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12 pages, 1376 KiB  
Article
A High Dynamic Range and Fast Response Logarithmic Amplifier Employing Slope-Adjustment and Power-Down Mode
by Yanhu Wang, Rui Teng, Yuanjie Zhou, Mengchen Lu, Wei Ruan and Jiapeng Li
Micromachines 2025, 16(7), 741; https://doi.org/10.3390/mi16070741 - 25 Jun 2025
Viewed by 236
Abstract
Based on the GSMC 180 nm SiGe BiCMOS process, a parallel-summation logarithmic amplifier is presented in this paper. The logarithmic amplifier adopts a cascaded structure of nine-stage fully-differential limiting amplifiers (LA) to achieve high dynamic range. The ten-stage rectifier completes the conversion of [...] Read more.
Based on the GSMC 180 nm SiGe BiCMOS process, a parallel-summation logarithmic amplifier is presented in this paper. The logarithmic amplifier adopts a cascaded structure of nine-stage fully-differential limiting amplifiers (LA) to achieve high dynamic range. The ten-stage rectifier completes the conversion of amplified voltage to a logarithmic current signal. A log slope adjuster is proposed. It can provide slopes of 17–30 mV/dB by configuring an off-chip resistor to meet the detection requirements of different input power. Meanwhile, a power-down control unit is designed to reduce the power consumption to only 162 μW in standby mode. The post-simulation results show that under 5 V power supply voltage, the dynamic range exceeds 80 dB and the 3 dB bandwidth is 20 MHz–4 GHz. It also has a fast response time of 42 ns with a power consumption of 109 mW in normal operation mode. Full article
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14 pages, 2954 KiB  
Article
Towards Sustainable Magnetic Resonance Neuro Imaging: Pathways for Energy Optimization and Cost Reduction Strategies
by Zélie Alerte, Mateusz Chodorowski, Samy Ammari, Alex Rovira, Julien Ognard and Douraied Ben Salem
Appl. Sci. 2025, 15(3), 1305; https://doi.org/10.3390/app15031305 - 27 Jan 2025
Cited by 1 | Viewed by 2190
Abstract
We evaluated the energy consumption of a 3T MRI using a central monitoring system, focusing on hospital energy costs during peak winter months from 2021 to 2023. We analyzed consumption during non-productive phases like end-of-day standby and assessed their impact. For active use, [...] Read more.
We evaluated the energy consumption of a 3T MRI using a central monitoring system, focusing on hospital energy costs during peak winter months from 2021 to 2023. We analyzed consumption during non-productive phases like end-of-day standby and assessed their impact. For active use, we compared standard and AI-enhanced protocols on phantoms, scheduling high-demand protocols during off-peak hours to benefit from lower energy prices. Standard protocols consumed 3.4 to 15 kWh, while optimized protocols used 2.3 to 10.6 kWh, reducing consumption by 32% on average. Savings per scan ranged from EUR 0.03 to EUR 3.7. The electrical consumption of a brain MRI protocol is equivalent to that of 3–4 knee protocols or 2–3 lumbar spine protocols. Using AI-optimized protocols and management, 41 protocols can be completed in 12 h, up from 30, reducing daily costs by EUR 2.38 to EUR 29.18. Annually, AI-optimized protocols could save 7900 to 8800 kWh per MRI unit, totaling 10,500 to 11,600 MWh across France’s MRI fleet, equivalent to the yearly consumption of about 4700 to 5300 people. Optimizing MRI resource use can expand patient access while significantly reducing the associated energy footprint. These findings support the implementation of more sustainable practices in medical imaging without compromising care quality. Full article
(This article belongs to the Special Issue MR-Based Neuroimaging)
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6 pages, 147 KiB  
Perspective
Consequences of Hospital Closures for the Health Insurance Industry in the United States
by Rainer W. G. Gruessner
Hospitals 2025, 2(1), 2; https://doi.org/10.3390/hospitals2010002 - 26 Jan 2025
Viewed by 1138
Abstract
Hospital and health system bankruptcies and closures continue to rise in the United States. They are troubling news not only for patients and communities but also for insurance companies. Hospital closures often lead to higher costs for insurers due to increased claim denials, [...] Read more.
