Volume 1 Optimization Methods Applied to Power Systems Francisco G. Montoya and Raúl Baños Navarro www.mdpi.com/journal/energies Edited by Printed Edition of the Special Issue Published in Energies Optimization Methods Applied to Power Systems Optimization Methods Applied to Power Systems Volume 1 Special Issue Editors Francisco G. Montoya Ra ́ ul Ba ̃ nos Navarro MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editors Francisco G. Montoya University of Almer ́ ıa Spain Ra ́ ul Ba ̃ nos Navarro University of Almer ́ ıa Spain Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Energies (ISSN 1996-1073) from 2018 to 2019 (available at: https://www.mdpi.com/journal/energies/special issues/optimization) For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year , Article Number , Page Range. Volume 1 ISBN 978-3-03921-130-2 (Pbk) ISBN 978-3-03921-131-9 (PDF) Volume 1-2 ISBN 978-3-03897- 154-8 (Pbk) ISBN 978-3-03897- 15 5 - 5 (PDF) c © 2019 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Preface to ”Optimization Methods Applied to Power Systems” . . . . . . . . . . . . . . . . . . ix Francisco G. Montoya, Ra ́ ul Ba ̃ nos, Alfredo Alcayde and Francisco Manzano-Agugliaro Optimization Methods Applied to Power Systems Reprinted from: Energies 2019 , 12 , 2302, doi:10.3390/en12122302 . . . . . . . . . . . . . . . . . . . 1 Li Zhang, Xiyue LuoYang, Yanjie Le, Fan Yang, Chun Gan and Yinxian Zhang A Thermal Probability Density–Based Method to Detect the Internal Defects of Power Cable Joints Reprinted from: Energies 2018 , 11 , 1674, doi:10.3390/en11071674 . . . . . . . . . . . . . . . . . . . 9 Mostafa Abdo, Salah Kamel, Mohamed Ebeed, Juan Yu and Francisco Jurado Solving Non-Smooth Optimal Power Flow Problems Using a Developed Grey Wolf Optimizer Reprinted from: Energies 2018 , 11 , 1692, doi:10.3390/en11071692 . . . . . . . . . . . . . . . . . . . 22 Nian Liu, Bin Guo, Zifa Liu, Yongli Wang Distributed Energy Sharing for PVT-HP Prosumers in Community Energy Internet: A Consensus Approach Reprinted from: Energies 2018 , 11 , 1891, doi:10.3390/en11071891 . . . . . . . . . . . . . . . . . . . 38 Lin Lin, Lin Xue, Zhiqiang Hu and Nantian Huang Modular Predictor for Day-Ahead Load Forecasting and Feature Selection for Different Hours Reprinted from: Energies 2018 , 11 , 1899, doi:10.3390/en11071899 . . . . . . . . . . . . . . . . . . . 56 Zhi Wu, Xiao Du, Wei Gu, Ping Ling, Jinsong Liu and Chen Fang Optimal Micro-PMU Placement Using Mutual Information Theory in Distribution Networks Reprinted from: Energies 2018 , 11 , 1917, doi:10.3390/en11071917 . . . . . . . . . . . . . . . . . . . 86 Jiangtao Yu, Chang-Hwan Kim, Abdul Wadood, Tahir Khurshiad and Sang-Bong Rhee A Novel Multi-Population Based Chaotic JAYA Algorithm with Application in Solving Economic Load Dispatch Problems Reprinted from: Energies 2018 , 11 , 1946, doi:10.3390/en11081946 . . . . . . . . . . . . . . . . . . . 105 Yonghui Sun, Yi Wang, Linquan Bai, Yinlong Hu, Denis Sidorov and Daniil Panasetsky Parameter Estimation of Electromechanical Oscillation Based on a Constrained EKF with C&I-PSO Reprinted from: Energies 2018 , 11 , 2059, doi:10.3390/en11082059 . . . . . . . . . . . . . . . . . . . 130 Zahir Sahli, Abdellatif Hamouda, Abdelghani Bekrar and Damien Trentesaux Reactive Power Dispatch Optimization with Voltage Profile Improvement Using an Efficient Hybrid Algorithm † Reprinted from: Energies 2018 , 11 , 2134, doi:10.3390/en11082134 . . . . . . . . . . . . . . . . . . . 145 Ana Ogando-Mart ́ ınez, Javier L ́ opez-G ́ omez and Lara Febrero-Garrido Maintenance Factor Identification in Outdoor Lighting Installations Using Simulation and Optimization Techniques Reprinted from: Energies 2018 , 11 , 2169, doi:10.3390/en11082169 . . . . . . . . . . . . . . . . . . . 166 v Guillermo Gutierrez-Alcaraz and Victor H. Hinojosa Using Generalized Generation Distribution Factors in a MILP Model to Solve the Transmission-Constrained Unit Commitment Problem Reprinted from: Energies 2018 , 11 , 2232, doi:10.3390/en11092232 . . . . . . . . . . . . . . . . . . . 