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Barely three months into the new year and we are happy to announce a monumental milestone reached - 150 million downloads.
\n\nThis achievement solidifies IntechOpen’s place as a pioneer in Open Access publishing and the home to some of the most relevant scientific research available through Open Access.
\n\nWe are so proud to have worked with so many bright minds throughout the years who have helped us spread knowledge through the power of Open Access and we look forward to continuing to support some of the greatest thinkers of our day.
\n\nThank you for making IntechOpen your place of learning, sharing, and discovery, and here’s to 150 million more!
\n\n\n\n\n'}],latestNews:[{slug:"intechopen-signs-new-contract-with-cepiec-china-for-distribution-of-open-access-books-20210319",title:"IntechOpen Signs New Contract with CEPIEC, China for Distribution of Open Access Books"},{slug:"150-million-downloads-and-counting-20210316",title:"150 Million Downloads and Counting"},{slug:"intechopen-secures-indefinite-content-preservation-with-clockss-20210309",title:"IntechOpen Secures Indefinite Content Preservation with CLOCKSS"},{slug:"intechopen-expands-to-all-global-amazon-channels-with-full-catalog-of-books-20210308",title:"IntechOpen Expands to All Global Amazon Channels with Full Catalog of Books"},{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"},{slug:"all-intechopen-books-available-on-perlego-20201215",title:"All IntechOpen Books Available on Perlego"}]},book:{item:{type:"book",id:"485",leadTitle:null,fullTitle:"Diagnosis and Treatment of Abdominal and Thoracic Aortic Aneurysms Including the Ascending Aorta and the Aortic Arch",title:"Diagnosis and Treatment of Abdominal and Thoracic Aortic Aneurysms Including the Ascending Aorta and the Aortic Arch",subtitle:null,reviewType:"peer-reviewed",abstract:"This book considers diagnosis and treatment of abdominal and thoracic aortic aneurysms. It addresses vascular and cardiothoracic surgeons and interventional radiologists, but also anyone engaged in vascular medicine. The book focuses amongst other things on operations in the ascending aorta and the aortic arch. Surgical procedures in this area have received increasing attention in the last few years and have been subjected to several modifications. Especially the development of interventional radiological endovascular techniques that reduce the invasive nature of surgery as well as complication rates led to rapid advancements. Thoracoabdominal aortic aneurysm (TAAA) repair still remains a challenging operation since it necessitates extended exposure of the aorta and reimplantation of the vital aortic branches. Among possible postoperative complications, spinal cord injury (SCI) seems one of the most formidable morbidities. Strategies for TAAA repair and the best and most reasonable approach to prevent SCI after TAAA repair are presented.",isbn:null,printIsbn:"978-953-307-524-2",pdfIsbn:"978-953-51-6515-6",doi:"10.5772/996",price:119,priceEur:129,priceUsd:155,slug:"diagnosis-and-treatment-of-abdominal-and-thoracic-aortic-aneurysms-including-the-ascending-aorta-and-the-aortic-arch",numberOfPages:220,isOpenForSubmission:!1,isInWos:1,hash:"7643f2ff916be49ce4255ea9c55fa82d",bookSignature:"Reinhart T. Grundmann",publishedDate:"October 5th 2011",coverURL:"https://cdn.intechopen.com/books/images_new/485.jpg",numberOfDownloads:38504,numberOfWosCitations:5,numberOfCrossrefCitations:4,numberOfDimensionsCitations:11,hasAltmetrics:0,numberOfTotalCitations:20,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 20th 2010",dateEndSecondStepPublish:"November 17th 2010",dateEndThirdStepPublish:"March 24th 2011",dateEndFourthStepPublish:"April 23rd 2011",dateEndFifthStepPublish:"June 22nd 2011",currentStepOfPublishingProcess:5,indexedIn:"1,2,3,4,5,6",editedByType:"Edited by",kuFlag:!1,editors:[{id:"37604",title:"Prof.",name:"Reinhart",middleName:"Thomas",surname:"Grundmann",slug:"reinhart-grundmann",fullName:"Reinhart Grundmann",profilePictureURL:"https://mts.intechopen.com/storage/users/37604/images/23_n.jpg",biography:"Dr. Reinhart T. Grundmann works currently as an independent medical expert. He is a professor of surgery at the University of Cologne and he has the qualification of general and vascular surgery. He is the former medical director of the B.Braun company, one of the leading providers of healthcare solutions. In the last eight years he has been working as the medical director of the Clinics Altotting-Burghausen, Germany. Dr. Grundmann was from 1992 until 2008 the managing director of the Zentralblatt fur Chirurgie and he is currently a member of the Editorial Board of World Journal of Gastrointestinal Surgery. He edited from 2001 to 2005 the Jahrbuch der Chirurgie- the book which provides an information on the latest developments in surgery. Dr. Grundmann already published more than 260 scientific publications, including books and the book chapters. His recent research interests lie in the field of efficiency and efectiveness in surgery. In this frame, he published a workflows on liver surgery, gastric cancer, obesity surgery and surgery for abdominal and carotide artery stenosis treatment.",institutionString:null,position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"3",institution:{name:"Kreiskliniken Reutlingen",institutionURL:null,country:{name:"Germany"}}}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"1138",title:"Abdominal Surgery",slug:"abdominal-surgery"}],chapters:[{id:"21698",title:"Definitions, History and General Considerations