Hospital and health system bankruptcies and closures continue to rise in the United States. They are troubling news not only for patients and communities but also for insurance companies. Hospital closures often lead to higher costs for insurers due to increased claim denials, delayed payments, reduced provider network and access to care, higher out-of-network costs, and a disruption of our healthcare system. These factors ultimately impact the health insurance companies’ bottom lines as well as their ability to manage patient care effectively with the risk of causing customer/patient dissatisfaction. Insurance companies can help prevent hospital closures, especially in rural areas, by implementing some of the following mechanisms: timely and adequate payments; improved patient-centric payment systems; and standby capacity payments to cover minimum fixed costs. Such early strategic investments have the potential to offset the higher costs for insurance companies associated with hospital closures and improve the sustainability of the U.S. healthcare system. Full article
15 pages, 2276 KiB  
Article
Reliability and Sensitivity Analysis of Wireless Sensor Network Using a Continuous-Time Markov Process
by Amit Kumar, Sujata Jadhav and Omar Mutab Alsalami
Mathematics 2024, 12(19), 3057; https://doi.org/10.3390/math12193057 - 29 Sep 2024
Cited by 2 | Viewed by 1723
Abstract
A remarkably high growth has been observed in the uses of wireless sensor networks (WSNs), due to their momentous potential in various applications, namely the health sector, smart agriculture, safety systems, environmental monitoring, military operations, and many more. It is quite important that [...] Read more.
A remarkably high growth has been observed in the uses of wireless sensor networks (WSNs), due to their momentous potential in various applications, namely the health sector, smart agriculture, safety systems, environmental monitoring, military operations, and many more. It is quite important that a WSN must have high reliability along with the least MTTF. This paper introduces a continuous-time Markov process, which is a special case of stochastic process, based on modeling of a wireless sensor network for analyzing the various reliability indices of the same. The modeling has been conducted by considering the different components, including the sensing unit, transceiver, microcontroller, power supply, standby power supply unit, and their failures/repairs, which may occur during their functioning. The study uncovered different important assessment parameters like reliability, components-wise reliability, MTTF, and sensitivity analysis. The critical components of a WSN are identified by incorporating the concept of sensitivity analysis. The outcomes emphasize that the proposed model will be ideal for understanding different reliability indices of WSNs and guiding researchers and potential users in developing a more robust wireless sensor network system. Full article
(This article belongs to the Special Issue Graph Theory and Network Theory)
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28 pages, 769 KiB  
Article
C0–Semigroups Approach to the Reliability Model Based on Robot-Safety System
by Ehmet Kasim and Aihemaitijiang Yumaier
Axioms 2024, 13(7), 423; https://doi.org/10.3390/axioms13070423 - 24 Jun 2024
Cited by 1 | Viewed by 1033
Abstract
This paper considers a system with one robot and n safety units (one of which works while the others remain on standby), which is described by an integro-deferential equation. The system can fail in the following three ways: fails with an incident, fails [...] Read more.
This paper considers a system with one robot and n safety units (one of which works while the others remain on standby), which is described by an integro-deferential equation. The system can fail in the following three ways: fails with an incident, fails safely and fails due to the malfunction of the robot. Using the C0semigroups theory of linear operators, we first show that the system has a unique non-negative, time-dependent solution. Then, we obtain the exponential convergence of the time-dependent solution to its steady-state solution. In addition, we study the asymptotic behavior of some time-dependent reliability indices and present a numerical example demonstrating the effects of different parameters on the system. Full article
(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)
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16 pages, 9312 KiB  
Article
Village Settlements’ Perspective on Rural Water Accessibility: A Mountainous Water Security Measurement Approach
by Jie Li, Ruijing Qiao, Lexuan Liu, Kai Wu, Pengbo Du, Kun Ye and Wei Deng
Sustainability 2024, 16(11), 4372; https://doi.org/10.3390/su16114372 - 22 May 2024
Viewed by 1891
Abstract
In rural planning, ensuring sustainable water management is pivotal, particularly in addressing the challenges posed by the absence of comprehensive rural water security assessments. Despite the abundance of water resources in mountainous regions, their accessibility and utilization remain significant hurdles for local populations, [...] Read more.