179 Xiaofeng Dong, Xiaoshun Zhang and Tong Jiang Adaptive Consensus Algorithm for Distributed Heat-Electricity Energy Management of an Islanded Microgrid Reprinted from: Energies 2018 , 11 , 2236, doi:10.3390/en11092236 . . . . . . . . . . . . . . . . . . . 196 Sirote Khunkitti, Apirat Siritaratiwat, Suttichai Premrudeepreechacharn, Rongrit Chatthaworn and Neville R. Watson A Hybrid DA-PSO Optimization Algorithm for Multiobjective Optimal Power Flow Problems Reprinted from: Energies 2018 , 11 , 2270, doi:10.3390/en11092270 . . . . . . . . . . . . . . . . . . . 213 Jiyuan Kuang, Chenghui Zhang, Fan Li and Bo Sun Dynamic Optimization of Combined Cooling, Heating, and Power Systems with Energy Storage Units Reprinted from: Energies 2018 , 11 , 2288, doi:10.3390/en11092288 . . . . . . . . . . . . . . . . . . . 234 Ha-Lim Lee and Yeong-Han Chun Using Piecewise Linearization Method to PCS Input/Output-Efficiency Curve for a Stand-Alone Microgrid Unit Commitment Reprinted from: Energies 2018 , 11 , 2468, doi:10.3390/en11092468 . . . . . . . . . . . . . . . . . . . 250 Leehter Yao, Wei Hong Lim, Sew Sun Tiang, Teng Hwang Tan, Chin Hong Wong and Jia Yew Pang Demand Bidding Optimization for an Aggregator with a Genetic Algorithm Reprinted from: Energies 2018 , 11 , 2498, doi:10.3390/en11102498 . . . . . . . . . . . . . . . . . . . 263 Nasser Yimen, Oumarou Hamandjoda, Lucien Meva’a, Benoit Ndzana and Jean Nganhou Analyzing of a Photovoltaic/Wind/Biogas/Pumped-Hydro Off-Grid Hybrid System for Rural Electrification in Sub-Saharan Africa—Case Study of Djound ́ e in Northern Cameroon Reprinted from: Energies 2018 , 11 , 2644, doi:10.3390/en11102644 . . . . . . . . . . . . . . . . . . . 285 Nam-Kyu Kim, Myung-Hyun Shim and Dongjun Won Building Energy Management Strategy Using an HVAC System and Energy Storage System Reprinted from: Energies 2018 , 11 , 2690, doi:10.3390/en11102690 . . . . . . . . . . . . . . . . . . . 315 Joao Ferreira, Gustavo Callou, Dietmar Tutsch and Paulo Maciel PLDAD—An Algorihm to Reduce Data Center Energy Consumption Reprinted from: Energies 2018 , 11 , 2821, doi:10.3390/en11102821 . . . . . . . . . . . . . . . . . . . 330 Chang Ye, Shihong Miao, Yaowang Li, Chao Li and Lixing Li Hierarchical Scheduling Scheme for AC/DC Hybrid Active Distribution Network Based on Multi-Stakeholders Reprinted from: Energies 2018 , 11 , 2830, doi:10.3390/en11102830 . . . . . . . . . . . . . . . . . . . 354 vi About the Special Issue Editors Francisco G. Montoya , professor at the Engineering Department and the Electrical Engineering Section in the University of Almeria (Spain), received his M.S. from the University of Malaga and his Ph.D. from the University of Granada (Spain). He has published over 70 papers in JCR journals and is the author or coauthor of books published by MDPI, RA-MA, and others. His main interests are power quality, smart metering, smart grids and evolutionary optimization applied to power systems, and renewable energy. Recently, he has become passionately interested in Geometric Algebra as applied to Power Theory. Ra ́ ul Ba ̃ nos Navarro is an associate professor at the Department of Engineering, University of Almeria (Spain). He received his first Bachelor’s degree in Computer Science at the University of Almeria and his second Bachelor’s degree in Economics by the National University of Distance Education (UNED). He wrote his Ph.D. dissertation on computational methods applied to optimization of energy distribution in power networks. His research activity includes computational optimization, power systems, renewable energy systems, and engineering economics. The research is being carried out at Napier University (Edinburgh, UK) and at the Universidade do Algarve (Portugal). As a result of his research, he has published more than 150 papers in peer-reviewed journals, books, and conference proceedings. vii Preface to ”Optimization Methods Applied to Power Systems” Power systems are made up of extensive complex networks governed by physical laws in which unexpected and uncontrolled events can occur. This complexity has increased considerably in recent years due to the increase in distributed generation associated with increased generation capacity from renewable energy