Related to the Aortic Aneurysms",doi:"10.5772/19027",slug:"definitions-history-and-general-considerations-related-to-the-aortic-aneurysms",totalDownloads:1950,totalCrossrefCites:0,totalDimensionsCites:0,signatures:"Guillermo Careaga-Reyna",downloadPdfUrl:"/chapter/pdf-download/21698",previewPdfUrl:"/chapter/pdf-preview/21698",authors:[{id:"33340",title:"Dr.",name:"Guillermo",surname:"Careaga-Reyna",slug:"guillermo-careaga-reyna",fullName:"Guillermo Careaga-Reyna"}],corrections:null},{id:"21699",title:"Presentation of Abdominal Aortic Aneurysm in Clinical Practice, a Review",doi:"10.5772/20175",slug:"presentation-of-abdominal-aortic-aneurysm-in-clinical-practice-a-review",totalDownloads:6137,totalCrossrefCites:0,totalDimensionsCites:0,signatures:"Simone Knaap and Wayne Powell II",downloadPdfUrl:"/chapter/pdf-download/21699",previewPdfUrl:"/chapter/pdf-preview/21699",authors:[{id:"37686",title:"MSc",name:"Simone",surname:"Knaap",slug:"simone-knaap",fullName:"Simone Knaap"},{id:"45585",title:"Dr.",name:"Wayne",surname:"Powell II",slug:"wayne-powell-ii",fullName:"Wayne Powell II"}],corrections:null},{id:"21700",title:"Screening for Abdominal Aortic Aneurysm",doi:"10.5772/17846",slug:"screening-for-abdominal-aortic-aneurysm",totalDownloads:1195,totalCrossrefCites:0,totalDimensionsCites:0,signatures:"Sima Sayyahmelli and Rakhshandeh Alipanahi",downloadPdfUrl:"/chapter/pdf-download/21700",previewPdfUrl:"/chapter/pdf-preview/21700",authors:[{id:"29623",title:"Dr.",name:"Sima",surname:"Sayyahmelli",slug:"sima-sayyahmelli",fullName:"Sima Sayyahmelli"},{id:"41265",title:"Dr.",name:"Rakhshandeh",surname:"Alipanahi",slug:"rakhshandeh-alipanahi",fullName:"Rakhshandeh Alipanahi"}],corrections:null},{id:"21701",title:"Color-Doppler Ultrasonography in the Monitoring of Endovascular Abdominal Aortic Aneurysm Repair",doi:"10.5772/18593",slug:"color-doppler-ultrasonography-in-the-monitoring-of-endovascular-abdominal-aortic-aneurysm-repair",totalDownloads:3176,totalCrossrefCites:1,totalDimensionsCites:1,signatures:"Enrique M. 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Gorlitzer, G. Weiss, F. Waldenberger and M. 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\r\n\tUbiquitous computing is often mentioned as an application domain with blurry or even undefined rules, boundaries, and examples. Fortunately, there are several concepts, developments, and pieces of research that have been put forward into this book (data integration, distributed systems, data enhancement via blockchain or machine learning, etc.) which explain what ubiquitous computing is and how it can be used to everyone´s advantage. All these contributions are based on research works and developments involving areas of knowledge such as the Internet of Things, Autonomous Systems, Cyber-Physical Systems, and Wireless Sensor Networks. Among other topics, heterogeneous hardware integration, low capability distributed systems, microservices, security deployments for autonomous devices, or data mining procedures are fully mentioned and described here. In this way, this book provides a holistic view onto the field of ubiquitous computing and all its features, both related to the software and hardware, while at the same time offering knowledge from cutting edge projects that provide the backbone of the contents that have been included.
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Partnership and in SEPT. At Mohawk College, he designed and developed the first-ever degree program in Process Automation, in addition, to jointly securing funding with two other colleagues to establish a Process Automation Applied Research Centre.",coeditorOneBiosketch:"Dr. Gao has published over 100 journal and conference papers, 1 book,\r\nand 4 book chapters in areas of advanced robotics, automation, and artificial Intelligence. \r\nHe serves as the Editor-in-Chief of the International Journal of Intelligent Machines and\r\nRobotics; he is also the Editor-in-Chief of the Journal of Robotic and Mechatronic Systems.",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"333793",title:"Dr.",name:"Ishwar",middleName:null,surname:"Singh",slug:"ishwar-singh",fullName:"Ishwar Singh",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0033Y000031TBdSQAW/Profile_Picture_1616070554137",biography:null,institutionString:"McMaster University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"McMaster University",institutionURL:null,country:{name:"Canada"}}}],coeditorOne:{id:"353808",title:"Dr.",name:"Zhen",middleName:null,surname:"Gao",slug:"zhen-gao",fullName:"Zhen Gao",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0033Y0000364SnZQAU/Profile_Picture_1615808028038",biography:"Zhen Gao is an assistant professor in the School of Engineering Practice and Technology\r\n(SEPT) at McMaster University which he joined in July 2014. Since September 2020, he was\r\nappointed as Program Lead for a Master’s program in Systems & Technology which was focused\r\non Cyber Physical System. He has published over 100 journal and conference papers, 1 book,\r\nand 4 book chapters in areas of advanced robotics, automation and artificial Intelligence. Dr. Gao\r\nis the Associate Editor for the Conference Editorial Board of the IEEE Robotics and Automation\r\nSociety, 2021 IEEE International Conference on Robotics and Automation. He was the sessional\r\nchair For 9th International Conference on Interactive, Collaborative, and Blended Learning, and\r\nfor International Conference on Interactive Mobile Communication, Technologies and Learning.