jr. received Jesus as his Savior at the age of 16 and was filled with the Holy Spirit at the age of 19. He soon sensed a calling into ministry which led him to enroll in Southwestern Assemblies of God University in 1977. He met his future wife, Lisa, that same year and in 1978 they were married. Jim and Lisa have four daughters and four grandchildren.
Jim completed his BS degree in missions in 1980. Jim and Lisa, served as Youth Pastor of two churches and then Senior Pastor of two churches before becoming resident missionaries in Africa. They lived and served in Kinshasa, Democratic Republic of Congo and in Durban, Republic of South Africa during the years of 1986-1991. They returned to the US and began pastoring Lighthouse Christian Center in Perry, Oklahoma from 1992 until 2001. Jim completed his Master of Divinity at Oral Roberts University in 1998. From 2003 to 2016, Jim served as a Hospice Chaplain in Oklahoma City.
Lisa completed her BSN in 2000 at Oklahoma City University and her MSN in Nursing Education at Oklahoma Baptist University in 2013. She has served as a Nurse at several hospitals around Oklahoma including the Veterans Administration Medical Center in Oklahoma City. For the last three years she has served as a Nursing Instructor at Springlake Metro Tech in Oklahoma City.
Jim was ordained with World Ministry Fellowship in 1986 and has served on the Advisory Board, the COC and the International Mission's Board. He is currently Pastor of New Beginning Fellowship Church in Oklahoma City. Jim is president of McCool Ministries, Inc. and continues to take mission trips to the Congo, Liberia and Uganda.
Fiifi & Sybil Pentsil
Fiifi and Sybil Pentsil have been members of World Ministry Fellowship since 1999. They have been in ministry for over 20 years and currently serve as founding pastors of House of Worship in the beautiful state of Maryland. Before joining the Executive Board, Fiifi served on the WMF Ordination Council. He travels extensively, teaching in both ministry and secular settings. Sybil is a practicing pediatrician who also teaches internationally. They live in Owings Mills, MD with their three sons.
Bob & Sue Long
Bob Long graduated from Texas A & M University in 1966 as a 2nd Lieutenant in the US Army Artillery and today serves as a Chaplain of his county's Honor Guard which honors veterans by conducting military services at the graveside.
Bob left the military for ministry in 1972 having been licensed with WMF in 1971. At the request of the founder of WMF, Bill Brown, Bob organized the Advisory Board and has served as Chairman of the Ordination Council. He has served on the Executive Board for many years and has completed two terms as President.
Bob is a pastor in his community of Bastrop, Texas. He is looked to as the elder Pastor of the city by other Pastors, most of whom he meets with weekly for prayer and fellowship.
Bob and Sue are involved in the family ranching and banking business. He and Sue have been married 54 years. They have 3 grown children, 9 grand children and 2 great grand children.
© 2014-2018 World Ministry Fellowship Contact Us

redpajama_set_name: RedPajamaCommonCrawl


text:
John Cena is being paid millions of dollars to sell garbage bags
Be gone, wimpy garbage bags.
By Nicole Gallucci on June 2, 2016
WWE superstar John Cena makes a special appearance at WrestleMania 32 at AT&T Stadium on Sunday, April 3, 2016, in Arlington, Texas. Credit: mashable composite: Brandon Wade/AP Images for WWE and pepifoto/Getty Images
John Cena wants to inspire all of us to take out the trash.
According to UPROXX, the latest edition of the Wrestling Observer Newsletter has announced that the wrestler signed a hefty "multi-million dollar" deal to become the new spokesperson for...Hefty.
Yes, Hefty as in the trash bags.
SEE ALSO: Little girl delivers birthday cupcake to her 'favorite, awesome, smiley garbage man'
For this multi-million dollar trash bag deal, Cena will reportedly be starring in a several commercials to promote Hefty's "Ultra Strong" garbage bags. Ultra strong garbage bags? Ultra strong wrestler? We see what you did there, Hefty.
This will not be Cena's first product endorsement. Aside from being a pro-wrestler and actor, Cena is also known for partnering with Gillette and creating some true cinematic masterpieces.
Here are two of his old school commercials to get you psyched for what's to come:
Can't wait to take out the trash like a champ.
How HBO Max's 'Station Eleven' is different from the book
Now that the whole season is out, how does "Station Eleven" compare to its source material?
By Belen Edwards


New date for Regatta confirmed!!
The Annual Woodbridge Regatta has been moved to a new date from the original one proposed. From 2nd July to 16th July. As this is a River Deben based event they needed to make sure there was water for the sailing, rowing and raft races which make up such an important part of this historic event.


