75 research outputs found

    A testbed based performance evaluation of smart grid wireless neighborhood area networks routing protocols

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    Smart Grid networks have a data communication network associated with the electrical energy distribution infrastructure. This network connects all the sub- scribers’ homes with the data control centers of the supplying companies, which in turn have access to the global Internet network. They are in charge of transporting the needed information between the elements that comprise the electricity network and the control centers. A part of these networks is the so-called Neighborhood Area Networks (NANs), which transports the data from the subscriber’s home to some data concentrators. This article presents a comparison of the performance of different routing protocols that can be used in this part of the data network, when a wireless technology is selected. For this comparison, a hardware testbed has been implemented, with a simple initial configuration, which allows the comparison of the OLSR v1, OLSR v2 and HWMP protocols. The numerical results are presented in terms of network throughput, protocol overhead, number of retransmissions, net- work transit and packet transfer times.This work was supported by the Spanish Research Council under project MAGOS (TEC2017-84197-C4-3-R), and Juan Pablo Astudillo LeΓ³n is the recipient of a full scholarship from the SecretarΓ­a de EducaciΓ³n Superior, Ciencia, TecnologΓ­a e InnovaciΓ³n (SENESCYT), Ecuador.Peer ReviewedPostprint (published version

    On Reliability of Smart Grid Neighborhood Area Networks

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    With the integration of the advanced computing and communication technologies, smart grid system is dedicated to enhance the efficiency and the reliability of future power systems greatly through renewable energy resources, as well as distributed communication intelligence and demand response. Along with advanced features of smart grid, the reliability of smart grid communication system emerges to be a critical issue, since millions of smart devices are interconnected through communication networks throughout critical power facilities, which has an immediate and direct impact on the reliability of the entire power infrastructure. In this paper, we present a comprehensive survey of reliability issues posted by the smart grid with a focus on communications in support of neighborhood area networks (NAN). Specifically, we focus on network architecture, reliability requirements and challenges of both communication networks and systems, secure countermeasures, and case studies in smart grid NAN. We aim to provide a deep understanding of reliability challenges and effective solutions toward reliability issues in smart grid NAN

    A review on various Smart Grid Technologies used in Power System

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    Electrical infrastructure is expanding day by day due to which smart grid gives better vision for electrical reliability. Various parameters like quality and quantity of power transmitted should be available with the electricity board which can be achieved using smart sensing, metering and communication technologies. If all the above requirements are met in power system then it is called smart grid (SG). SG also helps consumers to manage the load patters and also to manage their expenses. The main component of SG is the communication technology to share data between consumers and grid since grid operators requires real time data to schedule their supply. The Wireless Sensor Network (WSN) uses Aggregation Protocol with Error Detection (APED) to improve the security of data. The SG with SCADA is facilitated by data acquisitions which includes the meter reading, system conditions, etc. that are monitored and transmitted at regular intervals in real time. This paper reviews the modern technologies used in smart grid communication based on IEEE 802.15.4 standard to the SG and how it is modified to ensure effective, efficient and economical and secured communication of the huge real time data from the smart meters

    A Scalable Geographic Routing Protocol for Virtual Power Plant Communications

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    International audienceICT is an enabling technology for the integration of distributed energy resources and storage (DERS) within the power grid as well as implementation for innovative services such as demand side management (DSM) and demand response (DR). Nevertheless, individual DERS are too small to be allowed access to energy market, likewise utilities are unable to effectively control and manage small DERS. Virtual power plants are a concept, that can solve this sparsity problem, they attempt to aggregate DERS to present them to the rest of the power grid as a unique technical and/or commercial entity. This contribution deals with ICT for the VPPs. It presents a novel geographic routing protocol that is able to support different control strategies for the VPPs and accommodate their dynamic structure with seamless enrollment and dis-enrollment of prosumers