In rural planning, ensuring sustainable water management is pivotal, particularly in addressing the challenges posed by the absence of comprehensive rural water security assessments. Despite the abundance of water resources in mountainous regions, their accessibility and utilization remain significant hurdles for local populations, often hindering sustainable development. This study proposed a rural water accessibility (RWA) model, focusing on village settlements (VSs) as fundamental units for water utilization. The model examines two critical aspects of mountainous water security that are essential for sustainability: the supply–demand relation between VSs and their water sources, and the water availability to characterize difficulties in obtaining water sources in complex terrain. Using data from 1156 natural VSs in Dongchuan District, Kunming, water demand was calculated based on population and local average rural water demand per person. Springs and streams were identified as main and standby water sources, respectively. The RWA model evaluates the supply–demand balance and assesses water availability using the least-cost path (LCP) method. The results establish RWA grades, indicating water security conditions for VSs. This approach effectively identifies supply–demand relations and determines water demand gaps, facilitating targeted water management in rural areas, especially during droughts. It enables managers to accurately gauge the grade of water accessibility for each VS, allowing for prompt and tailored emergency water supply interventions. Furthermore, aggregating the RWA of each VS can provide valuable insights for devising sustainable water management strategies in mountainous regions. Full article
(This article belongs to the Section Sustainable Water Management)
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25 pages, 5635 KiB  
Article
Research on Market Evaluation Model of Reserve Auxiliary Service Based on Two-Stage Optimization of New Power System
by Boyang Qu and Lisi Fu
Energies 2024, 17(8), 1921; https://doi.org/10.3390/en17081921 - 17 Apr 2024
Cited by 2 | Viewed by 992
Abstract
Large-scale fluctuating and intermittent new energy power generation in a new power system is gradually connected to the grid. In view of the impact of the uncertainty of wind power on the spinning reserve capacity of thermal power units in the new power [...] Read more.
Large-scale fluctuating and intermittent new energy power generation in a new power system is gradually connected to the grid. In view of the impact of the uncertainty of wind power on the spinning reserve capacity of thermal power units in the new power system’s day-ahead dispatching and reserve auxiliary service market, the original dispatching mode and intensity can no longer meet the system demand. To address this problem, the establishment of a wind power grid-connected new power system’s standby auxiliary service market reward and punishment assessment mechanism is undertaken to fundamentally reduce the demand for auxiliary services of the new power system pressure. In the first part of this paper, a two-stage optimal scheduling strategy is proposed for the first day of the year that takes into account the operational risk and standby economics. First, a data-driven method is used to generate the forecast value of the wind power interval before the day, and a unit start–stop optimization model (the first-stage optimization model) is established by taking into account the CvaR (conditional value at risk) theory to optimize the risk loss of wind abandonment and loss of load and the fuel cost of each unit, and an optimization algorithm is used to carry out the three scenarios and the corresponding four scenarios to optimize the configuration of the start–stop state and power output of each unit. The optimization algorithm is used to optimize the starting and stopping status and output of each unit for three circumstances and four corresponding scenarios. Then, in the second stage, a standby auxiliary service market incentive and penalty assessment model is established to effectively coordinate the sharing of rotating standby capacity and cost among thermal power units through the incentive and penalty mechanism so as to make a reasonable and efficient allocation of wind power output, curtailable load, and synchronized standby capacity. The new power system with improved IEEE30 nodes is simulated and verified, and it is found that the two-stage optimization model obtains a scheduling strategy that takes into account the system operating cost, standby economy, and reliability, and at the same time, through the standby auxiliary service market incentive and penalty assessment mechanism, the extra cost caused by standby cost mismatch can be avoided. This evaluation model provides a reference for the safe, efficient, flexible, and nimble operation of the new power system, improves the economic efficiency and improves the auxiliary service market mechanism. Full article
(This article belongs to the Section F: Electrical Engineering)
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16 pages, 2818 KiB  
Article
Q-Learning and Efficient Low-Quantity Charge Method for Nodes to Extend the Lifetime of Wireless Sensor Networks
by Kunpeng Xu, Zheng Li, Ao Cui, Shuqin Geng, Deyong Xiao, Xianhui Wang and Peiyuan Wan
Electronics 2023, 12(22), 4676; https://doi.org/10.3390/electronics12224676 - 17 Nov 2023
Cited by 1 | Viewed by 1522
Abstract
With the rapid development of the Internet of Things (IoT), improving the lifetime of nodes and networks has become increasingly important. Most existing medium access control protocols are based on scheduling the standby and active periods of nodes and do not consider the [...] Read more.