text:
\section{Introduction}\label{sec.intro}
\IEEEPARstart{U}{nder} the dual pressure of the gradual exhaustion of non-renewable energy and the increasingly prominent ecological and environmental problems, how to achieve a clean and sustainable energy supply has become a critical issue that needs to be addressed \cite{li2018two}. As a promising solution, wind power has been penetrating the power system in recent years. Accurate forecasting methods can mitigate the impact of the randomness and volatility of wind power generation on the operation and dispatch of the power system, and accelerate the large-scale grid connection of wind farms\cite{arora2022probabilistic}\cite{buhan2015multistage}. Protecting the data security and privacy is becoming one of the most important challenges to enable efficient data openness and sharing among stakeholders in modern energy systems. With the continuous improvement of privacy protection awareness, it is also crucial to find solutions to protect users' data privacy while ensuring the performance of the forecasting model \cite{zeadally2013towards}.
\subsection{Literature Review}
Wind power forecasting methods can be summarized as physical and statistical prediction methods according to their modeling approaches. The main idea of the physical prediction method is to convert the data output by the numerical weather prediction (NWP) system to the wind turbine data, and then make the wind power prediction based on the predicted wind speed and the power curve of the wind turbine\cite{sweeney2020future}. This method has relatively a low prediction accuracy and is generally applied to newly established wind farms that lack of massive historical data. Statistical forecasting methods are mainly based on a large amount of historical data and using different statistical models for wind power forecasting, including time series analysis and machine learning algorithms. 1) Time series analysis methods: Ref. \cite{rajagopalan2009wind} uses autoregressive and moving average (ARMA) models for wind power prediction; to improve the prediction accuracy, \cite{liu2021short} proposes a new seasonal autoregressive integrated moving average (ARIMA) for short-term wind speed forecasting; Ref. \cite{cassola2012wind} uses the famous kalman filtering (KF) to predict wind speed and wind power. However, traditional time series prediction methods have very rigorous requirements on parameters model, and the choice of parameters model can directly determine the model performance. 2) Machine learning algorithms: In \cite{hu2015short}, a new framework called heteroscedastic support vector regression is designed for wind speed prediction, and a brand new method for wind speed prediction combines improved empirical mode decomposition (EMD) and generic algorithm-back propagation (GA-BP) neural network are proposed in \cite{wang2016wind}. With the rise of deep learning, more sophisticated neural networks are applied to predict wind speed and wind power. Ref. \cite{khodayar2017rough} designs a deep neural network (DNN) architecture with stacked autoencoder and stacked denoising autoencoder for wind speed forecasting; \cite{wang2018deep} adopts k-means clustering algorithm to process NWP data and then uses deep belief network for short-term wind power prediction. The traditional supervised learning prediction model has a good prediction performance but requires high-quality data for training. In recent years, deep reinforcement learning, which combines perception and decision-making capabilities, has been applied for prediction problems to achieve a good performance. In  \cite{zhang2021novel}, a novel forecasting method based on deep deterministic policy gradient (DDPG) is designed for load forecasting, and a hybrid ensemble deep reinforcement learning model is proposed in \cite{liu2020new} for short-term wind speed forecasting. The basis for machine learning methods to obtain accurate prediction results is the massive amount of training data, which is very difficult for some newly built wind farms. At present, major methods generally use centralized training technology, which requires a central organization to collect data. However, due to some commercial factors, wind farms belonging to different stakeholders are not willing to share private data with others \cite{li2018optimal567}, so the central organization has to consider the issue of privacy protection when collecting and storing data.

\begin{table}[t]
  \centering
    \begin{tabular}{|ll|}
    \hline
          &  \\
    \textbf{Nomenclature} &  \\
          &  \\
    \textbf{Acronyms} &  \\
    DRL   & Deep Reinforcement Learning \\
    FedDRL & Federated Deep Reinforcement Learning \\
    DDPG  & Deep Deterministic Policy Gradient  \\
    NWP   & Numerical Weather Prediction \\
    ARMA  & Autoregressive and Moving Average \\
    ARIMA & Autoregressive Integrated Moving Average \\
    KF    & Kalman Filtering \\
    EMD   & Empirical Mode Decomposition  \\
    GA-BP & Generic Algorithm-Back Propagation \\
    DNN  & Deep Neural Network  \\
    ADMM  & Alternate Direction Method of Multipliers \\
    MLR   & Mixed Logistic Regression \\
    BPNN  & Back Propagation Neural Network \\
    RDPG  & Recurrent Deterministic Policy Gradient \\
    NMAE  & Normalized Mean Absolute Error \\
    NRMSE & Normalized Root Mean Square Error \\
    NREL  & National Renewable Energy Laboratory \\
          &  \\
    \textbf{Symbols} &  \\
    \textit{s} & State \\
    \textit{a} & Action \\
    \multicolumn{1}{|p{6.875em}}{\textit{r}} & Reward \\
    $\pi$ & Policy \\
    \multicolumn{1}{|p{6.875em}}{$\gamma$} & Discount factor \\
    $\theta ^{\mu}$ & Parameters of Main Actor network \\
    $\theta ^ Q$ & Parameters of Main Critic network \\
    $\theta ^{\mu '}$ & Parameters of Target Actor network \\
    $\theta ^ {Q'}$ & Parameters of Target Critic network \\
    $\varsigma$ & Soft update factor \\
    $N$ & Total number of clients \\
    $n$ & client number\\
    $\psi_C$ & Performance metrics of the centralized model \\
    $\psi_F$ & Performance metrics of the federated model \\
    $T$ & Size of minibatch\\
    $P^w$  & Wind power \\
    \textit{j} & Number of selected time periods \\
    \textit{V} & Total number of samples \\
    \textit{y} & Actual value \\
    \textit{p} & Prediction result \\
    $y^n$  & Normalized actual value \\
    $p^n$ & Normalized prediction result \\
    \textit{M} & Local episode  \\
    \textit{W} & Global epoch \\
    \textit{K} & Synchronization interval \\
    \textit{E} & Client ratio \\
    \textit{S} & Central server \\
    $L_C$ & Network load of the centralized forecasting method \\
    $L_F$ & Network load of FedDRL \\
    \textit{D} & Size of the private data \\
    \textit{I} & Size of the model information \\
    \textit{h} & Hops between each client and the central server \\
    \textit{U } & Networking load gain \\
    $p$ & Number of lag observations \\
    $d$ & Degree of differencing \\
    $q$ & Size of the moving average window\\
    \hline
    \end{tabular}%
  \label{tab:addlabel}%
\end{table}%

In recent years, many countries have promulgated relevant laws and regulations on data privacy protection to supervise the storage and application of data, and some researches using distributed structures have discussed the issue of data privacy protection \cite{voigt2017eu}. In \cite{zhang2018distributed}, a privacy protection method is proposed for wind power probabilistic forecasting which adopts the alternate direction method of multipliers (ADMM) structure. However, the central node in this method can recover the private data which may cause a confidentiality breach, resulting in the leakage of data privacy. To reduce the occurrence of this kind of privacy leakage issue, some research add random noise to the original data or coefficients when using the ADMM structure for renewable energy prediction \cite{dwork2010differential}, \cite{zhang2016dynamic}. but this method may cause a decrease in the prediction performance \cite{gonccalves2021critical}. With the continuous increase of wind farms around the world, accurate wind power prediction is more important for the stable operation and scheduling of the power system \cite{li2022deep} \cite{li2021optimal678}, which requires a large amount of historical data as support, and these data contain a lot of user privacy. In this context, it makes sense to explore a method that can both guarantee prediction accuracy and data privacy protection.

