Mathematics

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20 pages, 4438 KiB

Open AccessArticle

An Effective Hybrid-Energy Framework for Grid Vulnerability Alleviation under Cyber-Stealthy Intrusions

by Abdulaziz Almalaq, Saleh Albadran, Amer Alghadhban, Tao Jin and Mohamed A. Mohamed

Mathematics 2022, 10(14), 2510; https://doi.org/10.3390/math10142510 - 19 Jul 2022

Cited by 6 | Viewed by 1545

In recent years, the occurrence of cascading failures and blackouts arising from cyber intrusions in the underlying configuration of power systems has increasingly highlighted the need for effective power management that is able to handle this issue properly. Moreover, the growing use of [...] Read more.

In recent years, the occurrence of cascading failures and blackouts arising from cyber intrusions in the underlying configuration of power systems has increasingly highlighted the need for effective power management that is able to handle this issue properly. Moreover, the growing use of renewable energy resources demonstrates their irrefutable comparative usefulness in various areas of the grid, especially during cascading failures. This paper aims to first identify and eventually protect the vulnerable areas of these systems by developing a hybrid structure-based microgrid against malicious cyber-attacks. First, a well-set model of system vulnerability indices is presented to indicate the generation unit to which the lines or buses are directly related. Indeed, we want to understand what percentage of the grid equipment, such as the lines, buses, and generators, are vulnerable to the outage of lines or generators arising from cyber-attacks. This can help us make timely decisions to deal with the reduction of the vulnerability indices in the best way possible. The fact is that employing sundry renewable resources in efficient areas of the grid can remarkably improve system vulnerability mitigation effectiveness. In this regard, this paper proposes an outstanding hybrid-energy framework of AC/DC microgrids made up of photovoltaic units, wind turbine units, tidal turbine units, and hydrogen-based fuel cell resources, all of which are in grid-connect mode via the main grid, with the aim to reduce the percentage of the system that is vulnerable. To clearly demonstrate the proposed solution’s effectiveness and ease of use in the framework, a cyber-attack of the false data injection (FDI) type is modeled and developed on the studied system to corrupt information (for instance, via settings on protective devices), leading to cascading failures or large-scale blackouts. Another key factor that can have a profound impact on the unerring vulnerability analysis concerns the uncertainty parameters that are modeled by the unscented transform (UT) in this study. From the results, it can be inferred that vulnerability percentage mitigation can be achieved by the proposed hybrid energy framework based on its effectiveness in the system against the modeled cyber-attacks. Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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19 pages, 465 KiB

Open AccessArticle

Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach

by Shafiq Ahmad, Firoz Ahmad, Intekhab Alam, Abdelaty Edrees Sayed and Mali Abdollahian

Mathematics 2022, 10(14), 2435; https://doi.org/10.3390/math10142435 - 13 Jul 2022

Viewed by 1692

Abstract

The geometric programming problem (GPP) is a beneficial mathematical programming problem for modeling and optimizing nonlinear optimization problems in various engineering fields. The structural configuration of the GPP is quite dynamic and flexible in modeling and fitting the reliability optimization problems efficiently. The [...] Read more.

The geometric programming problem (GPP) is a beneficial mathematical programming problem for modeling and optimizing nonlinear optimization problems in various engineering fields. The structural configuration of the GPP is quite dynamic and flexible in modeling and fitting the reliability optimization problems efficiently. The work’s motivation is to introduce a bounded solution approach for the GPP while considering the variation among the right-hand-side parameters. The bounded solution method uses the two-level mathematical programming problems and obtains the solution of the objective function in a specified interval. The benefit of the bounded solution approach can be realized in that there is no need for sensitivity analyses of the results output. The demonstration of the proposed approach is shown by applying it to the system reliability optimization problem. The specific interval is determined for the objective values and found to be lying in the optimal range. Based on the findings, the concluding remarks are presented. Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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26 pages, 4408 KiB

Open AccessArticle

A Multi-Agent Approach for Self-Healing and RES-Penetration in Smart Distribution Networks

by Ahmed Maged Abdelhamid, Nahla E. Zakzouk and Samah El Safty

Mathematics 2022, 10(13), 2275; https://doi.org/10.3390/math10132275 - 29 Jun 2022

Cited by 5 | Viewed by 1703

Abstract

Smart grid technology has gained much consideration recently to make use of intelligent control in the automatic fault-detection and self-healing of electric networks. This ensures a reliable electricity supply and an efficient operation of the distribution system against disasters with minimum human interaction. [...] Read more.