With the rapid development of the Internet of Things (IoT), improving the lifetime of nodes and networks has become increasingly important. Most existing medium access control protocols are based on scheduling the standby and active periods of nodes and do not consider the alarm state. This paper proposes a Q-learning and efficient low-quantity charge (QL-ELQC) method for the smoke alarm unit of a power system to reduce the average current and to improve the lifetime of the wireless sensor network (WSN) nodes. Quantity charge models were set up, and the QL-ELQC method is based on the duty cycle of the standby and active times for the nodes and considers the relationship between the sensor data condition and the RF module that can be activated and deactivated only at a certain time. The QL-ELQC method effectively overcomes the continuous state–action space limitation of Q-learning using the state classification method. The simulation results reveal that the proposed scheme significantly improves the latency and energy efficiency compared with the existing QL-Load scheme. Moreover, the experimental results are consistent with the theoretical results. The proposed QL-ELQC approach can be applied in various scenarios where batteries cannot be replaced or recharged under harsh environmental conditions. Full article
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26 pages, 4211 KiB  
Article
Component Criticality Analysis for Improved Ship Machinery Reliability
by Abdullahi Abdulkarim Daya and Iraklis Lazakis
Machines 2023, 11(7), 737; https://doi.org/10.3390/machines11070737 - 13 Jul 2023
Cited by 6 | Viewed by 3567
Abstract
Redundancy in ship systems is provided to ensure operational resilience through equipment backups, which ensure system availability and offline repairs of machinery. The electric power generation system of ships provides the most utility of all systems; hence, it is provided with a good [...] Read more.
Redundancy in ship systems is provided to ensure operational resilience through equipment backups, which ensure system availability and offline repairs of machinery. The electric power generation system of ships provides the most utility of all systems; hence, it is provided with a good level of standby units to ensure reliable operations. Nonetheless, the occurrence of undesired blackouts is common onboard ships and portends a serious danger to ship security and safety. Therefore, understanding the contributing factors affecting system reliability through component criticality analysis is essential to ensuring a more robust maintenance and support platform for efficient ship operations. In this regard, a hybrid reliability and fault detection analysis using DFTA and ANN was conducted to establish component criticality and related fault conditions. A case study was conducted on a ship power generation system consisting of four marine diesel power generation plants onboard an Offshore Patrol Vessel (OPV). Results from the reliability analysis indicate an overall low system reliability of less than 70 percent within the first 24 of the 78 operational months. Component criticality-using reliability importance measures obtained through DFTA was used to identify all components with more than a 40 percent contribution to subsystem failure. Additionally, machine learning was used to aid the reliability analysis through feature engineering and fault identification using Artificial Neural Network classification. The ANN has identified a failure pattern threshold at about 200 kva, which can be attributed to overheating, hence establishing a link between component failure and generator performance. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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16 pages, 4011 KiB  
Article
Novel Analysis between Two-Unit Hot and Cold Standby Redundant Systems with Varied Demand
by Reetu Malhotra, Faten S. Alamri and Hamiden Abd El-Wahed Khalifa
Symmetry 2023, 15(6), 1220; https://doi.org/10.3390/sym15061220 - 7 Jun 2023
Cited by 13 | Viewed by 2118
Abstract
Decisive applications, such as control systems and aerial navigation, require a standby system to meet stringent safety, availability, and reliability. The paper evaluates the availability, reliability, and other measures of system effectiveness for two stochastic models in a symmetrical way with varying demand: [...] Read more.
Decisive applications, such as control systems and aerial navigation, require a standby system to meet stringent safety, availability, and reliability. The paper evaluates the availability, reliability, and other measures of system effectiveness for two stochastic models in a symmetrical way with varying demand: Model 1 (a two-unit cold standby system) and Model 2 (a two-unit hot standby system). In Model 1, the standby unit needs to be activated before it may begin to function; in Model 2, the standby unit is always operational unless it fails. The current study demonstrates that the hot standby system is more expensive than the cold standby system under two circumstances: a decrease in demand or the hot standby unit’s failure rate exceeding a predetermined threshold. The cold standby system’s activation time is at most a certain threshold, and turning both units on at once is necessary to handle the increasing demand. In that case, the hot standby will be more expensive than the cold standby system. The authors used semi-Markov and regenerative point techniques to analyze both models. They collected actual data from a cable manufacturing plant to illustrate the findings. Plotting several graphs and obtaining cut-off points make it easier to choose the standby to employ. Full article
(This article belongs to the Special Issue Stochastic Analysis with Applications and Symmetry)
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13 pages, 2823 KiB  
Article
Deep-Learning-Based ADHD Classification Using Children’s Skeleton Data Acquired through the ADHD Screening Game
by Wonjun Lee, Deokwon Lee, Sanghyub Lee, Kooksung Jun and Mun Sang Kim
Sensors 2023, 23(1), 246; https://doi.org/10.3390/s23010246 - 26 Dec 2022
Cited by 16 | Viewed by 4718
Abstract
The identification of attention deficit hyperactivity disorder (ADHD) in children, which is increasing every year worldwide, is very important for early diagnosis and treatment. However, since ADHD is not a simple disease that can be diagnosed with a simple test, doctors require a [...] Read more.