sources. Therefore, the analysis, design, and operation of current and future electrical systems require an efficient approach to different problems such as load flow, parameters and position finding, filter designing, fault location, contingency analysis, system restoration after blackout, islanding detection, economic dispatch, unit commitment, etc. The evolution is so frenetic that it is necessary for engineers to have sufficiently updated material to face the new challenges involved in the management of new generation networks (smart grids). Given the complexity of these problems, the efficient management of electrical systems requires the application of advanced optimization methods for decision-making processes. Electrical power systems have so greatly benefited from scientific and engineering advancements in the use of optimization techniques to the point that these advanced optimization methods are required to manage the analysis, design, and operation of electrical systems. Considering the high complexity of large-scale electrical systems, efficient network planning, operation, or maintenance requires the use of advanced techniques. Accordingly, besides classical optimization techniques such as Linear and Nonlinear Programming or Integer and Mixed-Integer Programming, other advanced techniques have been applied to great effect in the study of electrical systems. Specifically, bio-inspired meta-heuristics have allowed scientists to consider the optimization of problems of great importance and obtain quality solutions in reduced response times thanks to the increasing calculation power of the current computers. Therefore, this book includes recent advances in the application optimization techniques that directly apply to electrical power systems so that readers may familiarize themselves with new methodologies directly explained by experts in the field. Francisco G. Montoya, Ra ́ ul Ba ̃ nos Navarro Special Issue Editors ix energies Editorial Optimization Methods Applied to Power Systems Francisco G. Montoya *, Ra ú l Baños, Alfredo Alcayde and Francisco Manzano-Agugliaro Department of Engineering, University of Almeria, ceiA3, 04120 Almeria, Spain; rbanos@ual.es (R.B.); aalcayde@ual.es (A.A.); fmanzano@ual.es (F.M.-A.) * Correspondence: pagilm@ual.es; Tel.: + 34-950-015791; Fax: + 34-950-015491 Received: 6 May 2019; Accepted: 13 June 2019; Published: 17 June 2019 1. Introduction Continuous advances in computer hardware and software are enabling researchers to address optimization solutions using computational resources, as can be seen in the large number of optimization approaches that have been applied to the energy field. Power systems are made up of extensive complex networks governed by physical laws in which unexpected and uncontrolled events can occur. This complexity has increased considerably in recent years due to the increase in distributed generation associated with increased generation capacity from renewable energy sources. Therefore, the analysis, design, and operation of current and future electrical systems require an e ffi cient approach to di ff erent problems (like load flow, parameters and position finding, filter design, fault location, contingency analysis, system restoration after blackout, islanding detection of distributed generation, economic dispatch, unit commitment, etc.). Given the complexity of these problems, the e ffi cient management of electrical systems requires the application of advanced optimization methods that take advantage of high-performance computer clusters. This special issue belongs to the section “Electrical Power and Energy System”. The topics of interest in this special issue include di ff erent optimization methods applied to any field related to power systems, such as conventional and renewable energy generation, distributed generation, transport and distribution of electrical energy, electrical machines and power electronics, intelligent systems, advances in electric mobility, etc. The optimization methods of interest for publication include, but are not limited to: • Expert Systems • Artificial Neural Networks • Fuzzy Logic • Genetic Algorithms • Evolutionary Algorithms • Simulated Annealing • Tabu Search • Ant Colony Optimization • Particle Swarm Optimization • Multi-Objective Optimization • Parallel Computing • Linear and Nonlinear Programming • Integer and Mixed-Integer Programming • Dynamic Programming • Interior Point Methods • Lagrangian Relaxation and Benders Decomposition-Based Methods • General Stochastic Techniques. Energies 2019 , 12 , 2302; doi:10.3390 / en12122302 www.mdpi.com / journal / energies 1 Energies 2019 , 12 , 2302 2. Statistics of the Special Issue The statistics of the call for papers for this special issue related to published or rejected items were: Total submissions (113), published (36; 31.8%), and rejected (77; 68.3%). The authors’ geographical distribution by countries for published papers is shown in Table 1, where it is possible to observe 144 authors from 19 di ff erent countries. Note that it is usual for an article to be signed by more than one author, and for authors to collaborate with others of di ff erent a ffi liation. Table 1. Geographic distribution by countries of authors. Country Number of Authors China 80 Spain 11 South Korea 9 Cameroon 5 Malaysia 5 United States 5 Taiwan 4 Thailand 4 Viet Nam 4 Brazil 3 Egypt 3 Algeria 2 France 2 Russian Federation 2 Chile 1 Germany 1 Mexico 1 New Zealand 1 Singapore 1 Total 144 3. Authors of this Special Issue The authors of this special issue and their main bibliometric indicators are summarized in Table 2, where they have been ordered from the highest to the lowest H-index. The novel authors, those considered with an H-index equal to zero are 29, and those of H-index equal to 1 are 27. On the other hand, the internationally recognized authors, those considered with an H-index of 10 or higher, are 31. It is remarkable that these authors (H-index ≥ 10), on average, have more than 123 co-authors, more than 110 documents published, and more than 1069 citations. Table 2. A ffi liations and bibliometric indicators for the authors. Author A ffi liation Jurado F. Universidad de Jaen Watson N. University of Canterbury Trentesaux D. University of Valenciennes et du Hainaut-Cambresis Liu N. North China Electric Power University Premrudeepreechacharn S. Chiang Mai University Sun Y. Hohai University Gu W. Southeast University Aguado, J.A. Universidad de M á laga Baños R. Universidad de Almeria Montoya F. Universidad de Almeria Maciel P. Universidade Federal de Pernambuco Liu M. South China University of Technology Zhang C. Shandong University Liu Z. North China Electric Power University 2 Energies 2019 , 12 , 2302 Table 2. Cont. Author A ffi liation Wu Z. Southeast University Miao S. Huazhong University of Science and Technology Yu J. Chongqing University Ferreira J. Universidade de Pernambuco Won D. Inha University, Incheon Bai L. The University of North Carolina at Charlotte Hu Y. Hohai University Yao L. National Taipei University of Technology Lim W. UCSI University Yang F. Chongqing University Sun H. Hebei University of Technology Callou G. Universidade Federal Rural de Pernambuco Lee J. University of Louisiana at Lafayette Zhao D. North China Electric Power University Zhang X. Shantou University Li Y. Zhejiang University City College Guti é rrez-Alcaraz G. Tecnol ó gico Nacional de M é xico / I.T. Huang N. Northeast Electric Power University Xiang J. Zhejiang University Morshed M. University of Louisiana at Lafayette Sun B. Shandong University Bekrar A. University of Valenciennes et du Hainaut-Cambresis Rhee S. Yeungnam University Kamel S. Aswan University Xie M. South China University of Technology Tutsch D. Bergische Universitat Wuppertal Sidorov D. Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences Zhang X. Nanyang Technological University Zhou B. China Southern Power Grid Perng J. National Sun Yat-Sen University Taiwan Panasetsky D. Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences Zheng T. Tsinghua University Li J. Northeast China Institute of Electric Power Engineering Hinojosa V. Universidad T é cnica Federico Santa Mar í a Siritaratiwat A. Khon Kaen University Hua D. South China University of Technology Hamouda A. Universit é Ferhat Abbas de S é tif Zhang L. Tianjin University of Commerce Alcayde A. Universidad de Almeria Ge W. State Grid Liaoning Electric Power Supply Co., Ltd. Zhang L. Chongqing University Zhang C. Hunan University Wu J. Beihang University Wang Y. North China Electric Power University Febrero-Garrido L. Defense University Center Chambers T. University of Louisiana at Lafayette Truong A. HCMC University of Technology and Education Nganhou J. University of Yaound é Li Y. Huazhong University of Science and Technology Lin L. Jilin Institute of Chemical Technology Jiang T. North China Electric Power University Ebeed M. Sohag University Chatthaworn R. Khon Kaen University Duong T. Industrial University of Ho Chi Minh City Hamandjoda O. University of Yaound é 3 Energies 2019 , 12 , 2302 Table 2. Cont. Author A ffi liation Chun Y. Hongik University Ye C. Huazhong University of Science and Technology Mei S. Qinghai University Nguyen T. Industrial University of Ho Chi Minh City Mao T. China Southern Power Grid Wang Y. Hohai University Arrabal-Campos F. Universidad de Almeria Tiang S. UCSI University Hmida J. University of Louisiana at Lafayette Tan T. UCSI University Chen S. Anqing Teachers College Sahli Z. Universit é Ferhat Abbas de S é tif Kim C. Yeungnam University Li F. Shandong University Meva’a L. University of Yaound é Wadood A. Yeungnam University Le Y. State Grid Zhejiang Electric Power Corporation Khunkitti S. Khon Kaen University Hong Wong C. UCSI University Shim M. Inha University, Incheon Dong X. North China Electric Power University Du Y. State Grid Ganzhou Electric Power Supply Company Xie L. China Electric Power Research Institute Li L. Huazhong University of Science and Technology Du X. Southeast University Fang C. State Grid Shanghai Municipal Electric Power Company Ndzana B. University of Yaound é Yew Pang J. Heriot-Watt University, Malaysia Hu Z. Zhejiang Electric Power CorporationWenzhou Power Supply Company Chen Y. Zhejiang University Liu J. State Grid Shanghai Municipal Electric Power Company Xue L. Northeast China Institute of Electric Power Engineering Yimen N. University of Yaound é Khurshiad T. Yeungnam University Kim N. Hyosung Group Shao B. State Grid Liaoning Electric Power Company Limited Electric Power Research Institute Guo B. Jilin University Li K. Beihang University Kuang J. Shandong University Yu J. Anyang Institute of Technology Sun J. Beihang University Ling P. State Grid Shanghai Municipal Electric Power Company Guo B. North China Electric Power University Li C. Huazhong University of Science and Technology Leiva, J Universidad de Malaga Li J. Electric Power Research Institute of State Grid Liaoning Electric Power Co. Ltd. Kuo Y. Taiwan Power Company Yang X. Chongqing University Yu L. Tianjin University of Commerce Zhang Y. Zhoushan Power Company of State Grid Niu F. Zhejiang University Ogando-Mart í nez A. Universidad de Vigo Han X. State Grid Sichuan Electric Power Company Ren X. Tianjin University of Commerce Gan C. Zhoushan Power Company of State Grid 4 Energies 2019 , 12 , 2302 Table 2. Cont. Author A ffi liation Xiao L. Tianjin University of Commerce Fan C. State Grid Sichuan Electric Power Research Institute Ton T. Thu Duc College of Technology Zhang J. Northeast Electric Power University Chen H. Tsinghua University Zhou H. Northeast Electric Power University L ó pez-G ó mez J. Universidad de Vigo Jiang S. Anqing Teachers College Lu S. Taiwan Power Company Sun G. South China University of Technology Cheng P. Guangzhou Power Supply Bureau Co., Ltd. Li X. North China Electric Power University Cheng W. Shenzhen Power Supply Bureau Co., Ltd. Cheng R. Shenzhen Power Supply Bureau Co., Ltd. Lee H. Korea Electrotechnology Research Institute Chen Z. State Grid Sichuan Electric Power Research Institute Shi J. Shenzhen Power Supply Bureau Co., Ltd. Abdo M. Aswan University Carmona R. Universidad de Malaga Wei W. South China University of Technology 4. Brief Overview of the Contributions to this Special Issue 4.1. Keyword Analysis The analysis of the keywords identifies or summarizes the work of the researchers. This section analyses the keywords obtained from the 36 manuscripts published in