Existing research contributes magnificently to the wind power forecasting problem, however, there are still the following research gaps to be solved:
\begin{enumerate}
    \item Prediction accuracy is extremely important to the problem of wind power prediction. Discovering a method to upgrade the performance of the forecasting model is necessary. Most of the current research uses centralized forecasting methods, which may lead to some data security and privacy protection issues.
    \item Massive high-quality historical data is an essential condition for obtaining a forecasting model with good performance. However, due to some commercial factors, wind farms with different stakeholders are reluctant to share their private data. How to solve the data island problem, that is, to break the phenomenon that the data of different wind farms are stored independently and isolated from each other, which is not considered in most existing research.
    \item For wind power forecasting, the centralized prediction methods require a central organization with powerful computing ability and large storage capacity, and the data is prone to leakage when it is collected and stored.
\end{enumerate}

\subsection{Contribution of This Paper}
To fill the above-mentioned gaps, a federated deep reinforcement learning (FedDRL) for ultra-short-term wind power forecasting is proposed in this paper. The main contributions of this paper are the following threefold:
\begin{enumerate}
    \item This paper uses the deep deterministic policy gradient (DDPG) algorithm in deep reinforcement learning (DRL) as the basic prediction model for ultra-short-term wind power forecasting which can improve the forecasting accuracy compared with the traditional forecasting methods. In addition, we combine automatic machine learning with DRL for hyperparameters selection to simplify the deployment of the forecasting model.
    \item To handle the data privacy and openness, we propose a FedDRL forecasting scheme that combines federated learning and DRL for ultra-short-term wind power forecasting of multiple wind farms. To the best of our knowledge, this paper is the first study to use federated learning for wind power forecasting. The proposed forecasting scheme can not only solve the problem of data islands but also has the advantage of privacy-preserving and reducing communication pressure under the premise of ensuring high-quality forecasting performance compared with the most used centralized forecasting methods.
    \item We use real-world historical data for simulations to verify the effectiveness of the proposed FedDRL scheme and prove that the scheme has superior forecasting performance than traditional prediction methods and the communication pressure is significantly mitigated. In addition, we also design experiments with different parameter settings to confirm the robustness of the proposed scheme.
\end{enumerate}

\subsection{Organization of This Paper} The organization of the paper is as follows: Section \ref{sec.DDPG&FED} contains the basic principles of DDPG and federated learning. Section \ref{sec.PROPOSED METHODOLOGY} introduces the methodology of the proposed FedDRL, including the transformation of the prediction problem, the structure of FedDRL, and the steps of using the proposed FedDRL for wind power prediction. Section \ref{sec.CASE STUDY} will show the results of case studies in detail and give specific conclusions and future works in the Section \ref{sec.conclusion}.

\section{RELATED PRELIMINARY WORKS}\label{sec.DDPG&FED}
This section introduces the basic theoretical knowledge related to the proposed FedDRL scheme, including a detailed description of the DDPG algorithm and the federated learning framework.
\subsection{Deep Deterministic Policy Gradient}
DRL is a branch of machine learning, which combines deep learning and reinforcement learning. As an algorithm of deep reinforcement learning, DDPG has an efficient and stable ability in solving continuous action space problems \cite{mnih2015human}.

DDPG is an algorithm based on the Actor-Critic framework which has four neural networks. Both the Actor and Critic contain a main network and a target network. The role of the target network is to stabilize the training of the algorithm.

The Actor part makes the decision of action $a$ based on the current state $s$, and after interacting with the environment, it obtains the feedback of the next state $s'$ and the reward $r$. The purpose of the Actor part is to obtain the policy with the highest total reward under a certain goal by continuously communicating with the environment, which is expressed as
\begin{equation}\label{eq.object function}
    \begin{aligned}
       J({\theta ^\mu }) = {E_{{\theta ^\mu }}}[{r_1} + \gamma {r_2} + {\gamma ^2}{r_3} + ... + {\gamma ^{i - 1}}{r_i}]
    \end{aligned}
\end{equation}
where $\gamma$ is the discount factor, $\theta^\mu$ is the parameters of the main actor network $a=\pi(s|\theta^\mu)$.

The main actor network is updated by the stochastic gradient method, and the gradient information can be approximated as follows during the update process \cite{silver2014deterministic}.
\begin{equation}\label{eq.update main actor network}
    \begin{aligned}
       \nabla _{{\theta ^\mu }}J \approx \frac{1}{T}\sum\limits_i {[\nabla {}_aQ(s,a|{\theta ^Q}){|_{s = {s_i},a = \pi ({s_i})}}\nabla {}_{{\theta ^\mu }}\pi (s|{\theta ^\mu })|_{s = {s_i}}]}
    \end{aligned}
\end{equation}
where $T$ is the size of the minibatch, $\theta^Q$ is the parameters of the main critic network $Q(s,a|\theta^Q)$.

After the Actor part makes a decision, the Critic part evaluates it and updates the main critic network with the goal of minimizing the loss function, the loss function is
\begin{equation}\label{eq.loss c}
    L({\theta ^Q}) = {E_{s,a,r,s' \sim D}}\left[ {{{\left( {TargetQ - Q(s,a|{\theta ^Q})} \right)}^2}} \right]
\end{equation}
\begin{equation}
    TargetQ = r + \gamma Q'(s',\pi (s'|{\theta ^{\mu '}})|{\theta ^{Q'}})
\end{equation}
where $Q'$ denotes the target Q-value function; $\theta ^{\mu '}$
is the target actor network parameters and $\theta ^{Q'}$ is the target critic network parameters. The gradient information is updated by
\begin{small}
\begin{equation}\label{eq.update the main critic network}
    \begin{aligned}
     \nabla _{{\theta ^Q}}L = {E_{s,a,r,s'\sim D}}\left[ {\left( {TargetQ - Q(s,a|{\theta ^Q})} \right){\nabla _{{\theta ^Q}}}Q(s,a|{\theta ^Q})} \right]
    \end{aligned}
\end{equation}
\end{small}

For the target networks, DDPG uses a soft method to update its parameters.
\begin{equation}\label{eq.update target networks}
    \begin{aligned}
     \begin{array}{l}
{\theta ^{Q'}} \leftarrow \varsigma {\theta ^Q} + (1 - \varsigma ){\theta ^{Q'}}\\
{\theta ^{\mu '}} \leftarrow \varsigma {\theta ^\mu } + (1 - \varsigma ){\theta ^{\mu '}}
\end{array}
    \end{aligned}
\end{equation}
where $\varsigma$ is the soft update factor.