\r\nDr. Gao served as the Program Committee Member for World Congress on Intelligent Control\r\nand Automation, International Conference on Information and Automation, IEEE Conference on\r\nRobotics and Biomimetics, IEEE International Conference on Real-time Computing and\r\nRobotics, IEEE International Conference on Automation and Logistics, and International\r\nConference on Intelligent Robotics and Applications, and IEEE Canadian Conference on\r\nElectrical and Computer Engineering. His current research interests include industrial\r\ncontrollers, advanced robotics and automation, artificial intelligence, neural network and pattern\r\nrecognition. He serves as the Editor-in-Chief of International Journal of Intelligent Machines and\r\nRobotics; he is also the Editor-in-Chief of Journal of Robotic and Mechatronic Systems.",institutionString:"McMaster University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"McMaster University",institutionURL:null,country:{name:"Canada"}}},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"9",title:"Computer and Information Science",slug:"computer-and-information-science"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"280415",firstName:"Josip",lastName:"Knapic",middleName:null,title:"Mr.",imageUrl:"https://mts.intechopen.com/storage/users/280415/images/8050_n.jpg",email:"josip@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"314",title:"Regenerative Medicine and Tissue Engineering",subtitle:"Cells and Biomaterials",isOpenForSubmission:!1,hash:"bb67e80e480c86bb8315458012d65686",slug:"regenerative-medicine-and-tissue-engineering-cells-and-biomaterials",bookSignature:"Daniel Eberli",coverURL:"https://cdn.intechopen.com/books/images_new/314.jpg",editedByType:"Edited by",editors:[{id:"6495",title:"Dr.",name:"Daniel",surname:"Eberli",slug:"daniel-eberli",fullName:"Daniel Eberli"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"2270",title:"Fourier Transform",subtitle:"Materials Analysis",isOpenForSubmission:!1,hash:"5e094b066da527193e878e160b4772af",slug:"fourier-transform-materials-analysis",bookSignature:"Salih Mohammed Salih",coverURL:"https://cdn.intechopen.com/books/images_new/2270.jpg",editedByType:"Edited by",editors:[{id:"111691",title:"Dr.Ing.",name:"Salih",surname:"Salih",slug:"salih-salih",fullName:"Salih Salih"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"872",title:"Organic Pollutants Ten Years After the Stockholm Convention",subtitle:"Environmental and Analytical Update",isOpenForSubmission:!1,hash:"f01dc7077e1d23f3d8f5454985cafa0a",slug:"organic-pollutants-ten-years-after-the-stockholm-convention-environmental-and-analytical-update",bookSignature:"Tomasz Puzyn and Aleksandra Mostrag-Szlichtyng",coverURL:"https://cdn.intechopen.com/books/images_new/872.jpg",editedByType:"Edited by",editors:[{id:"84887",title:"Dr.",name:"Tomasz",surname:"Puzyn",slug:"tomasz-puzyn",fullName:"Tomasz Puzyn"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"65420",title:"A Distributed Optimization Method for Optimal Energy Management in Smart Grid",doi:"10.5772/intechopen.84136",slug:"a-distributed-optimization-method-for-optimal-energy-management-in-smart-grid",body:'In any energy system, optimal energy management (OEM) is an essential problem because it directly affects to both the technical (e.g., operation and control) and economic (i.e., profit) aspects of such energy system. Recently, smart grid has been proposed as a solution to improve the greenhouse gas emissions and the efficiency and energy management in electric power grids [1]. Important components in smart grid are renewable energy sources (RESs) and distributed energy resources (DERs), e.g., rooftop photovoltaic (PV), electric vehicles (EVs), distributed energy storage systems (ESSs), etc. Those RESs and DERs are expected to replace the polluted fossil-based energy sources for generating electric power and to increase the mobility and flexibility of power grids.
However, the fluctuating and intermittent nature of RESs and the close or on-site location of DERs to end users make the OEM problem in smart grids more complex than that in traditional power grids. This urges the development of new concepts and approaches to deal with challenges that arose in smart grids. Some examples include demand side management (DSM) and real-time (dynamic) pricing (RTP) [2, 3]. As one of the main DSM activities [3, 4, 5], demand response (DR) motivates changes in electric use by end-use customers, in response to changes in the price of electricity over time, or gives incentive payments designed to induce lower electricity use at times of high market prices or when grid reliability is jeopardized [6]. DR not only shifts the load in peak times but also increases the grid’s energy efficiency and customers’ benefits.
Traditionally, the OEM problem in transmission power networks is treated as the economic dispatch (ED) problem (see, e.g., [7]). Nonetheless, DSM including DR is often not included in the ED problem. To overcome this drawback, the social welfare maximization (SWM) problem is set up and solved, where the benefits from both the suppliers and the consumers are taken into account [8, 9, 10, 11, 12, 13, 14]. The effectiveness of the SWM problem has been verified in [15]. On the other hand, in distribution power networks, the OEM problem is usually investigated with the existence of an intermediate player called the aggregator who manages the power exchange between a small distribution grid and a larger or main grid. Therefore, the OEM problem in such situations means to maximize the benefits of the DER owners, consumers, and the aggregator.