Smart grid technology has gained much consideration recently to make use of intelligent control in the automatic fault-detection and self-healing of electric networks. This ensures a reliable electricity supply and an efficient operation of the distribution system against disasters with minimum human interaction. In this paper, a fully decentralized multi-agent system (MAS) algorithm, for self-healing in smart distribution systems, is proposed. The novelty of the proposed algorithm, compared to related work, is its ability to combine the zone and feeder agents, specified for system self-healing, with micro-grid agents. This enables the system to successfully achieve functions of fault locating and isolation along with service-restoration using expert rules while considering both operational constraint and load priorities. Meanwhile, managing the power flow and controlling the distributed generator (DG) contribution, in the considered network, is a bonus merit for the proposed algorithm. Hence, system self-healing as well as strengthening energy security and resiliency are guaranteed. The proposed algorithm is tested on a 22 kV radial distribution system through several case-studies with/without a DG wind-energy source. The employed agents are implemented in the Java Agent Developing Framework (JADE) environment to communicate and make decisions. Power system simulation and calculations are carried out in MATLAB to validate the agents’ decisions. Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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19 pages, 3311 KiB

Open AccessArticle

On Optimal Settings for a Family of Runge–Kutta-Based Power-Flow Solvers Suitable for Large-Scale Ill-Conditioned Cases

by Marcos Tostado-Véliz, Talal Alharbi, Hisham Alharbi, Salah Kamel and Francisco Jurado

Mathematics 2022, 10(8), 1279; https://doi.org/10.3390/math10081279 - 12 Apr 2022

Cited by 1 | Viewed by 1563

Abstract

Growing demand, interconnection of multiple systems, and difficulty in upgrading existing infrastructures are limiting the capabilities of conventional computational tools employed in power system analysis. Recent studies manifest the importance of efficiently solving well- and ill-conditioned Power-Flow cases in a modern power-system paradigm. [...] Read more.

Growing demand, interconnection of multiple systems, and difficulty in upgrading existing infrastructures are limiting the capabilities of conventional computational tools employed in power system analysis. Recent studies manifest the importance of efficiently solving well- and ill-conditioned Power-Flow cases in a modern power-system paradigm. While the well-conditioned cases are easily solvable using standard methods, the ill-conditioned ones suppose a challenge for such solvers. In this regard, methods based on the Continuous Newton’s principle have demonstrated their ability to address ill-conditioned cases with acceptable efficiency. This paper demonstrates that the approaches proposed so far do not extract the best numerical properties of such solvers. To fill this gap, an optimization framework is proposed by which the parameters involved in the two-stage Runge–Kutta-based solvers are appropriately set, so that the stability and convergence order of the numerical mapping are maximized. By using the developed optimization technique, three solvers with quadratic, cubic, and 4th order of convergence are developed. The new proposals are tested on a variety of large-scale ill-conditioned cases. Results obtained were promising, outperforming other conventional and robust approaches. Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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15 pages, 1267 KiB

Open AccessArticle

Preventive Maintenance of the k-out-of-n System with Respect to Cost-Type Criterion

by Vladimir Rykov, Olga Kochueva and Yaroslav Rykov

Mathematics 2021, 9(21), 2798; https://doi.org/10.3390/math9212798 - 4 Nov 2021

Cited by 8 | Viewed by 1765

Abstract

In a previous paper, the problem of how the preventive maintenance organization for the k-out-of-n: F system could be used, in order to maximize system availability, was considered. The current paper continues these investigations using a different optimization criterion. The [...] Read more.

In a previous paper, the problem of how the preventive maintenance organization for the k-out-of-n: F system could be used, in order to maximize system availability, was considered. The current paper continues these investigations using a different optimization criterion. The proposed approach is based on decision making theory for regenerative processes. We propose a general procedure for comparing different preventive maintenance strategies based on the ordered statistics distributions, aiming to choose the best one with respect to cost-type criterion. The lifetime distributions of system units are usually unknown and only one or two of their moments are available. For this reason, we pay special attention to the sensitivity analysis of decision making about preventive maintenance, taking into account the shape of the system unit lifetime distributions. A numerical study of two examples based on a real-world system illustrates the results of the proposed approach. Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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13 pages, 2023 KiB

Open AccessArticle

One Cut-Point Phase-Type Distributions in Reliability. An Application to Resistive Random Access Memories

by Christian Acal, Juan E. Ruiz-Castro, David Maldonado and Juan B. Roldán

Mathematics 2021, 9(21), 2734; https://doi.org/10.3390/math9212734 - 28 Oct 2021

Cited by 6 | Viewed by 1491

Abstract

A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non-homogeneous phase-type distribution. It is built by considering one cut-point in the non-negative semi-line of a phase-type distribution. The density [...] Read more.

A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non-homogeneous phase-type distribution. It is built by considering one cut-point in the non-negative semi-line of a phase-type distribution. The density function is defined and the main measures associated, such as the reliability function, hazard rate, cumulative hazard rate and the characteristic function, are also worked out. This new class of distributions enables us to decrease the number of parameters in the estimate when inference is considered. Additionally, the likelihood distribution is built to estimate the model parameters by maximum likelihood. Several applications considering Resistive Random Access Memories compare the adjustment when phase type distributions and one cut-point phase-type distributions are considered. The developed methodology has been computationally implemented in R-cran. Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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23 pages, 2780 KiB

Open AccessArticle

Retrial Queues with Unreliable Servers and Delayed Feedback

by Agassi Melikov, Sevinj Aliyeva and Janos Sztrik

Mathematics 2021, 9(19), 2415; https://doi.org/10.3390/math9192415 - 28 Sep 2021

Cited by 7 | Viewed by 2101

Abstract

In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli retrial is allowed upon the arrival of both primary (from outside) and feedback customers (from orbit), as well as the Bernoulli feedback that may occur after each [...] Read more.