    Emergency aware congestion control for smart grid neighborhood area networks

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    Β© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The evolution of traditional electricity distribution infrastructures towards Smart Grid networks has generated the need to carry out new research. There are many fields that have attracted the attention of researchers, among which is the improvement of the performance of the so-called Neighborhood Area Networks (NAN). In this sense, and given the critical nature of some of the data transmitted by these networks, maintaining an adequate quality of service (QoS) is absolutely necessary. In emergency situations, this need becomes even more evident. This article presents a congestion control mechanism, whose parameters are modified according to the network state of emergency. The mechanism also applies a multi-channel allocation technique, together with a differentiation in the QoS offered to the different data flows according to their relevance. These proposals have been evaluated in the context of a wireless mesh networks (WMN) made up by a set of smart meter devices, where various smart grids (SG) applications are sending their data traffics. Each SG application must meet its unique quality of service (QoS) requirements, such as reliability and delay. To evaluate the proposals, some NAN scenarios have been built by using the ns-3 simulator and its 802.11s basic model, which was modified to implement the proposed techniques. Compared with the basic Hybrid Wireless Mesh Protocol (HWMP), Emergency Aware Congestion Control proposal (EA-HWMP), shows significant improvements in terms of packet delivery ratio, network throughput and transit time.Peer ReviewedPostprint (published version

    An Efficient and Secure Cluster-Based Architecture for AMI Communication in Smart Grid

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    ABSTRACT Smart Grid has revolutionized Traditional Grid System by merging bi-directional communication network and information technology. Advanced Metering Infrastructure (AMI) is an integral part of Smart Grid used to measure power consumed and demands at consumer-end. In this article, we propose an efficient and secure cluster-based architecture for AMI in Smart Grid, which fulfills the primary security requirements like confidentiality, authentication and integrity. Analysis shows that the proposed secure architecture for AMI in Smart Grid is efficient in terms of resource utilization

    ΠœΠ΅Ρ‚ΠΎΠ΄Ρ‹ формирования мноТСств состояний Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… сСтСй для Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Ρ… ΠΌΠ΅Ρ€ связности