The identification of attention deficit hyperactivity disorder (ADHD) in children, which is increasing every year worldwide, is very important for early diagnosis and treatment. However, since ADHD is not a simple disease that can be diagnosed with a simple test, doctors require a large period of time and substantial effort for accurate diagnosis and treatment. Currently, ADHD classification studies using various datasets and machine learning or deep learning algorithms are actively being conducted for the screening diagnosis of ADHD. However, there has been no study of ADHD classification using only skeleton data. It was hypothesized that the main symptoms of ADHD, such as distraction, hyperactivity, and impulsivity, could be differentiated through skeleton data. Thus, we devised a game system for the screening and diagnosis of children’s ADHD and acquired children’s skeleton data using five Azure Kinect units equipped with depth sensors, while the game was being played. The game for screening diagnosis involves a robot first travelling on a specific path, after which the child must remember the path the robot took and then follow it. The skeleton data used in this study were divided into two categories: standby data, obtained when a child waits while the robot demonstrates the path; and game data, obtained when a child plays the game. The acquired data were classified using the RNN series of GRU, RNN, and LSTM algorithms; a bidirectional layer; and a weighted cross-entropy loss function. Among these, an LSTM algorithm using a bidirectional layer and a weighted cross-entropy loss function obtained a classification accuracy of 97.82%. Full article
(This article belongs to the Special Issue Advanced Sensors Technologies Applied in Mobile Robot)
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13 pages, 2156 KiB  
Article
Capacity Allocation Strategy Using Virtual Synchronous Compensator for Renewable Energy Stations Based on Fuzzy Chance Constraints
by Zhi Xu, Pengfei Song, Chunya Yin, Pengpeng Kang and Baoyu Zhai
Energies 2022, 15(24), 9306; https://doi.org/10.3390/en15249306 - 8 Dec 2022
Cited by 6 | Viewed by 1513
Abstract
The uncertainty of high penetration of renewable energy brings challenges to the safe and stable operation of a power system; the virtual synchronous compensation (VSCOM) can shift the demand and compensate real-time discrepancy between generation and demand, and can improve the active support [...] Read more.
The uncertainty of high penetration of renewable energy brings challenges to the safe and stable operation of a power system; the virtual synchronous compensation (VSCOM) can shift the demand and compensate real-time discrepancy between generation and demand, and can improve the active support ability for the power system. This paper proposes a novel capacity allocation strategy using VSCOM for renewable energy stations based on fuzzy constraints. Firstly, the basic framework of the VSCOM is constructed with energy storage and reactive power generator (SVG) unit. Secondly, the inertia and standby capacity requirements of high penetration of renewable energy system are modeled; on this basis, a capacity allocation model of each sub unit of the VSCOM is developed, and the investment economy and stable support needs are considered. Thirdly, the uncertainty set of wind power output is defined based on the historical data to find a decision that minimizes the worst-case expected where the worst case should be taken. Finally, the simulation results show that the proposed optimal sizing strategy can effectively take advantage of stability and economy, and the VSCOM can meet the inertia support demand of 98.6% of a high proportion of renewable energy systems. Full article
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17 pages, 1750 KiB  
Review
Novel Gas Turbine Challenges to Support the Clean Energy Transition
by Hiyam Farhat and Coriolano Salvini
Energies 2022, 15(15), 5474; https://doi.org/10.3390/en15155474 - 28 Jul 2022
Cited by 21 | Viewed by 2850
Abstract
The ongoing energy transformation, which is fueled by environmentally cautious policies, demands a full synergy with existing back-up gas turbines (GTs). Renewable energy sources (RESs), such as wind and solar, are intermittent by nature and present large variations across the span of the [...] Read more.