To overcome the problems of correlated data and non-stationary distribution of empirical data, DDPG introduces Experience Replay to store the information obtained by each Actor in a buffer, which improves the utilization of data and enhances the training effect.

\subsection{Federated Learning}

Federated learning, as a machine learning framework, is first proposed by the Google R$\&$D team and applied to the keyboard prediction model for mobile phones. Compared with traditional centralized training methods\cite{li2020federated}, federated learning can not only solve the problem of data islands but also has the advantages of protecting data privacy and alleviating communication pressure. At present, it has been combined with different fields and achieved satisfactory results, such as cyber-attack detection\cite{wu2020fedhome}, traffic flow prediction\cite{liu2020privacy}, spatiotemporal scenario generation of renewable energy\cite{li2022privacy}.

Federated learning is mainly composed of a federated server and multiple clients. Unlike the traditional centralized method that requires the data of each client to be gathered in a centralized workstation, most of the training process in federated learning is done locally on each client's edge device. Therefore, the raw data is not shared between each other, it has a good privacy protection ability. Federated learning can solve the problems of data islands and privacy protection by sharing parameters, and its working principle is as follows: Firstly, an initial global model is allocated to each client by the federated server, and each client uses its private data to train the model locally. Secondly, when the local training is completed, the client uploads the weight parameters of each local model to the federated server, and then the parameters of the global model will be updated according to the collected parameters of each client. Finally, the federated server passes the updated global model parameters to each client again. Repeat the above process until the pre-set criteria are satisfied. The overall structure of federated learning is shown in Fig. \ref{fig.FL}.

\begin{figure}[t]
	\centering
	\includegraphics[width=3.5in]{Figures/fedrated_learning.pdf}
	\caption{{The basic structure of federated learning.}}
	\label{fig.FL}
\end{figure}

The basic requirement of using the federated learning framework is to ensure the model's performance. Compared with the centralized training methods, the performance of the federated learning method needs to meet the following requirements.
\begin{equation}\label{eq.performance}
    \left| {{\psi _C} - {\psi _F}} \right| \textless \sigma
\end{equation}
where $\psi_C$ is the evaluation criteria  of the centralized model, $\psi _F$ is the evaluation criteria of the federated model, and $\sigma$ is a small non-negative number. It can be seen form (\ref{eq.performance}) that the performance of the model that uses the federated learning framework for distributed training is very similar to that of the model that aggregates all data for centralized training\cite{yang2019federated}.

\section{PROPOSED METHODOLOGY}\label{sec.PROPOSED METHODOLOGY}
The method of using DRL to solve the prediction problem is first explained in this section, and then the specific operation process of the proposed FedDRL is described in detail.
\subsection{Problem Formulation}
The highly fluctuating of wind power significantly affects the accuracy of wind power forecasting. To improve the forecasting accuracy and enhance the robustness of the forecasting model, we use the DDPG algorithm in DRL as the basic model for wind power forecasting in this work.

To use DDPG for wind power prediction, this paper converts the prediction problem into a decision-making problem. We select the wind power for several consecutive time periods to construct a vector as follows, which is used as state, $s_t$.
\begin{equation}
    s_t = [P^w_{t-(j-1)}, P^w_{t-(j-2)}, P^w_{t-(j-3)}, P^w_{t-(j-4)}, ..., P^w_{j-1}, P^w_t]
\end{equation}
where $P^w$ is wind power, $j$ is the number of selected time periods. The agent makes a decision based on $s_t$, and outputs the predicted value of wind power as action, $a_t$, after which the agent will obtain the next state $s_{t+1}$ and reward $r$. For the wind power forecasting problem, the reward $r$ of the proposed FedDRL is defined as an error zone, not just the error between the model output and the label in traditional supervised learning. Therefore, the sensitivity of the prediction model to noise data can be reduced, and the robustness of the prediction model can be improved \cite{kuremoto2019training}. The reward function set in this work is as follows.
\begin{equation}\label{eq.reward function}
    r =  - \left| {{a_r} - {a_t}} \right|
\end{equation}
where $a_r$ is the true value of wind power. In the Actor part, the loss function is constructed to minimize the prediction errors. In the Critic part, the goal of the loss function is to continuously shrink the difference between the actual and the predicted reward.

After the above-mentioned method is used to transform the prediction problem into a decision-making problem, DDPG can be reasonably used as the wind power forecasting model in this work. The actor outputs the predicted value according to the observation, which is evaluated by the critic, and the neural networks are updated according to the temporal-difference error (TD-error), finally, a prediction model with good performance is obtained. The specific steps of using DDPG for wind power forecasting are as follows.

\emph{\textbf{Step 1:}} Construct a vector consisting of wind power for several consecutive time periods as the state.

\emph{\textbf{Step 2:}} Predict a wind power value as an action based on the current state.

\emph{\textbf{Step 3:}} Calculate the difference between the predicted value and the real value, and take the negative number of its absolute value as a reward; then get the next state.

\emph{\textbf{Step 4:}} Update the actor and critic neural network, and a model with good prediction performance can be obtained through continuous training.

\subsection{FedDRL Framework}
Traditional centralized prediction methods may have data leakage problems in the process of data collection and storage, which involves sensitive privacy issues. The emergence of federated learning undoubtedly provides an effective solution to the above problems.