To suppress the redundancy or to supplement the lack of energy from the fluctuating outputs of RESs, and to make the energy scheduling more flexible, ESSs are being introduced into smart grids as a solution. For instance, in power distribution systems or microgrids, EV’s batteries are sources of mobile and distributed ESSs that might contribute to the energy efficiency, security, and flexibility of such distribution systems or microgrids. The stability and robustness of vehicle-to-grid (V2G) energy networks have been investigated in [16]. The problem of power scheduling with electric vehicle (PSwEV) in a microgrid has been introduced under a multi-agent setting in [17]. Due to the increase of market share of EVs and plug-in hybrid electric vehicles (PHEVs) predicted until 2050 [18], it is reasonable to believe that the PSwEV problem will be popular and important in the near future.
To solve optimization problems arising in OEM problems, the existing methods can be classified depending on the centralized or distributed nature of such methods and the heuristic or analytical characteristic of the obtained solution. The security and resiliency of centralized approaches are weak due to a single point of failure and the huge communication and data processing, at the central unit. Those limitations can be improved by distributed approaches using multi-agent system (MAS), where each agent corresponds to a bus or a portion of the grid and each agent only communicates with a few other neighboring agents. On the other hand, the heuristic methods (e.g., [19, 20]) usually require a long running time and local solutions, which are less effective than analytical methods for convex optimization problems. Thus, distributed and analytical approaches will be developed in the current chapter to solve convex optimization problems representing OEM problems in smart grids.
A MAS-based distributed method for solving the ED problem in smart grid was proposed in [7] where the power losses are approximated by quadratic functions and the nonlinear coupling of oscillating agents is employed for decentralized solution derivation from the Karush-Kuhn-Tucker (KKT) conditions. The projected gradient methods were utilized in [10] to solve the SWM problem, where a MAS was utilized to derive the supply-demand mismatch in a distributed fashion. Another method named dual decomposition was used in [8] to get a distributed solution when the power balance is not strictly required. If the power balance is required, a distributed observer design was employed in [11] to estimate the power mismatch. The Vickrey-Clarke-Groves (VCG) mechanism was used in [9], but it is centralized. A distributed method was presented in [12], but the communication structure was all-to-all. Next, two consensus protocols were introduced in [13] to derive a distributed method for solving the SWM problem. Lastly, the SWM problem with transmission losses modeled by a quadratic function was investigated in [14].
This chapter presents an approach named sequential distributed consensus-based ADMM (SDC-ADMM) for solving nonlinear convex optimization problems having both equality and inequality constraints, which include those from OEM problems in smart grids. The attractive features of this approach are as follows: (i) viable for a general and broad class of constrained convex programming, (ii) distributed implementation, (iii) analytical updates of variables, and (iv) unnecessary checking of the active constraints in the KKT conditions, e.g., as in [7], which slows down the convergence speed and increases the computational complexity. Then the effectiveness of the proposed approach will be demonstrated through two specific OEM problems in smart grids, namely, dynamic SWM (DSWM) and PSwEV.
The rest of this chapter is organized as follows. Section 2 introduces a class of constrained optimization problems in power grids followed by two specific problems. Then an approach to solve those optimization problems is given in Section 3. Simulation results to illustrate the proposed approach are provided in Section 4. Finally, Section 5 summarizes the chapter.
A lot of OEM problems in power grids can be represented by the following general form of constrained convex programming:
where
Due to the global constraint (2), (1) is a centralized optimization problem. However, (1) is decomposable into subproblems corresponding to individual time slots; hence we can derive a sub-optimal solution to (1) by resolving it sequentially, i.e., from
Consider a smart grid consisting of
The generation cost for CG unit
where
where
where
where
for
In this problem, we include battery operation into the microgrid to suppress the high demand at the high-cost time of utility electricity. Furthermore, we consider EV battery instead of the stationary battery storage to reduce the installation cost of the battery system.
Our microgrid model consists of
The generation cost function
For the microgrid internal trading, the revenue function of DGs has the following form:
Load demands are assumed as fixed parameters in this problem. The electricity cost of load demands is calculated by
For simplicity, we assume that EVs have only one round-trip route per day, and the home of each EV owner is the only charging point for each EV.
Denote
To reduce computational cost,
The state of charge (SOC) of EV battery at the starting point of a next time slot depends on the SOC at the starting point of current time slot and a charging/discharging efficiency
SOC constraint is as follows:
When EVs are at home (from the arrival time to the next departure time), their charging/discharging scheduling can be utilized for DR actions. The variable
Algorithm 1: |
---|
1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: |
The battery life function of EVs depends on EVs charging/discharging power [23], as follows:
where
The revenue function of EVs is defined in [21], taking into account the battery life cost:
The revenue function of the microgrid operator is calculated by
where
With the existence of EVs and the MG, the power balance constraint in the microgrid has more terms than that in the DSWM problem, as follows:
The PSwEV problem is to maximize the total revenue of DGs, EVs, load demands, and the microgrid operator, as follows:
s.t. (22), (9), (10), (13)–(19), and (21)
where
Substituting (11), (12) and (18)–(20) into (23), the PSwEV maximization programming in (23) can be rewritten as a minimization problem below:
As mentioned in Section 2, the optimization problem (1) will be solved by a sequential approach presented in the current section, which separates (1) into the following subproblems
and solves them starting from
The SDC-ADMM approach is based on MAS and consensus theory so that it can be run in parallel in all generation and consumption units. Hence, the MAS description for smart grid needs to be introduced first. More specifically, each agent is assigned to a generation or demand unit, and the communication among agents is represented by an undirected graph
To develop the SDC-ADMM approach, (25) is first reformulated into the 2-block form of ADMM. The following closed convex sets are defined corresponding to the global and local constraints:
together with their indicator functions [24]
Hence, (25) can be rewritten as follows:
Because the indicator function of a closed, non-empty convex set is proper, closed, and convex [25], the cost functions in (28) are also proper, closed, and convex with respect to
where
This algorithm is stopped if the criteria
with
In the following, the variables
The update of
of which the strong duality holds [25]. Let
Since
where
Consequently, the following consensus law is utilized:
where
Then the consensus of all agents is achieved, where the consensus states are
Thus, the optimal Lagrange multiplier can be obtained in a distributed manner by
Remark 1: If
The update of
Further, (42) and (43) is decentralized because both the cost function (42) and the constraint (43) are individually decomposable. Therefore, each agent (unit) just needs to solve a local scalar-constrained quadratic programming:
which is easily solved by existing methods.