this special issue [ 1 – 36 ]. The keyword analysis of the papers of this special issue shows a wide variety of terms, reaching 135 di ff erent keywords. Figure 1 shows a cloud of words using author keywords. The most used and highlighted keywords are: Optimal power flow, genetic algorithm, optimization, particle swarm optimization, demand response, energy management, metaheuristic, and wind power. If we split the author keywords in simple words, it is possible to get Figure 2, where the highlighted words are now: Optimal, power, energy, system, and algorithm. Figure 1. Cloud word of the author keywords related to the special issue. 5 Energies 2019 , 12 , 2302 Figure 2. Cloud word for split author keywords related to the special issue. 4.2. Analysis of Author Relationship Figure 3 shows a graph with the authors of this special issue. Each author is a node and a di ff erent color indicates their a ffi liation country. If an author collaborates with another one, then a link highlights the relationship between them. The larger the size of the node, the larger the H-index of this author. As expected, there is no relationship between authors of the di ff erent manuscripts, unless they are authors who have contributed to more than one, but they were exactly the same authors. What does attract attention is that there are at least nine papers with international collaboration, i.e., between authors from di ff erent countries, and two of them are collaborations between authors from at least three di ff erent countries. Figure 3. International interconnection between authors. 6 Energies 2019 , 12 , 2302 Conflicts of Interest: The authors declare no conflict of interest References 1. Leiva, J.; Carmona Pardo, R.; Aguado, J.A. Data Analytics-Based Multi-Objective Particle Swarm Optimization for Determination of Congestion Thresholds in LV Networks. Energies 2019 , 12 , 1295. [CrossRef] 2. Alcayde, A.; Baños, R.; Arrabal Campos, F.M.; Montoya, F.G. Optimization of the Contracted Electric Power by Means of Genetic Algorithms. Energies 2019 , 12 , 1270. [CrossRef] 3. Montoya, F.G.; Alcayde, A.; Arrabal Campos, F.M.; Baños, R. Quadrature Current Compensation in Non-Sinusoidal Circuits Using Geometric Algebra and Evolutionary Algorithms. Energies 2019 , 12 , 692. [CrossRef] 4. Chen, Z.; Han, X.; Fan, C.; Zheng, T.; Mei, S. A Two-Stage Feature Selection Method for Power System Transient Stability Status Prediction. Energies 2019 , 12 , 689. [CrossRef] 5. Xie, M.; Du, Y.; Cheng, P.; Wei, W.; Liu, M. A Cross-Entropy-Based Hybrid Membrane Computing Method for Power System Unit Commitment Problems. Energies 2019 , 12 , 486. [CrossRef] 6. Chen, S.; Chen, H.; Jiang, S. Optimal Decision-Making to Charge Electric Vehicles in Heterogeneous Networks: Stackelberg Game Approach. Energies 2019 , 12 , 325. [CrossRef] 7. Mao, T.; Zhang, X.; Zhou, B. Intelligent Energy Management Algorithms for EV-charging Scheduling with Consideration of Multiple EV Charging Modes. Energies 2019 , 12 , 265. [CrossRef] 8. Xiao, L.; Sun, H.; Zhang, L.; Niu, F.; Yu, L.; Ren, X. Applications of a Strong Track Filter and LDA for On-Line Identification of a Switched Reluctance Machine Stator Inter-Turn Shorted-Circuit Fault. Energies 2019 , 12 , 134. [CrossRef] 9. Viet Truong, A.; Ngoc Ton, T.; Thanh Nguyen, T.; Duong, T. Two States for Optimal Position and Capacity of Distributed Generators Considering Network Reconfiguration for Power Loss Minimization Based on Runner Root Algorithm. Energies 2019 , 12 , 106. [CrossRef] 10. Perng, J.W.; Kuo, Y.C.; Lu, S.P. Grounding System Cost Analysis Using Optimization Algorithms. Energies 2018 , 11 , 3484. [CrossRef] 11. Li, X.; Zhao, D.; Guo, B. Decentralized and Collaborative Scheduling Approach for Active Distribution Network with Multiple Virtual Power Plants. Energies 2018 , 11 , 3208. [CrossRef] 12. Cheng, W.; Cheng, R.; Shi, J.; Zhang, C.; Sun, G.; Hua, D. Interval Power Flow Analysis Considering Interval Output of Wind Farms through A ffi ne Arithmetic and Optimizing-Scenarios Method. Energies 2018 , 11 , 3176. [CrossRef] 13. Chen, Y.; Xiang, J.; Li, Y. SOCP Relaxations of Optimal Power Flow Problem Considering