We propose a FedDRL prediction scheme, which adopts federated learning as the overall framework, the federated server and each client hold a DDPG prediction model as the global model and the local model, respectively. The FedDRL forecasting scheme is mainly controlled by two parameters, the customer's participation ratio $E$ and synchronization interval $K$. We assume that each wind farm has the ability to independently train a global model. Considering that the computing power of each wind farm may be weak, the customer's local training only takes a small number of iterations. The framework of the proposed FedDRL is shown in Fig. \ref{fig.FedDRL}.

\begin{figure}[t]
	\centering
	\includegraphics[width=3.6in]{Figures/framework.pdf}
	\caption{{FedDRL framework.}}
	\label{fig.FedDRL}
\end{figure}

Since tuning the hyperparameters of the model is a very time-consuming and labor-intensive task, to simplify the deployment of FedDRL, we adopt an automatic machine learning method based on Bayesian optimization called metis to automatically select the hyperparameters of the global model \cite{li2018metis}. We set the actor and critic as a fixed-depth neural network, and let the metis tuner confirm the hyperparameters, such as hidden neurons and learning rate of the actor and critic network.

The federated averaging algorithm is the core mechanism for FedDRL to achieve user privacy protection and reduce communication pressure. The main idea of the federated averaging algorithm is to aggregate the model parameters trained locally by the participating clients in each round to the federated server, and then perform the averaging operation on them \cite{mcmahan2017communication}. In FedDRL, we collect the client parameters in each training round which is mainly about the trained parameters of the actor and critic networks in the local model and average them to update the global model. The process is expressed as

 \begin{equation}\label{eq.fedavg}
           \begin{array}{l}
\theta _S^Q \leftarrow \frac{1}{{{N_e}}}\sum\limits_{e = 1}^{{N_e}} {\theta _e^Q} ,{\rm{ }}\theta _S^\mu  \leftarrow \frac{1}{{{N_e}}}\sum\limits_{e = 1}^{{N_e}} {\theta _e^\mu } ,\\
\theta _S^{Q'} \leftarrow \frac{1}{{{N_e}}}\sum\limits_{e = 1}^{{N_e}} {\theta _e^{Q'},{\rm{ }}\theta _S^{\mu '} \leftarrow \frac{1}{{{N_e}}}\sum\limits_{e = 1}^{{N_e}} {\theta _e^{\mu '}} }
\end{array}
        \end{equation}
where $N$ is the total number of clients, $e$ is the client number participating in the training epoch; $\theta _S^\mu$ and $\theta _S^Q$ are the main actor and critic network parameters of the global model, $\theta _S^{\mu '}$ and $\theta _S^{Q'}$ are the target actor and critic network parameters of the global model; $\theta _e^\mu$ and $\theta _e^Q$ are the main actor and critic network parameters of each local model, $\theta _e^{\mu '}$ and $\theta _e^{Q'}$ are the target actor and critic network parameters of each local model. After the global model is updated, the parameters will be returned to clients to update the local model.

\subsection{FedDRL-based Wind Power Forecasting}
We propose a prediction scheme that combines federated learning and DRL. On the basis of ensuring the performance of the prediction model, the proposed FedDRL can not only solve the problem of data islands among wind farms but also protect clients' data privacy. The specific process of FedDRL mainly includes the following four steps.

\emph{\textbf{Step 1:}} Initial model allocation. The local model in each wind farm and the global model are all initialized. The federated server obtains a global model based on public data with hyperparameters automatically selected by the metis tuner, and then pass the global model to participating wind farms.

\emph{\textbf{Step 2:}} Local model training and parameters upload. Each wind farm updates the local model according to the received global model and then uses their private data to train the model locally. After the training is completed, each wind farm uploads the trained weight information of the actor and critic network to the federated server.

\emph{\textbf{Step 3:}} Global model update. The federated server gathers the weight information uploaded by each wind farm and uses the FederatedAveraging algorithm to update the global model. The updated global model is re-distributed to each client.

\emph{\textbf{Step 4:}} Wind power forecasting. Repeat \emph{\textbf{Steps 2}} and \emph{\textbf{3}} until the global model meets the required criteria and stops training. The federated server transmits the trained model to each wind farm, and each wind farm uses it to forecast wind power.

\begin{algorithm}[t]
\small
\color{black}
\renewcommand{\algorithmicrequire}{\textbf{Require:}}
\renewcommand{\algorithmicensure}{\textbf{Require:}}
    \caption{Federated Deep Reinforcement Learning (Fed-DRL)}
    \label{alg:fed}
	\begin{algorithmic}[1]
    \REQUIRE Local episode $M$; Global epoch $W$; Synchronization interval $K$, Client ratio $E$.
    \ENSURE A global DDPG model with parameters ($\theta _S^Q,\theta _S^\mu$ ) , ($\theta _S^{Q'},\theta _S^{\mu '}$) for main critic network and actor network , target critic network and actor network on central server $S$; local DDPG model with parameters $\{ \theta _{}^Q,\theta _{}^\mu \} _{i = 1}^N$, $\{ \theta _{}^{Q'},\theta _{}^{\mu '}\} _{i = 1}^N$ for main critic network and actor network, target critic network and actor network on $N$ client  $\{ C\} _{i = 1}^N$
    \FOR{global epoch $w=1,2,\ldots, W$}
    \STATE Randomly select $N_e$ clients from all clients $ \{ C\}$ using $E
    \FOR{each selected client $e$ \textbf{in parallel}}
    \color{black}
    \FOR{episode $m= 1,2,\ldots,M$ }
    \STATE Initialize a random process $H$ for action exploration.
    \STATE  Receive initial observation state $s$.
    \FOR{$t=1,2,\ldots, T$}
    \STATE Select action $a$ according to the current policy and exploration noise.
    \STATE Execute action $a$ and get reward $r$ and new state $s'$.
    \STATE Store transition ($s, a, r, s'$) in replay buffer.
    \STATE Sample a minibatch from replay buffer.
    \STATE Update main actor network by (\ref{eq.update main actor network})
    \STATE Update main critic network by (\ref{eq.update the main critic network})
    \STATE Update the target networks by (\ref{eq.update target networks})
    \ENDFOR
    \ENDFOR
    \ENDFOR
    \IF {$w \mod K = 0$}
        \STATE All selected clients send parameters to server, and the server update the parameters of the global model by (\ref{eq.fedavg}).
        \STATE The server send back parameters and clients update local parameters
        \begin{equation*}
           \{ \theta _{}^Q,\theta _{}^\mu \} _{i = 1}^N \leftarrow (\theta _S^Q,\theta _S^\mu ),{\rm{ }}\{ \theta _{}^{Q'},\theta _{}^{\mu '}\} _{i = 1}^N \leftarrow (\theta _S^{Q'},\theta _S^{\mu '})
        \end{equation*}
    \ENDIF
    \ENDFOR
  \end{algorithmic}
\end{algorithm}