In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli retrial is allowed upon the arrival of both primary (from outside) and feedback customers (from orbit), as well as the Bernoulli feedback that may occur after each service in this system. Servers can break down both during the service of customers and when they are idle. If a server breaks down during the service of a customer, then the interrupted customer, in accordance with the Bernoulli scheme, decides either to leave the system or join a common orbit of retrial and feedback customers. An approximate method, based on the space merging approach of three-dimensional Markov chains, is proposed for the calculation of the steady-state probabilities, as well as performance measures of the system. The results of the numerical experiments are demonstrated. Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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17 pages, 1575 KiB

Open AccessArticle

On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

by Talal Alharbi, Marcos Tostado-Véliz, Omar Alrumayh and Francisco Jurado

Mathematics 2021, 9(17), 2019; https://doi.org/10.3390/math9172019 - 24 Aug 2021

Cited by 3 | Viewed by 1748

Abstract

Recently, the high-order Newton-like methods have gained popularity for solving power flow problems due to their simplicity, versatility and, in some cases, efficiency. In this context, recent research studied the applicability of the 4th order Jarrat’s method as applied to power flow calculation [...] Read more.

Recently, the high-order Newton-like methods have gained popularity for solving power flow problems due to their simplicity, versatility and, in some cases, efficiency. In this context, recent research studied the applicability of the 4th order Jarrat’s method as applied to power flow calculation (PFC). Despite the 4th order of convergence of this technique, it is not competitive with the conventional solvers due to its very high computational cost. This paper addresses this issue by proposing two efficient modifications of the 4th order Jarrat’s method, which present the fourth and sixth order of convergence. In addition, continuous versions of the new proposals and the 4th order Jarrat’s method extend their applicability to ill-conditioned cases. Extensive results in multiple realistic power networks serve to sow the performance of the developed solvers. Results obtained in both well and ill-conditioned cases are promising. Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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17 pages, 849 KiB

Open AccessArticle

Reliability and Inference for Multi State Systems: The Generalized Kumaraswamy Case

by Vlad Stefan Barbu, Alex Karagrigoriou and Andreas Makrides

Mathematics 2021, 9(16), 1834; https://doi.org/10.3390/math9161834 - 4 Aug 2021

Cited by 2 | Viewed by 1475

Abstract

Semi-Markov processes are typical tools for modeling multi state systems by allowing several distributions for sojourn times. In this work, we focus on a general class of distributions based on an arbitrary parent continuous distribution function G with Kumaraswamy as the baseline distribution [...] Read more.

Semi-Markov processes are typical tools for modeling multi state systems by allowing several distributions for sojourn times. In this work, we focus on a general class of distributions based on an arbitrary parent continuous distribution function G with Kumaraswamy as the baseline distribution and discuss some of its properties, including the advantageous property of being closed under minima. In addition, an estimate is provided for the so-called stress–strength reliability parameter, which measures the performance of a system in mechanical engineering. In this work, the sojourn times of the multi-state system are considered to follow a distribution with two shape parameters, which belongs to the proposed general class of distributions. Furthermore and for a multi-state system, we provide parameter estimates for the above general class, which are assumed to vary over the states of the system. The theoretical part of the work also includes the asymptotic theory for the proposed estimators with and without censoring as well as expressions for classical reliability characteristics. The performance and effectiveness of the proposed methodology is investigated via simulations, which show remarkable results with the help of statistical (for the parameter estimates) and graphical tools (for the reliability parameter estimate). Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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19 pages, 5787 KiB

Open AccessArticle

Time-Dependent Reliability Analysis of Plate-Stiffened Prismatic Pressure Vessel with Corrosion

by Younseok Choi, Junkeon Ahn and Daejun Chang

Mathematics 2021, 9(13), 1544; https://doi.org/10.3390/math9131544 - 1 Jul 2021

Cited by 6 | Viewed by 2346

Abstract

In this study, the structural reliability of plate-stiffened prismatic pressure vessels was analyzed over time. A reliability analysis was performed using a time-dependent structural reliability method based on the response surface method (RSM). The plate-stiffened prismatic pressure vessel had a rectangular cross-section with [...] Read more.

In this study, the structural reliability of plate-stiffened prismatic pressure vessels was analyzed over time. A reliability analysis was performed using a time-dependent structural reliability method based on the response surface method (RSM). The plate-stiffened prismatic pressure vessel had a rectangular cross-section with repeated internal load-bearing structures. For the structural analysis, this repeated structure was modeled as a strip, and a structural reliability analysis was performed to identify changes in the reliability index when general corrosion and pitting corrosion occurred in the outer shell. Pitting corrosion was assumed to be randomly distributed on the outer shell, and the reliability index according to the degree of pit (DOP) and time was analyzed. Analysis results confirmed that the change in the reliability index was larger when pitting corrosion was applied compared with when only general corrosion was applied. Additionally, it was confirmed that above a certain DOP, the reliability index was affected. Full article

(This article belongs to the Special Issue Advances in Reliability Modeling, Optimization and Applications)

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