Current Margins in Radial Networks. Energies 2018 , 11 , 3164. [CrossRef] 14. Li, J.J.; Shao, B.Z.; Li, J.H.; Ge, W.C.; Zhang, J.H.; Zhou, H.Y. Intelligent Regulation Method for a Controllable Load Used for Improving Wind Power Integration. Energies 2018 , 11 , 3085. [CrossRef] 15. Wu, J.; Li, K.; Sun, J.; Xie, L. A Novel Integrated Method to Diagnose Faults in Power Transformers. Energies 2018 , 11 , 3041. [CrossRef] 16. Ben Hmida, J.; Javad Morshed, M.; Lee, J.; Chambers, T. Hybrid Imperialist Competitive and Grey Wolf Algorithm to Solve Multiobjective Optimal Power Flow with Wind and Solar Units. Energies 2018 , 11 , 2891. [CrossRef] 17. Ye, C.; Miao, S.; Li, Y.; Li, C.; Li, L. Hierarchical Scheduling Scheme for AC / DC Hybrid Active Distribution Network Based on Multi-Stakeholders. Energies 2018 , 11 , 2830. [CrossRef] 18. Ferreira, J.; Callou, G.; Tutsch, D.; Maciel, P. PLDAD—An Algorihm to Reduce Data Center Energy Consumption. Energies 2018 , 11 , 2821. [CrossRef] 19. Kim, N.K.; Shim, M.H.; Won, D. Building Energy Management Strategy Using an HVAC System and Energy Storage System. Energies 2018 , 11 , 2690. [CrossRef] 20. Yimen, N.; Hamandjoda, O.; Meva’a, L.; Ndzana, B.; Nganhou, J. Analyzing of a photovoltaic / wind / biogas / pumped-hydro o ff -grid hybrid system for rural electrification in Sub-Saharan Africa—Case study of Djound é in Northern Cameroon. Energies 2018 , 11 , 2644. [CrossRef] 21. Yao, L.; Lim, W.; Tiang, S.; Tan, T.; Wong, C.; Pang, J. Demand bidding optimization for an aggregator with a Genetic Algorithm. Energies 2018 , 11 , 2498. [CrossRef] 7 Energies 2019 , 12 , 2302 22. Lee, H.L.; Chun, Y.H. Using Piecewise Linearization Method to PCS Input / Output-E ffi ciency Curve for a Stand-Alone Microgrid Unit Commitment. Energies 2018 , 11 , 2468. [CrossRef] 23. Kuang, J.; Zhang, C.; Li, F.; Sun, B. Dynamic Optimization of Combined Cooling, Heating, and Power Systems with Energy Storage Units. Energies 2018 , 11 , 2288. [CrossRef] 24. Khunkitti, S.; Siritaratiwat, A.; Premrudeepreechacharn, S.; Chatthaworn, R.; Watson, N. A Hybrid DA-PSO Optimization Algorithm for Multiobjective Optimal Power Flow Problems. Energies 2018 , 11 , 2270. [CrossRef] 25. Dong, X.; Zhang, X.; Jiang, T. Adaptive Consensus Algorithm for Distributed Heat-Electricity Energy Management of an Islanded Microgrid. Energies 2018 , 11 , 2236. [CrossRef] 26. Gutierrez Alcaraz, G.; Hinojosa, V. Using Generalized Generation Distribution Factors in a MILP Model to Solve the Transmission-Constrained Unit Commitment Problem. Energies 2018 , 11 , 2232. [CrossRef] 27. Ogando Mart í nez, A.; L ó pez G ó mez, J.; Febrero-Garrido, L. Maintenance Factor Identification in Outdoor Lighting Installations Using Simulation and Optimization Techniques. Energies 2018 , 11 , 2169. [CrossRef] 28. Sahli, Z.; Hamouda, A.; Bekrar, A.; Trentesaux, D. Reactive Power Dispatch Optimization with Voltage Profile Improvement Using an E ffi cient Hybrid Algorithm. Energies 2018 , 11 , 2134. [CrossRef] 29. Sun, Y.; Wang, Y.; Bai, L.; Hu, Y.; Sidorov, D.; Panasetsky, D. Parameter Estimation of Electromechanical Oscillation Based on a Constrained EKF with C&I-PSO. Energies 2018 , 11 , 2059. 30. Yu, J.; Kim, C.H.; Wadood, A.; Khurshiad, T.; Rhee, S.B. A novel multi-population based chaotic JAYA algorithm with application in solving economic load dispatch problems. Energies 2018 , 11 , 1946. [CrossRef] 31. Wu, Z.; Du, X.; Gu, W.; Ling, P.; Liu, J.; Fang, C. Optimal Micro-PMU Placement Using Mutual Information Theory in Distribution Networks. Energies 2018 , 11 , 1917. [CrossRef] 32. Lin, L.; Xue, L.; Hu, Z.; Huang, N. Modular predictor for day-ahead load forecasting and feature selection for di ff erent hours. Energies 2018 , 11 , 1899. [CrossRef] 33. Liu, N.; Guo, B.; Liu, Z.; Wang, Y. Distributed Energy Sharing for PVT-HP Prosumers in Community Energy Internet: A Consensus Approach. Energies 2018 , 11 , 1891. [CrossRef] 34. Abdo, M.; Kamel, S.; Ebeed, M.; Yu, J.; Jurado, F. Solving Non-Smooth Optimal Power Flow Problems Using a Developed Grey Wolf Optimizer. Energies 2018 , 11 , 1692. [CrossRef] 35. Zhang, L.; LuoYang, X.; Le, Y.; Yang, F.; Gan, C.; Zhang, Y. A Thermal Probability Density–Based Method to Detect the Internal Defects of Power Cable Joints. Energies 2018 , 11 , 1674. [CrossRef] 36. Bravo Rodr í guez, J.C.; del Pino L ó pez, J.C.; Cruz Romero, P. A Survey on Optimization Techniques Applied to Magnetic Field Mitigation in Power Systems. Energies 2019 , 12 , 1332. [CrossRef] © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http: // creativecommons.org / licenses / by / 4.0 / ). 