The complete FedDRL algorithm is shown in Algorithm \ref{alg:fed}.

\begin{figure*}[t]
	\centering
	\includegraphics[width=7.2in]{Figures/4l.pdf}	\caption{{\color{black}Forecasting results of different wind farms.}}
	\label{fig_4results}
\end{figure*}

\subsection{Evaluation Indices}
This paper uses the more common normalized mean absolute error (NMAE) and normalized root mean square error (NRMSE) as evaluation indicators to assess the forecasting performance of the proposed forecasting scheme\cite{zhao2016novel}.

\begin{equation}
    \begin{aligned}
     NMAE = \frac{1}{V}[\sum\nolimits_{i = 1}^V {(|y_i^{n} - {p_i^{n}}|)]} {\rm{ }}
    \end{aligned}
\end{equation}

\begin{equation}
    \begin{aligned}
      NRMSE = \sqrt {\frac{1}{V}\sum\limits_{i = 1}^V {{{\left( {y_i^{n} - p_i^{n}} \right)}^2}} }
    \end{aligned}
\end{equation}

\begin{equation}
    y_i^n = \frac{{{y_i}}}{{\max _{i = 1}^V{y_i}}}
\end{equation}

\begin{equation}
    p_i^n = \frac{{{p_i}}}{{\max _{i = 1}^V{y_i}}}
\end{equation}
where $V$ denotes the total number of samples, $i$ represent the samples number; $y$ denotes the real value, $p$ is the prediction result; $y^n$ and $p^n$ are the normalized value of $y$ and $p$.

\subsection{Networking Load Gain}\label{sec.load gain}
The proposed FedDRL forecasting scheme can not only protect the data privacy of each client but also has the advantage of relieving communication pressure. To verify the communication advantages of the FedDRL, we define the network load of the centralized forecasting method and the proposed forecasting scheme as follows,  respectively.
\begin{equation}
    {L_C} = \sum\limits_{n = 1}^N D  \times {h_n}\ , \ \ \ {L_F} = I \times \sum\limits_{w = 1}^W {} \sum\limits_{n = 1}^N {{h_n}}
\end{equation}
where $D$ is the size of the private data of each client in the centralized method, $I$ is the size of the model information that each client needs to transmit in FedDRL, and $h$ is the hops between each client and the central server. Then the networking load gain $U$ is defined as follows.
\begin{equation}
    U = 1 - {{{L_F}} \mathord{\left/
 {\vphantom {{{L_F}} {{L_C}}}} \right.
 \kern-\nulldelimiterspace} {{L_C}}}
\end{equation}

\begin{figure}[t!]
	\centering
	\includegraphics[width=3.6in]{Figures/pdf1.pdf}	\caption{{\color{black}Probability distribution of forecasting errors}}
	\label{fig_pdf}
\end{figure}

\begin{figure}[t]
	\centering
	\includegraphics[width=3.6in]{Figures/possess.pdf}	\caption{{\color{black}Changes in reward value during training}}
	\label{fig_prossess}
\end{figure}

\begin{figure}[t]
	\centering
	\includegraphics[width=3.6in]{Figures/KE.pdf}	\caption{{\color{black}The simulations results with different federated parameters setting}}
	\label{fig_KE}
\end{figure}

\section{CASE STUDY}\label{sec.CASE STUDY}
This article uses real-world historical data for simulations and verifies the effectiveness and superiority of the proposed forecasting scheme by comparing the predicted results with real data. In addition, we also designed experiments on the influence of different federal parameter settings on FedDRL to verify the robustness of the proposed forecasting scheme. In this work, all the simulations are implemented with Python 3.7, Tensorflow 2.0 on a PC platform with 2 Intel Core dual-core CPUs (2.6Hz) and
6 GB RAM.

\subsection{Forecasting Model Parameter Settings}
To improve the efficiency of model construction, this paper applies automatic machine learning to the proposed scheme based on our team's previous research\cite{li2021optimal1}. The appropriate hyperparameters for the forecasting model are chosen automatically. In this study, $j$ is set to 7 after conducting various simulations, since it can achieve satisfactory prediction performance in most cases. Federated parameters $K$ and $E$ are set to 100 and 100\%, respectively. The main model parameters are shown in Tab. \ref{tab.parameters of feddrl}.

\begin{table}[t]
  \centering
  \caption{Hyperparameters of FedDRL}\label{tab.parameters of feddrl}
    \begin{tabular}{cccc}
    \toprule
          & Learning rate & Hidden neurons & Activation function \\
    \midrule
    Actor & 0.0003 & 30    & Relu/Sigmoid \\
    Critic & 0.003 & 28    & Relu/Linear \\
    \bottomrule
    \end{tabular}%
  \label{tab:addlabel}%
\end{table}%

\subsection{Data Description}
In this work, we use the real-world datasets consisting of 11 wind farms with a sampling interval of 5 minutes in Washington State, USA to be the local datasets of clients, which are gained from National Renewable Energy Laboratory (NREL). The forecasting horizon is 5 minutes. When each wind farm uses a separate private dataset for local training, the ratio of training set to testing set is 4:1, which is in accordance with the setting in \cite{li2022privacy}.

\begin{figure*}[t]
	\centering
	\includegraphics[width=5.8in]{Figures/FvsC.pdf}	\caption{{\color{black}Forecasting results of the two methods}}
	\label{fig_FvsC}
\end{figure*}

\subsection{Forecasting Results and Performance Analysis}
\subsubsection{Forecasting results of different wind farms}
Fig. \ref{fig_4results} shows the forecasting results of four wind farms participating in the proposed FedDRL forecasting scheme. It can be seen that the final prediction results of each wind farm can exactly describe the real wind power output, which shows that the use of the proposed FedDRL scheme can eliminate the problem of data islands and enable different stakeholders to gain an accurate forecasting model without sharing their private data.