For the DSWM problem, (45) is simply an interval, and
The convergence of the proposed SDC-ADMM algorithm can be proved in a similar manner to that in [26]; hence it is ignored here for brevity. In the following, a summary for the algorithm is provided.
Algorithm 2: |
---|
Each agent determines its local constraint set Each agent calculates All agents run the consensus law (39) with initial values (38), then compute Each agent updates its variable Each agent updates its variable Each agent updates its variable break; |
For several grid optimization problems represented in the form of (1), e.g., economic dispatch or power scheduling, DSWM, PSwEV, etc., an electricity pricing mechanism is needed to drive the electricity trading in the grid. Interestingly, the optimal Lagrange multiplier associated with the equality constraint (2) is often regarded as the market-clearing price. That will be proved under mild assumptions in the following:
where
The optimal energy price in the system is achieved when the market is cleared, at which the marginal costs of all agents are the same. Hence,
In the proposed SDC-ADMM algorithm, this means
Substituting (48) into (35), we have
If
Thus, as long as the proposed SDC-ADMM algorithm converges, the optimal energy price
In this section, simulation results for two problems, DSWM and PSwEV, are provided to illustrate the effectiveness of the proposed SDC-ADMM algorithm.
For this problem, a modified IEEE 39-bus system (see Figure 1) is used as the test system where it is assumed that there are PV generation units in the system with the total maximum output of 210 MW. The parameters of generators and demand units are taken from [26]. The average PV output curve, which is shown in Figure 2, is suitably scaled from the real PV data collected in New England [28]. Moreover, an average load profile taken from New England Independent System Operator [29] is utilized and properly scaled to obtain the time-varying upper bounds of demand units. This load profile has two demand peaks at 11:00 am and 8:00 pm, and the highest demand is at 8:00 pm, as seen in Figure 3.
IEEE 39-bus system.
PV output.
Total CG power and demand.
Other parameters in the simulation are as follows. The absolute and relative tolerances are set to be
Figures 3 and 4 display the total and individual power generated and consumed in the test system which are obtained by the proposed SDC-ADMM algorithm. Thanks to PV energy, the peak demand is shifted from 8 pm to 1 pm at which the PV output is maximum, as observed in Figure 3.
Individual power profile.
Then the electricity price is exhibited in Figure 5 showing that it is highest at 8 pm and lowest at 1–2 pm. This explains why the peak demand can be shifted. Next, the total welfare in the grid is shown in Figure 6 where the maximum welfare is attained at 1 pm when the consumers use most energy and the CG units produce least energy. Finally, Figure 7 shows the convergence of the proposed SDC-ADMM algorithm.
Electricity price.
Total social welfare.
Algorithm convergence.
In this test case, a microgrid having 2 DGs, 16 EVs, 4 load demands, 4 PV generations, and a microgrid operator is considered with a 3-day duration. The total number of agents is 27, in which the controllable agents are those for 2 DGs, 16 EVs, and the microgrid operator. The total PV curve and the total demand curve are given in Figure 8. The prescribed electricity transaction price
PV and demand curves.
Transaction price by utility.
The departure and arrival time and required traveling energies of 16 EVs are randomly generated from mix Gaussian distributions of this parameter of an actual set of 1400 EVs. The maximum energy capacity of each EV battery is 17.6 kWh, and the SOC limits of each EV battery are set at 20 and 80% of the maximum energy capacity, respectively.
The absolute and relative tolerances are set to be
Consequently, the simulations for hundreds of different scenarios corresponding to the above random times are run with the proposed SDC-ADMM algorithm. The results for one specific scenario are then shown in Figures 10–12.
DG power, EV charging power, and transaction price inside microgrid.
The state of charge of all EVs.
SDC-ADMM convergence.
Figure 10 shows the benefit of utilizing PV generation and EV charging in the microgrid. First, DG output power is reduced around the time period of high PV output, while the load demand is quite high. Second, when PV output is high, the microgrid operator can sell the redundant electricity to the utility at the highest price. Last, even though EVs do not have much correlation to PV output due to the EV traveling times, they still benefit the microgrid with their optimal charging and discharging schedules in which the charging is executed at low-price time periods of utility, and vice versa, the discharging is made at high-price time periods of utility. Moreover, the discharging also provides microgrid electricity for selling to the utility at a high price.
Subsequently, the SOC profiles of 16 EVs are depicted in Figure 11. It can be observed that the EV batteries will be charged in the early morning when the electricity price is low, but not to the maximum allowed SOC, i.e., 80% of maximum battery capacity, because of the using of EV charging/discharging strategy in Algorithm 1 and the realistic EV data that only around 6 kWh is enough for each EV round-trip. Further, the charged/discharged SOCs of EVs are different due to their differences on charging/discharging times and required energy for traveling.
Finally, the convergence of the proposed SDC-ADMM algorithm in the PSwEV problem is shown in Figure 11, and the consensus processes in the distributed algorithm for calculating the optimal electric price inside the microgrid are displayed in Figures 12 and 13.
Consensus for computing
In this chapter, a distributed optimization algorithm called sequential distributed consensus-based alternating direction method of multipliers (SDC-ADMM) is proposed for optimal energy management in smart grids. This algorithm is applicable to a broad class of linear or nonlinear constrained convex programming, of which two specific problems in smart grids have been studied in this chapter. The first problem DSWM tries to maximize the total social welfare in transmission grids in the presence of renewable energy and power losses, while the second problem PSwEV considers the power scheduling in distribution microgrids with renewable energy, electric vehicle as mobile storage, and a microgrid operator. It is then shown that the proposed SDC-ADMM algorithm works well for both problems, in which an optimal real-time electricity pricing scheme is derived as a part of the algorithm which facilitates demand response. Additionally, the existence of renewable energy and electric vehicles with suitable charging and discharging strategies is benefit to the grid for reducing the electricity price and the output power from nonrenewable energy generation.
The authors declare no conflict of interest.
In any energy system, optimal energy management (OEM) is an essential problem because it directly affects to both the technical (e.g., operation and control) and economic (i.e., profit) aspects of such energy system. Recently, smart grid has been proposed as a solution to improve the greenhouse gas emissions and the efficiency and energy management in electric power grids [1]. Important components in smart grid are renewable energy sources (RESs) and distributed energy resources (DERs), e.g., rooftop photovoltaic (PV), electric vehicles (EVs), distributed energy storage systems (ESSs), etc. Those RESs and DERs are expected to replace the polluted fossil-based energy sources for generating electric power and to increase the mobility and flexibility of power grids.
However, the fluctuating and intermittent nature of RESs and the close or on-site location of DERs to end users make the OEM problem in smart grids more complex than that in traditional power grids. This urges the development of new concepts and approaches to deal with challenges that arose in smart grids. Some examples include demand side management (DSM) and real-time (dynamic) pricing (RTP) [2, 3]. As one of the main DSM activities [3, 4, 5], demand response (DR) motivates changes in electric use by end-use customers, in response to changes in the price of electricity over time, or gives incentive payments designed to induce lower electricity use at times of high market prices or when grid reliability is jeopardized [6]. DR not only shifts the load in peak times but also increases the grid’s energy efficiency and customers’ benefits.
Traditionally, the OEM problem in transmission power networks is treated as the economic dispatch (ED) problem (see, e.g., [7]). Nonetheless, DSM including DR is often not included in the ED problem. To overcome this drawback, the social welfare maximization (SWM) problem is set up and solved, where the benefits from both the suppliers and the consumers are taken into account [8, 9, 10, 11, 12, 13, 14]. The effectiveness of the SWM problem has been verified in [15]. On the other hand, in distribution power networks, the OEM problem is usually investigated with the existence of an intermediate player called the aggregator who manages the power exchange between a small distribution grid and a larger or main grid. Therefore, the OEM problem in such situations means to maximize the benefits of the DER owners, consumers, and the aggregator.
To suppress the redundancy or to supplement the lack of energy from the fluctuating outputs of RESs, and to make the energy scheduling more flexible, ESSs are being introduced into smart grids as a solution. For instance, in power distribution systems or microgrids, EV’s batteries are sources of mobile and distributed ESSs that might contribute to the energy efficiency, security, and flexibility of such distribution systems or microgrids. The stability and robustness of vehicle-to-grid (V2G) energy networks have been investigated in [16]. The problem of power scheduling with electric vehicle (PSwEV) in a microgrid has been introduced under a multi-agent setting in [17]. Due to the increase of market share of EVs and plug-in hybrid electric vehicles (PHEVs) predicted until 2050 [18], it is reasonable to believe that the PSwEV problem will be popular and important in the near future.
To solve optimization problems arising in OEM problems, the existing methods can be classified depending on the centralized or distributed nature of such methods and the heuristic or analytical characteristic of the obtained solution. The security and resiliency of centralized approaches are weak due to a single point of failure and the huge communication and data processing, at the central unit. Those limitations can be improved by distributed approaches using multi-agent system (MAS), where each agent corresponds to a bus or a portion of the grid and each agent only communicates with a few other neighboring agents. On the other hand, the heuristic methods (e.g., [19, 20]) usually require a long running time and local solutions, which are less effective than analytical methods for convex optimization problems. Thus, distributed and analytical approaches will be developed in the current chapter to solve convex optimization problems representing OEM problems in smart grids.
A MAS-based distributed method for solving the ED problem in smart grid was proposed in [7] where the power losses are approximated by quadratic functions and the nonlinear coupling of oscillating agents is employed for decentralized solution derivation from the Karush-Kuhn-Tucker (KKT) conditions. The projected gradient methods were utilized in [10] to solve the SWM problem, where a MAS was utilized to derive the supply-demand mismatch in a distributed fashion. Another method named dual decomposition was used in [8] to get a distributed solution when the power balance is not strictly required. If the power balance is required, a distributed observer design was employed in [11] to estimate the power mismatch. The Vickrey-Clarke-Groves (VCG) mechanism was used in [9], but it is centralized. A distributed method was presented in [12], but the communication structure was all-to-all. Next, two consensus protocols were introduced in [13] to derive a distributed method for solving the SWM problem. Lastly, the SWM problem with transmission losses modeled by a quadratic function was investigated in [14].