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    Reliability, survivability, and stability analysis tasks are typical not only for telecommunications, but also for systems whose components are subject to one or more types of failures, such as transport, power, mechanical systems, integrated circuits, and even software. The logical approach involves the decomposition of the system into a number of small functional elements, and within telecommunications networks they are usually separate network devices (switches, routers, terminals, etc.), as well as communication lines between them (copper-core, fiber-optic, coaxial cables, wireless media, and other transmission media). Functional relationships also define logical relationships between the failures of individual elements and the failure of the network as a whole. The assumption is also used that device failures are relatively less likely than communication line failures, which implies using the assumption of absolute stability (reliability, survivability) of these devices. Model of a telecommunication network in the form of the generalized model of Erdos–Renyi is presented. In the context of the stability of the telecommunications network, the analyzed property is understood as the connectivity of the network in one form or another. Based on the concept of stochastic connectivity of a network, as the correspondence of a random graph of the connectivity property between a given set of vertices, three connectivity measures are traditionally distinguished: two-pole, multi-pole, and all-pole. The procedures for forming an arbitrary structure of sets of paths and trees for networks are presented, as well as their generalization of multipolar trees. It is noted that multipolar trees are the most common concept of relatively simple chains and spanning trees. Solving such problems will allow us to proceed to calculating the probability of connectivity of graphs for various connectivity measures.Π—Π°Π΄Π°Ρ‡ΠΈ Π°Π½Π°Π»ΠΈΠ·Π° надСТности, ТивучСсти ΠΈ устойчивости Ρ…Π°Ρ€Π°ΠΊΡ‚Π΅Ρ€Π½Ρ‹ Π½Π΅ Ρ‚ΠΎΠ»ΡŒΠΊΠΎ для Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΉ, Π½ΠΎ ΠΈ для систСм, Ρ‡ΡŒΠΈ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ‚Ρ‹ ΠΏΠΎΠ΄Π²Π΅Ρ€ΠΆΠ΅Π½Ρ‹ ΠΎΠ΄Π½ΠΎΠΌΡƒ ΠΈΠ»ΠΈ нСскольким Π²ΠΈΠ΄Π°ΠΌ ΠΎΡ‚ΠΊΠ°Π·ΠΎΠ², Π½Π°ΠΏΡ€ΠΈΠΌΠ΅Ρ€ транспортныС, энСргСтичСскиС, мСханичСскиС систСмы, ΠΈΠ½Ρ‚Π΅Π³Ρ€Π°Π»ΡŒΠ½Ρ‹Π΅ Ρ†Π΅ΠΏΠΈ ΠΈ Π΄Π°ΠΆΠ΅ ΠΏΡ€ΠΎΠ³Ρ€Π°ΠΌΠΌΠ½ΠΎΠ΅ обСспСчСниС. ЛогичСский ΠΏΠΎΠ΄Ρ…ΠΎΠ΄ ΠΏΡ€Π΅Π΄ΠΏΠΎΠ»Π°Π³Π°Π΅Ρ‚ Π΄Π΅ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡ†ΠΈΡŽ систСмы Π½Π° ряд Π½Π΅Π±ΠΎΠ»ΡŒΡˆΠΈΡ… Ρ„ΡƒΠ½ΠΊΡ†ΠΈΠΎΠ½Π°Π»ΡŒΠ½Ρ‹Ρ… элСмСнтов, ΠΈ Π² Ρ€Π°ΠΌΠΊΠ°Ρ… Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… сСтСй ΠΎΠ½ΠΈ ΠΎΠ±Ρ‹Ρ‡Π½ΠΎ ΠΏΡ€Π΅Π΄ΡΡ‚Π°Π²Π»ΡΡŽΡ‚ собой ΠΎΡ‚Π΄Π΅Π»ΡŒΠ½Ρ‹Π΅ сСтСвыС устройства (ΠΊΠΎΠΌΠΌΡƒΡ‚Π°Ρ‚ΠΎΡ€Ρ‹, ΠΌΠ°Ρ€ΡˆΡ€ΡƒΡ‚ΠΈΠ·Π°Ρ‚ΠΎΡ€Ρ‹, Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π»Ρ‹ ΠΈ Ρ‚. ΠΏ.), Π° Ρ‚Π°ΠΊΠΆΠ΅ Π»ΠΈΠ½ΠΈΠΈ связи ΠΌΠ΅ΠΆΠ΄Ρƒ Π½ΠΈΠΌΠΈ (ΠΌΠ΅Π΄Π½ΠΎΠΆΠΈΠ»ΡŒΠ½Ρ‹Π΅, ΠΎΠΏΡ‚ΠΎΠ²ΠΎΠ»ΠΎΠΊΠΎΠ½Π½Ρ‹Π΅, ΠΊΠΎΠ°ΠΊΡΠΈΠ°Π»ΡŒΠ½Ρ‹Π΅ ΠΊΠ°Π±Π΅Π»ΠΈ, бСспроводная срСда ΠΈ Π΄Ρ€ΡƒΠ³ΠΈΠ΅ срСды ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡ΠΈ). Π€ΡƒΠ½ΠΊΡ†ΠΈΠΎΠ½Π°Π»ΡŒΠ½Ρ‹Π΅ взаимосвязи Π·Π°Π΄Π°ΡŽΡ‚ ΠΈ логичСскиС ΡΠΎΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρƒ ΠΎΡ‚ΠΊΠ°Π·Π°ΠΌΠΈ ΠΎΡ‚Π΄Π΅Π»ΡŒΠ½Ρ‹Ρ… элСмСнтов ΠΈ ΠΎΡ‚ΠΊΠ°Π·ΠΎΠΌ сСти Π² Ρ†Π΅Π»ΠΎΠΌ. Π’Π°ΠΊΠΆΠ΅ ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΠ΅Ρ‚ΡΡ Π΄ΠΎΠΏΡƒΡ‰Π΅Π½ΠΈΠ΅, Ρ‡Ρ‚ΠΎ ΠΎΡ‚ΠΊΠ°Π·Ρ‹ устройств ΡΠ²Π»ΡΡŽΡ‚ΡΡ ΡΡ€Π°Π²Π½ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎ ΠΌΠ΅Π½Π΅Π΅ вСроятными, Ρ‡Π΅ΠΌ ΠΎΡ‚ΠΊΠ°Π·Ρ‹ Π»ΠΈΠ½ΠΈΠΉ связи, Ρ‡Ρ‚ΠΎ ΠΏΠΎΠ΄Ρ€Π°Π·ΡƒΠΌΠ΅Π²Π°Π΅Ρ‚ использованиС прСдполоТСния ΠΎΠ± Π°Π±ΡΠΎΠ»ΡŽΡ‚Π½ΠΎΠΉ устойчивости (надСТности, ТивучСсти) Π΄Π°Π½Π½Ρ‹Ρ… устройств. МодСль Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ сСти прСдставлСна Π² Π²ΠΈΠ΄Π΅ ΠΎΠ±ΠΎΠ±Ρ‰Π΅Π½Π½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π­Ρ€Π΄Π΅ΡˆΠ° – РСньи. Π’ контСкстС устойчивости Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ сСти ΠΏΠΎΠ΄ Π°Π½Π°Π»ΠΈΠ·ΠΈΡ€ΡƒΠ΅ΠΌΡ‹ΠΌ свойством понимаСтся ΡΠ²ΡΠ·Π½ΠΎΡΡ‚ΡŒ сСти Π² Ρ‚ΠΎΠΉ ΠΈΠ»ΠΈ ΠΈΠ½ΠΎΠΉ Ρ„ΠΎΡ€ΠΌΠ΅. ΠžΡΠ½ΠΎΠ²Ρ‹Π²Π°ΡΡΡŒ Π½Π° прСдставлСнии понятия стохастичСской связности сСти ΠΊΠ°ΠΊ соотвСтствия Π½Π΅ΠΊΠΎΡ‚ΠΎΡ€ΠΎΠ³ΠΎ случайного Π³Ρ€Π°Ρ„Π° свойства связности Π·Π°Π΄Π°Π½Π½ΠΎΠΌΡƒ Π½Π°Π±ΠΎΡ€Ρƒ Π²Π΅Ρ€ΡˆΠΈΠ½, Ρ‚Ρ€Π°Π΄ΠΈΡ†ΠΈΠΎΠ½Π½ΠΎ Π²Ρ‹Π΄Π΅Π»ΡΡŽΡ‚ Ρ‚Ρ€ΠΈ ΠΌΠ΅Ρ€Ρ‹ связности: Π΄Π²ΡƒΡ…ΠΏΠΎΠ»ΡŽΡΠ½Π°Ρ, многополюсная ΠΈ всСполюсная. ΠŸΡ€Π΅Π΄ΡΡ‚Π°Π²Π»Π΅Π½Ρ‹ ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Ρ‹ формирования для сСтСй ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ»ΡŒΠ½ΠΎΠΉ структуры мноТСств ΠΏΡƒΡ‚Π΅ΠΉ, Π΄Π΅Ρ€Π΅Π²ΡŒΠ΅Π² ΠΈ, ΠΊΠ°ΠΊ ΠΈΡ… ΠΎΠ±ΠΎΠ±Ρ‰Π΅Π½ΠΈΠ΅, ΠΌΠ½ΠΎΠ³ΠΎΠΏΠΎΠ»ΡŽΡΠ½Ρ‹Ρ… Π΄Π΅Ρ€Π΅Π²ΡŒΠ΅Π². ΠžΡ‚ΠΌΠ΅Ρ‡Π΅Π½ΠΎ, Ρ‡Ρ‚ΠΎ ΠΌΠ½ΠΎΠ³ΠΎΠΏΠΎΠ»ΡŽΡΠ½Ρ‹Π΅ Π΄Π΅Ρ€Π΅Π²ΡŒΡ ΡΠ²Π»ΡΡŽΡ‚ΡΡ Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΠΎΠ±Ρ‰ΠΈΠΌ понятиСм ΠΎΡ‚Π½ΠΎΡΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎ простых Ρ†Π΅ΠΏΠ΅ΠΉ ΠΈ остовых Π΄Π΅Ρ€Π΅Π²ΡŒΠ΅Π². РСшСниС ΠΏΠΎΠ΄ΠΎΠ±Π½Ρ‹Ρ… Π·Π°Π΄Π°Ρ‡ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΡ‚ Π² дальнСйшСм ΠΏΠ΅Ρ€Π΅ΠΉΡ‚ΠΈ ΠΊ Π²Ρ‹Ρ‡ΠΈΡΠ»Π΅Π½ΠΈΡŽ вСроятности связности Π³Ρ€Π°Ρ„ΠΎΠ² для Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Ρ… ΠΌΠ΅Ρ€ связности