\subsubsection{Forecasting errors probability distribution of different wind farms}
The probability density diagram of the forecast errors of four wind farms is demonstrated in Fig. \ref{fig_pdf}. The total area enclosed by the curve and the coordinate axis in each figure is 1, which represents the range of higher and lower probability of forecasting errors. From the figure, we can find that the prediction errors of each wind farm are concentrated in a small range, which certifies that each client can achieve good prediction results relatively stably, and it also proves that the DDPG local prediction model has good robustness.

\subsubsection{Forecasting performance comparison between wind farms}
All clients participating in the proposed FedDRL scheme hope to achieve accurate predictions without sharing private data because of the concerns of privacy protection. Tab. \ref{tab.Prediction performance comparison} shows the evaluation indices of 4 randomly selected clients. We can learn from the table that although the forecasting errors of each wind field are different, the overall prediction results are relatively accurate, indicating that the proposed scheme can provide a good performance prediction model to the participating clients and protect the clients' privacy.

\begin{table}[t]
  \centering
  \caption{Prediction performance comparison}\label{tab.Prediction performance comparison}
    \begin{tabular}{crrrr}
    \toprule
    \textcolor[rgb]{ .067,  .067,  .067}{Indicators} & \multicolumn{1}{c}{\textcolor[rgb]{ .067,  .067,  .067}{Wind farm 1}} & \multicolumn{1}{c}{\textcolor[rgb]{ .067,  .067,  .067}{Wind farm 2}} & \multicolumn{1}{c}{\textcolor[rgb]{ .067,  .067,  .067}{Wind farm 3}} & \multicolumn{1}{c}{\textcolor[rgb]{ .067,  .067,  .067}{Wind farm 4}} \\
    \midrule
    \textcolor[rgb]{ .067,  .067,  .067}{NMAE} & 0.020651404
 & 0.021026766
 & 0.039084657 & 0.025438397
 \\
    \textcolor[rgb]{ .067,  .067,  .067}{NRMSE} & 0.037752126
 & 0.029915878
 & 0.055905707
 & 0.047609882
 \\
    \bottomrule
    \end{tabular}%
  \label{tab:addlabel}%
\end{table}%

\subsubsection{Training process analysis of the wind farms}
Fig. \ref{fig_prossess} depicts the change process of reward values of four randomly selected clients during training in our proposed FedDRL. The reward value of all clients fluctuates sharply in the initial stage of the iterative process, which means that each local model is constantly exploring various policies that can achieve good prediction effects when updating model parameters and performing local training; after a certain number of global epoch and local training, the prediction models of each client begin to converge, and the reward value tends to stabilize, indicating that the forecasting model has gradually explored a suitable policy and can accurately predict the wind power.

\subsubsection{Robustness test of FedDRL}
We conduct a simulation by changing the synchronization intervals $K$ and the clients' participating ratio $E$ to examine the robustness of the proposal.

Fig. \ref{fig_KE} exhibits the influence of different combinations between synchronization intervals of 50, 100, 200, and participation rates of 50\% and 100\% on the FedDRL training process. It can be learned from the figure that with different combinations of $K$ and $E$, the error of the proposed forecasting scheme will eventually converge to a small range. More importantly, when the participation ratio of clients is fixed, synchronization intervals have barely effect on the prediction process and results of the scheme; while for a given synchronization intervals, the participation ratio of clients will only slightly affect the convergence speed, and has no effect on the final prediction performance of the scheme. It can be concluded that the proposed forecasting scheme has good robustness to different federated parameters variations.

\begin{table}[t]
  \centering
  \caption{Forecasting performance of different methods}\label{tab.performance of different methods}
    \begin{tabular}{ccc}
    \toprule
    Method & NMAE  & NRMSE \\
    \midrule
    Proposed method & 0.0206514 & 0.0377521 \\
    RDPG  & 0.0316357 & 0.08384312 \\
    ARIMA & 0.0291881 & 0.07052312 \\
    BPNN  & 0.0790775 & 0.20001125 \\
    MLR   & 0.0924137 & 0.23703316 \\
    \bottomrule
    \end{tabular}%
  \label{tab:addlabel}%
\end{table}%

\subsection{Comparative Analysis of FedDRL and Traditional Centralized Forecasting Methods}

\subsubsection{Performance comparison of different forecasting methods}
This paper compares the prediction performance of the proposed prediction method with classic ARIMA, mixed logistic regression (MLR) prediction model, typical back propagation neural network (BPNN), and another reinforcement learning algorithm recurrent deterministic policy gradient (RDPG). We use FedDRL and other forecasting methods to predict the wind power of the same wind farm, and the centralized forecasting method is used by the comparison prediction approaches. In the ARIMA, the parameters of lag observations $p$, the number of times that the raw observations are differenced $d$, and the size of the moving average window $q$ are set to 2, 0, and 1. The hidden neurons and layers are set to 10 and 2 in the BPNN, respectively. The hidden neurons of Actor and Critic network in the RDPG are set to 34 and 36.

The results shown in Tab. \ref{tab.performance of different methods} suggest that judging from the performance indicators of various prediction methods, the error of the proposed method is smaller than that of other methods and the NMAE and NRMSE can reduce at least 29.25\% and 46.47\%, respectively, which proves that the  FedDRL does have the advantage in prediction accuracy.

\subsubsection{Forecasting results of FedDRL and centralized DDPG}

The wind power prediction results of the same wind farm using FedDRL and centralized DDPG models are shown in Fig. \ref{fig_FvsC}. Fig. \ref{fig_FvsC}(a) is the comparison between the wind power predicted by the two methods and the true value, Fig. \ref{fig_FvsC}(b) is the probability density of the forecasting wind power.