This chapter presents an approach named sequential distributed consensus-based ADMM (SDC-ADMM) for solving nonlinear convex optimization problems having both equality and inequality constraints, which include those from OEM problems in smart grids. The attractive features of this approach are as follows: (i) viable for a general and broad class of constrained convex programming, (ii) distributed implementation, (iii) analytical updates of variables, and (iv) unnecessary checking of the active constraints in the KKT conditions, e.g., as in [7], which slows down the convergence speed and increases the computational complexity. Then the effectiveness of the proposed approach will be demonstrated through two specific OEM problems in smart grids, namely, dynamic SWM (DSWM) and PSwEV.
The rest of this chapter is organized as follows. Section 2 introduces a class of constrained optimization problems in power grids followed by two specific problems. Then an approach to solve those optimization problems is given in Section 3. Simulation results to illustrate the proposed approach are provided in Section 4. Finally, Section 5 summarizes the chapter.
A lot of OEM problems in power grids can be represented by the following general form of constrained convex programming:
where
Due to the global constraint (2), (1) is a centralized optimization problem. However, (1) is decomposable into subproblems corresponding to individual time slots; hence we can derive a sub-optimal solution to (1) by resolving it sequentially, i.e., from
Consider a smart grid consisting of
The generation cost for CG unit
where
where
where
where
for
In this problem, we include battery operation into the microgrid to suppress the high demand at the high-cost time of utility electricity. Furthermore, we consider EV battery instead of the stationary battery storage to reduce the installation cost of the battery system.
Our microgrid model consists of
The generation cost function
For the microgrid internal trading, the revenue function of DGs has the following form:
Load demands are assumed as fixed parameters in this problem. The electricity cost of load demands is calculated by
For simplicity, we assume that EVs have only one round-trip route per day, and the home of each EV owner is the only charging point for each EV.
Denote
To reduce computational cost,
The state of charge (SOC) of EV battery at the starting point of a next time slot depends on the SOC at the starting point of current time slot and a charging/discharging efficiency
SOC constraint is as follows:
When EVs are at home (from the arrival time to the next departure time), their charging/discharging scheduling can be utilized for DR actions. The variable
Algorithm 1: |
---|
1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: |
The battery life function of EVs depends on EVs charging/discharging power [23], as follows:
where
The revenue function of EVs is defined in [21], taking into account the battery life cost:
The revenue function of the microgrid operator is calculated by
where
With the existence of EVs and the MG, the power balance constraint in the microgrid has more terms than that in the DSWM problem, as follows:
The PSwEV problem is to maximize the total revenue of DGs, EVs, load demands, and the microgrid operator, as follows:
s.t. (22), (9), (10), (13)–(19), and (21)
where
Substituting (11), (12) and (18)–(20) into (23), the PSwEV maximization programming in (23) can be rewritten as a minimization problem below:
As mentioned in Section 2, the optimization problem (1) will be solved by a sequential approach presented in the current section, which separates (1) into the following subproblems
and solves them starting from
The SDC-ADMM approach is based on MAS and consensus theory so that it can be run in parallel in all generation and consumption units. Hence, the MAS description for smart grid needs to be introduced first. More specifically, each agent is assigned to a generation or demand unit, and the communication among agents is represented by an undirected graph
To develop the SDC-ADMM approach, (25) is first reformulated into the 2-block form of ADMM. The following closed convex sets are defined corresponding to the global and local constraints:
together with their indicator functions [24]
Hence, (25) can be rewritten as follows:
Because the indicator function of a closed, non-empty convex set is proper, closed, and convex [25], the cost functions in (28) are also proper, closed, and convex with respect to
where
This algorithm is stopped if the criteria
with
In the following, the variables
The update of
of which the strong duality holds [25]. Let
Since
where
Consequently, the following consensus law is utilized:
where
Then the consensus of all agents is achieved, where the consensus states are
Thus, the optimal Lagrange multiplier can be obtained in a distributed manner by
Remark 1: If
The update of
Further, (42) and (43) is decentralized because both the cost function (42) and the constraint (43) are individually decomposable. Therefore, each agent (unit) just needs to solve a local scalar-constrained quadratic programming:
which is easily solved by existing methods.
For the DSWM problem, (45) is simply an interval, and
The convergence of the proposed SDC-ADMM algorithm can be proved in a similar manner to that in [26]; hence it is ignored here for brevity. In the following, a summary for the algorithm is provided.
Algorithm 2: |
---|
Each agent determines its local constraint set Each agent calculates All agents run the consensus law (39) with initial values (38), then compute Each agent updates its variable Each agent updates its variable Each agent updates its variable break; |
For several grid optimization problems represented in the form of (1), e.g., economic dispatch or power scheduling, DSWM, PSwEV, etc., an electricity pricing mechanism is needed to drive the electricity trading in the grid. Interestingly, the optimal Lagrange multiplier associated with the equality constraint (2) is often regarded as the market-clearing price. That will be proved under mild assumptions in the following:
where
The optimal energy price in the system is achieved when the market is cleared, at which the marginal costs of all agents are the same. Hence,
In the proposed SDC-ADMM algorithm, this means
Substituting (48) into (35), we have
If
Thus, as long as the proposed SDC-ADMM algorithm converges, the optimal energy price
In this section, simulation results for two problems, DSWM and PSwEV, are provided to illustrate the effectiveness of the proposed SDC-ADMM algorithm.