The ongoing energy transformation, which is fueled by environmentally cautious policies, demands a full synergy with existing back-up gas turbines (GTs). Renewable energy sources (RESs), such as wind and solar, are intermittent by nature and present large variations across the span of the day, seasons, and geographies. The gas turbine is seen as an essential part of the energy transition because of its superior operational flexibility over other non-renewable counterparts, such as hydro and nuclear. Besides the technical aspects, the latter are less popular due to controversies associated with safety, ecological, and social aspects. GTs can produce when required and with acceptable reaction times and load ranges. This allows a balance between the energy supply and demand in the grid, mitigating the variations in RESs. The increased cycling due to operational flexibility has adverse effects on GT components and the unit efficiency. The latter dictates how well GTs make use of the burned fuel and influence the emissions per energy unit. This paper investigates these aspects. First, it presents the effects of increased penetration of renewable energy sources (RESs) into the grid. Second, it defines the new operation requirements including more dynamic load regimes, the provision for high occurrences of starts and stops, continuous and variant load cycling operations, extended partial loading or stand-by, and other conditions not foreseen under the classic baseload or cyclic operations. Finally, it proposes the overhauling of the present GT inspection and lifing criteria to meet the new role of GTs. Full article
(This article belongs to the Special Issue Developing the World in 2021 with Clean and Safe Energy)
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34 pages, 3469 KiB  
Article
Reliability Analysis of MV Electric Distribution Networks Including Distributed Generation and ICT Infrastructure
by Miroslaw Parol, Jacek Wasilewski, Tomasz Wojtowicz, Bartlomiej Arendarski and Przemyslaw Komarnicki
Energies 2022, 15(14), 5311; https://doi.org/10.3390/en15145311 - 21 Jul 2022
Cited by 11 | Viewed by 3841
Abstract
In recent years, the increased distributed generation (DG) capacity in electric distribution systems has been observed. Therefore, it is necessary to research existing structures of distribution networks as well as to develop new (future) system structures. There are many works on the reliability [...] Read more.
In recent years, the increased distributed generation (DG) capacity in electric distribution systems has been observed. Therefore, it is necessary to research existing structures of distribution networks as well as to develop new (future) system structures. There are many works on the reliability of distribution systems with installed DG sources. This paper deals with a reliability analysis for both present and future medium voltage (MV) electric distribution system structures. The impact of DG technology used and energy source location on the power supply reliability has been analyzed. The reliability models of electrical power devices, conventional and renewable energy sources as well as information and communications technology (ICT) components have been proposed. Main contribution of this paper are the results of performed calculations, which have been analyzed for specific system structures (two typical present network structures and two future network structures), using detailed information on DG types, their locations and power capacities, as well as distribution system automation applied (automatic stand-by switching on—ASS and automatic power restoration—APR). The reliability of the smart grid consisting of the distribution network and the coupled communications network was simulated and assessed. The observations and conclusions based on calculation results have been made. More detailed modeling and consideration of system automation of distribution grids with DG units coupled with the communication systems allows the design and application of more reliable MV network structures. Full article
(This article belongs to the Special Issue Intelligent Forecasting and Optimization in Electrical Power Systems)
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21 pages, 575 KiB  
Article
Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K-Policy Inspection
by Delia Montoro-Cazorla and Rafael Pérez-Ocón
Mathematics 2022, 10(11), 1918; https://doi.org/10.3390/math10111918 - 3 Jun 2022
Cited by 2 | Viewed by 1696
Abstract
This paper presents an N warm standby system under shocks and inspections governed by Markovian arrival processes. The inspections detect the number of down units, and their replacement is carried out if there are a minimum K of failed units. This is a [...] Read more.
This paper presents an N warm standby system under shocks and inspections governed by Markovian arrival processes. The inspections detect the number of down units, and their replacement is carried out if there are a minimum K of failed units. This is a policy of the type (K,N) used in inventory theory. The study is performed via the up and down periods of the system (cycle); the distribution of these random times and the expected costs for each period comprising the cycle are determined on the basis of individual costs due to maintenance actions (per inspection and replacement of every unit) and others due to operation or inactivity of the system, per time unit. Intermediate addressed calculus are the distributions of the number of inspections by cycle and the expected cost involving every inspection, depending on the number of replaced units. The system is studied in transient and stationary regimes, and some reliability measures of interest and the cost rate are calculated. An optimization of these quantities is performed in terms of the number K in a numerical example. This general model extends to many others in the literature, and, by using the matrix-analytic method, compact and algorithmic expressions are achieved, facilitating its potential application. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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