    ΠœΠ΅Ρ‚ΠΎΠ΄Ρ‹ формирования мноТСств состояний Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… сСтСй для Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Ρ… ΠΌΠ΅Ρ€ связности

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    Π—Π°Π΄Π°Ρ‡ΠΈ Π°Π½Π°Π»ΠΈΠ·Π° надСТности, ТивучСсти ΠΈ устойчивости Ρ…Π°Ρ€Π°ΠΊΡ‚Π΅Ρ€Π½Ρ‹ Π½Π΅ Ρ‚ΠΎΠ»ΡŒΠΊΠΎ для Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΉ, Π½ΠΎ ΠΈ для систСм, Ρ‡ΡŒΠΈ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ‚Ρ‹ ΠΏΠΎΠ΄Π²Π΅Ρ€ΠΆΠ΅Π½Ρ‹ ΠΎΠ΄Π½ΠΎΠΌΡƒ ΠΈΠ»ΠΈ нСскольким Π²ΠΈΠ΄Π°ΠΌ ΠΎΡ‚ΠΊΠ°Π·ΠΎΠ², Π½Π°ΠΏΡ€ΠΈΠΌΠ΅Ρ€ транспортныС, энСргСтичСскиС, мСханичСскиС систСмы, ΠΈΠ½Ρ‚Π΅Π³Ρ€Π°Π»ΡŒΠ½Ρ‹Π΅ Ρ†Π΅ΠΏΠΈ ΠΈ Π΄Π°ΠΆΠ΅ ΠΏΡ€ΠΎΠ³Ρ€Π°ΠΌΠΌΠ½ΠΎΠ΅ обСспСчСниС. ЛогичСский ΠΏΠΎΠ΄Ρ…ΠΎΠ΄ ΠΏΡ€Π΅Π΄ΠΏΠΎΠ»Π°Π³Π°Π΅Ρ‚ Π΄Π΅ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡ†ΠΈΡŽ систСмы Π½Π° ряд Π½Π΅Π±ΠΎΠ»ΡŒΡˆΠΈΡ… Ρ„ΡƒΠ½ΠΊΡ†ΠΈΠΎΠ½Π°Π»ΡŒΠ½Ρ‹Ρ… элСмСнтов, ΠΈ Π² Ρ€Π°ΠΌΠΊΠ°Ρ… Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… сСтСй ΠΎΠ½ΠΈ ΠΎΠ±Ρ‹Ρ‡Π½ΠΎ ΠΏΡ€Π΅Π΄ΡΡ‚Π°Π²Π»ΡΡŽΡ‚ собой ΠΎΡ‚Π΄Π΅Π»ΡŒΠ½Ρ‹Π΅ сСтСвыС устройства (ΠΊΠΎΠΌΠΌΡƒΡ‚Π°Ρ‚ΠΎΡ€Ρ‹, ΠΌΠ°Ρ€ΡˆΡ€ΡƒΡ‚ΠΈΠ·Π°Ρ‚ΠΎΡ€Ρ‹, Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π»Ρ‹ ΠΈ Ρ‚. ΠΏ.), Π° Ρ‚Π°ΠΊΠΆΠ΅ Π»ΠΈΠ½ΠΈΠΈ связи ΠΌΠ΅ΠΆΠ΄Ρƒ Π½ΠΈΠΌΠΈ (ΠΌΠ΅Π΄Π½ΠΎΠΆΠΈΠ»ΡŒΠ½Ρ‹Π΅, ΠΎΠΏΡ‚ΠΎΠ²ΠΎΠ»ΠΎΠΊΠΎΠ½Π½Ρ‹Π΅, ΠΊΠΎΠ°ΠΊΡΠΈΠ°Π»ΡŒΠ½Ρ‹Π΅ ΠΊΠ°Π±Π΅Π»ΠΈ, бСспроводная срСда ΠΈ Π΄Ρ€ΡƒΠ³ΠΈΠ΅ срСды ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡ΠΈ). Π€ΡƒΠ½ΠΊΡ†ΠΈΠΎΠ½Π°Π»ΡŒΠ½Ρ‹Π΅ взаимосвязи Π·Π°Π΄Π°ΡŽΡ‚ ΠΈ логичСскиС ΡΠΎΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρƒ ΠΎΡ‚ΠΊΠ°Π·Π°ΠΌΠΈ ΠΎΡ‚Π΄Π΅Π»ΡŒΠ½Ρ‹Ρ… элСмСнтов ΠΈ ΠΎΡ‚ΠΊΠ°Π·ΠΎΠΌ сСти Π² Ρ†Π΅Π»ΠΎΠΌ. Π’Π°ΠΊΠΆΠ΅ ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΠ΅Ρ‚ΡΡ Π΄ΠΎΠΏΡƒΡ‰Π΅Π½ΠΈΠ΅, Ρ‡Ρ‚ΠΎ ΠΎΡ‚ΠΊΠ°Π·Ρ‹ устройств ΡΠ²Π»ΡΡŽΡ‚ΡΡ ΡΡ€Π°Π²Π½ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎ ΠΌΠ΅Π½Π΅Π΅ вСроятными, Ρ‡Π΅ΠΌ ΠΎΡ‚ΠΊΠ°Π·Ρ‹ Π»ΠΈΠ½ΠΈΠΉ связи, Ρ‡Ρ‚ΠΎ ΠΏΠΎΠ΄Ρ€Π°Π·ΡƒΠΌΠ΅Π²Π°Π΅Ρ‚ использованиС прСдполоТСния ΠΎΠ± Π°Π±ΡΠΎΠ»ΡŽΡ‚Π½ΠΎΠΉ устойчивости (надСТности, ТивучСсти) Π΄Π°Π½Π½Ρ‹Ρ… устройств. МодСль Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ сСти прСдставлСна Π² Π²ΠΈΠ΄Π΅ ΠΎΠ±ΠΎΠ±Ρ‰Π΅Π½Π½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π­Ρ€Π΄Π΅ΡˆΠ° – РСньи. Π’ контСкстС устойчивости Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ сСти ΠΏΠΎΠ΄ Π°Π½Π°Π»ΠΈΠ·ΠΈΡ€ΡƒΠ΅ΠΌΡ‹ΠΌ свойством понимаСтся ΡΠ²ΡΠ·Π½ΠΎΡΡ‚ΡŒ сСти Π² Ρ‚ΠΎΠΉ ΠΈΠ»ΠΈ ΠΈΠ½ΠΎΠΉ Ρ„ΠΎΡ€ΠΌΠ΅. ΠžΡΠ½ΠΎΠ²Ρ‹Π²Π°ΡΡΡŒ Π½Π° прСдставлСнии понятия стохастичСской связности сСти ΠΊΠ°ΠΊ соотвСтствия Π½Π΅ΠΊΠΎΡ‚ΠΎΡ€ΠΎΠ³ΠΎ случайного Π³Ρ€Π°Ρ„Π° свойства связности Π·Π°Π΄Π°Π½Π½ΠΎΠΌΡƒ Π½Π°Π±ΠΎΡ€Ρƒ Π²Π΅Ρ€ΡˆΠΈΠ½, Ρ‚Ρ€Π°Π΄ΠΈΡ†ΠΈΠΎΠ½Π½ΠΎ Π²Ρ‹Π΄Π΅Π»ΡΡŽΡ‚ Ρ‚Ρ€ΠΈ ΠΌΠ΅Ρ€Ρ‹ связности: Π΄Π²ΡƒΡ…ΠΏΠΎΠ»ΡŽΡΠ½Π°Ρ, многополюсная ΠΈ всСполюсная. ΠŸΡ€Π΅Π΄ΡΡ‚Π°Π²Π»Π΅Π½Ρ‹ ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Ρ‹ формирования для сСтСй ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ»ΡŒΠ½ΠΎΠΉ структуры мноТСств ΠΏΡƒΡ‚Π΅ΠΉ, Π΄Π΅Ρ€Π΅Π²ΡŒΠ΅Π² ΠΈ, ΠΊΠ°ΠΊ ΠΈΡ… ΠΎΠ±ΠΎΠ±Ρ‰Π΅Π½ΠΈΠ΅, ΠΌΠ½ΠΎΠ³ΠΎΠΏΠΎΠ»ΡŽΡΠ½Ρ‹Ρ… Π΄Π΅Ρ€Π΅Π²ΡŒΠ΅Π². ΠžΡ‚ΠΌΠ΅Ρ‡Π΅Π½ΠΎ, Ρ‡Ρ‚ΠΎ ΠΌΠ½ΠΎΠ³ΠΎΠΏΠΎΠ»ΡŽΡΠ½Ρ‹Π΅ Π΄Π΅Ρ€Π΅Π²ΡŒΡ ΡΠ²Π»ΡΡŽΡ‚ΡΡ Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΠΎΠ±Ρ‰ΠΈΠΌ понятиСм ΠΎΡ‚Π½ΠΎΡΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎ простых Ρ†Π΅ΠΏΠ΅ΠΉ ΠΈ остовых Π΄Π΅Ρ€Π΅Π²ΡŒΠ΅Π². РСшСниС ΠΏΠΎΠ΄ΠΎΠ±Π½Ρ‹Ρ… Π·Π°Π΄Π°Ρ‡ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΡ‚ Π² дальнСйшСм ΠΏΠ΅Ρ€Π΅ΠΉΡ‚ΠΈ ΠΊ Π²Ρ‹Ρ‡ΠΈΡΠ»Π΅Π½ΠΈΡŽ вСроятности связности Π³Ρ€Π°Ρ„ΠΎΠ² для Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Ρ… ΠΌΠ΅Ρ€ связности
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