For this problem, a modified IEEE 39-bus system (see Figure 1) is used as the test system where it is assumed that there are PV generation units in the system with the total maximum output of 210 MW. The parameters of generators and demand units are taken from [26]. The average PV output curve, which is shown in Figure 2, is suitably scaled from the real PV data collected in New England [28]. Moreover, an average load profile taken from New England Independent System Operator [29] is utilized and properly scaled to obtain the time-varying upper bounds of demand units. This load profile has two demand peaks at 11:00 am and 8:00 pm, and the highest demand is at 8:00 pm, as seen in Figure 3.
IEEE 39-bus system.
PV output.
Total CG power and demand.
Other parameters in the simulation are as follows. The absolute and relative tolerances are set to be
Figures 3 and 4 display the total and individual power generated and consumed in the test system which are obtained by the proposed SDC-ADMM algorithm. Thanks to PV energy, the peak demand is shifted from 8 pm to 1 pm at which the PV output is maximum, as observed in Figure 3.
Individual power profile.
Then the electricity price is exhibited in Figure 5 showing that it is highest at 8 pm and lowest at 1–2 pm. This explains why the peak demand can be shifted. Next, the total welfare in the grid is shown in Figure 6 where the maximum welfare is attained at 1 pm when the consumers use most energy and the CG units produce least energy. Finally, Figure 7 shows the convergence of the proposed SDC-ADMM algorithm.
Electricity price.
Total social welfare.
Algorithm convergence.
In this test case, a microgrid having 2 DGs, 16 EVs, 4 load demands, 4 PV generations, and a microgrid operator is considered with a 3-day duration. The total number of agents is 27, in which the controllable agents are those for 2 DGs, 16 EVs, and the microgrid operator. The total PV curve and the total demand curve are given in Figure 8. The prescribed electricity transaction price
PV and demand curves.
Transaction price by utility.
The departure and arrival time and required traveling energies of 16 EVs are randomly generated from mix Gaussian distributions of this parameter of an actual set of 1400 EVs. The maximum energy capacity of each EV battery is 17.6 kWh, and the SOC limits of each EV battery are set at 20 and 80% of the maximum energy capacity, respectively.
The absolute and relative tolerances are set to be
Consequently, the simulations for hundreds of different scenarios corresponding to the above random times are run with the proposed SDC-ADMM algorithm. The results for one specific scenario are then shown in Figures 10–12.
DG power, EV charging power, and transaction price inside microgrid.
The state of charge of all EVs.
SDC-ADMM convergence.
Figure 10 shows the benefit of utilizing PV generation and EV charging in the microgrid. First, DG output power is reduced around the time period of high PV output, while the load demand is quite high. Second, when PV output is high, the microgrid operator can sell the redundant electricity to the utility at the highest price. Last, even though EVs do not have much correlation to PV output due to the EV traveling times, they still benefit the microgrid with their optimal charging and discharging schedules in which the charging is executed at low-price time periods of utility, and vice versa, the discharging is made at high-price time periods of utility. Moreover, the discharging also provides microgrid electricity for selling to the utility at a high price.
Subsequently, the SOC profiles of 16 EVs are depicted in Figure 11. It can be observed that the EV batteries will be charged in the early morning when the electricity price is low, but not to the maximum allowed SOC, i.e., 80% of maximum battery capacity, because of the using of EV charging/discharging strategy in Algorithm 1 and the realistic EV data that only around 6 kWh is enough for each EV round-trip. Further, the charged/discharged SOCs of EVs are different due to their differences on charging/discharging times and required energy for traveling.
Finally, the convergence of the proposed SDC-ADMM algorithm in the PSwEV problem is shown in Figure 11, and the consensus processes in the distributed algorithm for calculating the optimal electric price inside the microgrid are displayed in Figures 12 and 13.
Consensus for computing
In this chapter, a distributed optimization algorithm called sequential distributed consensus-based alternating direction method of multipliers (SDC-ADMM) is proposed for optimal energy management in smart grids. This algorithm is applicable to a broad class of linear or nonlinear constrained convex programming, of which two specific problems in smart grids have been studied in this chapter. The first problem DSWM tries to maximize the total social welfare in transmission grids in the presence of renewable energy and power losses, while the second problem PSwEV considers the power scheduling in distribution microgrids with renewable energy, electric vehicle as mobile storage, and a microgrid operator. It is then shown that the proposed SDC-ADMM algorithm works well for both problems, in which an optimal real-time electricity pricing scheme is derived as a part of the algorithm which facilitates demand response. Additionally, the existence of renewable energy and electric vehicles with suitable charging and discharging strategies is benefit to the grid for reducing the electricity price and the output power from nonrenewable energy generation.
The authors declare no conflict of interest.
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\n\nCorresponding authors will receive a 25% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters. A 20% discount for publishing a long-form monographs, 25% for compacts and 23% for short-form monographs.
\n\n\n\nCorresponding authors will receive a 25% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters. A 20% discount for publishing a long-form monographs, 25% for compacts and 23% for short-form monographs.
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