The figure demonstrates that both the proposed FedDRL and the centralized DDPG show good forecasting performance, which can accurately describe the wind power output of the wind farm. The accuracy of wind power prediction using the proposed FedDRL is comparable to that using centralized DDPG. It is worth noting that the use of centralized methods for forecasting requires gathering data from various wind farms, which may involve sensitive user privacy issues. When the private data of multiple wind farms are gathered together, once the privacy data is leaked, it may cause very serious losses to each wind farm. While the method proposed in this paper can save the data of each wind farm locally for training, and achieve a similar prediction accuracy without transmitting raw data, which suggests that the proposed FedDRL can achieve the forecasting accuracy criterion without sacrificing user privacy.

\subsubsection{Networking load gain}
For ease of simulation, in this work, we assume that the distance between all clients and the server is 1-Hop. According to the formula in sec.\ref{sec.load gain}, we can calculate that when the synchronization interval is 50, 100, 200, the network load gain using the designed FedDRL is at least 88.34\%, 94.82\%, 97.08\% compared with the traditional centralized prediction method. This verifies that the proposed prediction scheme can significantly relieve the communication pressure. When the proposed method covers a wider area and has more participating clients, a better networking load gain will be obtained.

\section{conclusion}\label{sec.conclusion}
As a clean and renewable energy source, wind power has developed rapidly in recent years. The development of advanced and accurate forecasting methods can undoubtedly promote the large-scale grid connection of wind power and assist the operation of power system. To deal with data privacy and openness, this paper proposes a FedDRL scheme for ultra-short-term wind power forecasting which combines federated learning and DRL. The DDPG algorithm is used as the basic prediction model of the FedDRL scheme to improve the forecasting accuracy; compared with the traditional wind power forecasting method, the framework of federated learning enable each stakeholder in the proposed forecasting scheme to upload only relevant parameters and save the private data locally for training. The proposed scheme not only guarantees the accuracy of wind power forecasting, solves the problem of data islands, but also effectively protects user privacy and relieves communication pressure.

The results of the simulations demonstrate that the designed FedDRL scheme outperforms the traditional wind power prediction methods with stable and more accurate forecasting results in a privacy-preserving way. The NMAE of most wind farms is in a very small range from 0.0207 to 0.0433. Compared with the traditional centralized prediction method, the proposed prediction scheme can obtain at least 88.34\% network load gain. In addition, the experiments of setting different participation rates and synchronization intervals in the federation parameters also proved that the proposed scheme has good robustness.

In future work, we will focus on how to improve the training efficiency of the model and apply the proposed scheme to the real-time dispatch of power system with renewables. Furthermore, this work does not consider the effects of packet loss rate and communication delay, how to solve these problems to facilitate the industrial application of the proposed method is also an interesting topic.

redpajama_set_name: RedPajamaArXiv


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text:
Sørfold és un municipi situat al comtat de Nordland, Noruega. Té una població de 1.963 habitants (2016) i la seva superfície és de 1,636.61 km². Forma part de la regió tradicional de Salten. El centre administratiu és la població de Straumen. L'antic municipi de Folden va ser dividit entre Sørfold i Nordfold-Kjerringøy el gener del 1887. La forma escrita de la llengua noruega oficial al municipi és el Bokmål.

Nom
El municipi rep el nom del fiord Folda (que en antic nòrdic era Fold).

Escut
L'escut és modern, es va adoptar el 1987. Les armes mostren una roda de plata d'una turbina en una central hidroelèctrica sobre un fons blau. Els rius del municipi contenen molts salts d'aigua, que s'aprofiten per generar electricitat. Aquest fet ha proporcionat una font d'ingressos important per a la comunitat.

Geografia

El municipi de Sørfold es troba uns 120 quilòmetres al nord del cercle polar àrtic. La superfície total de Sørfold és de 1.636,61 quilòmetres quadrats, dels quals 141 quilòmetres quadrats són coberts de gel i neu permanents, i només 265,8 quilòmetres quadrats es troben per sota dels 150 metres de l'isolínia. La longitud total de la costa és de 249 quilòmetres. El 1987 només es cultivaven activament 3.2 quilòmetres quadrats de terreny.

Sørfold limita al nord amb el municipi de Hamarøy, i al sud amb el municipi de Fauske. A l'est limita amb el municipi suec de Jokkmokk.

El Parc Nacional de Rago, amb la seva naturalesa salvatge dominada per roques escarpades, rierols i boscos de pins, es troba a Sørfold. La glacera de Blåmannsisen, una de les més grans de Noruega, es troba parcialment al municipi. Hi ha diverses reserves naturals. La reserva natural de Veikdalen, aproximadament a 300 metres sobre el nivell del mar, protegeix un bosc de pi i bedoll en gran part no pertorbat (s'hi van talar arbres fins al 1918) amb molts pins dempeus morts.

Hi ha molts llacs grans a Sørfold, que són Andkjelvatnet, Faulvatnet, Forsvatnet, Grovatnet, Horndalsvatnet, Kobbvatnet, Kvitvatnet, Langvatnet, Leirvatnet, Litlverivatnet, Mørsvikvatnet, Nedre Veikvatnet, Røyrvatnet, Rundvatnet, Sildhopvatnet, Sisovatnet, Storskogvatnet, Straumvatnet i Trollvatnet.

Història
Carl von Linné va penetrar a Noruega per aquest municipi en la seva expedició científica a través de la Lapònia.

El petit poble de Mørsvikbotn es troba a la part nord del municipi. Al voltant de 5 quilòmetres al nord de Mørsvikbotn es troba el llac Mørsvikvatnet. En aquesta àrea, Mørsry, l'exèrcit alemany tenia un camp de presoners de guerra durant la Segona Guerra Mundial, que eren majoritàriament presos de guerra russos. Construïen la línia de ferrocarril Polarbanen, que havia d'enllaçar Fauske i Narvik. Allà s'hi poden observar algunes ruïnes del camp, els fonaments de la línia ferroviària, un túnel i carreteres. Un petit cementiri ara buit de soldats russos caiguts es troba prop del campament, a uns 50 metres del costat esquerre just abans del pont de formigó.

Referències

Enllaços externs

 Lloc web oficial del municipi

Municipis de Nordland


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