8 energies Article A Thermal Probability Density–Based Method to Detect the Internal Defects of Power Cable Joints Li Zhang 1 , Xiyue LuoYang 1, *, Yanjie Le 2 , Fan Yang 1 , Chun Gan 2 and Yinxian Zhang 2 1 State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China; zldy02@cqu.edu.cn (L.Z.); yangfancqu@gmail.com (F.Y.) 2 Zhoushan Power Company of State Grid, Zhoushan 316021, China; fylhfut@126.com (Y.L.); czxvbnmcz@126.com (C.G.); matthew920619@gmail.com (Y.Z.) * Correspondence: luoyangxiyue@163.com; Tel.: +86-187-2584-8089 Received: 22 May 2018; Accepted: 22 June 2018; Published: 27 June 2018 Abstract: Internal defects inside power cable joints due to unqualified construction is the main issue of power cable failures, hence in this paper a method based on thermal probability density function to detect the internal defects of power cable joints is presented. First, the model to calculate the thermal distribution of power cable joints is set up and the thermal distribution is calculated. Then a thermal probability density (TPD)-based method that gives the statistics of isothermal points is presented. The TPD characteristics of normal power cable joints and those with internal defects, including insulation eccentricity and unqualified connection of conductors, are analyzed. The results indicate that TPD differs with the internal state of cable joints. Finally, experiments were conducted in which surface thermal distribution was measured by FLIR SC7000, and the corresponding TPDs are discussed. Keywords: Cable joint; internal defect; thermal probability density 1. Introduction Unqualified construction and external destruction are the main issues in internal defects of power cable joints. The statistics show that more than 70% of defects occurred in cable joints during the past decade [ 1 ]. Internal defects of power cables will cause an increase of electromagnetic loss, insulation aging, and surface temperature changes. Excessive contact resistance due to unqualified connections of conductors and eccentricity of the core are common internal defects of cable joints. At present, many researchers concentrate on calculating and measuring power cable temperature characteristics, because the working conditions of cable joints can be derived from the surface temperature. Many measuring techniques have been proposed, including temperature sensors, optical fibers, infrared thermal imagers, and so on [ 2 – 4 ]. Due to the advantages of their noncontact, secure, and real-time characteristics [ 5 , 6 ], infrared thermal imagers are widely used in fault monitoring and diagnosing [7,8]. At present, researchers concentrate on thermal analysis to check the faults and ampacity of power cables. In [ 9 ], a method to invert the temperature of conductors in cable joints was proposed, which was composed of two parts, radial-direction temperature inversion (RDTI) in the cable and axial-direction temperature inversion (ADTI) in the conductor. Reference [ 10 ] stated that the failure of cables and their joints can be classified by estimating or measuring ambient temperature and other parameters, because the temperature of cable insulation is a function of both ambient temperature and thermal resistivity of the ground. Reference [ 11 ] applied thermographic analysis to analyze associated regions with high surface temperature and proposed a method to diagnose faulty connections of parallel conductors. In [ 12 ], an equivalent Laplace thermal model of single-core cable was developed with lumped parameter methods based on the thermal circuit model. Reference [ 13 ] found that the partial discharge Energies 2018 , 11 , 1674; doi:10.3390/en11071674 www.mdpi.com/journal/energies 9