Multi-state Reliability Model Research Articles

Reliability assessment of distribution networks with medium-voltage and low-voltage flexible interconnections considering graded transfer

Abstract For flexible interconnection, flexible interconnected devices (FID) are utilized to upgrade or build connection nodes, which can provide more ways for load recovery after faults, thereby improving the reliability level of the distribution network. Based on the characteristics of connection switch, medium-voltage (MV), and low-voltage (LV) flexible interconnection transfer methods, a reliability assessment method is proposed in this paper for medium-voltage and low-voltage flexible interconnection distribution networks (MLFIDN) considering graded transfer. First, a multi-state reliability model of the LV substation area and discrete probability distribution of DG output are established based on the system structure and composition. Then, the fault impact analysis based on graded transfer mode is proposed. A transfer recovery model that takes into account power balance, the node voltage, line current safety constraints, and flexible interconnection operation constraints is established. On this basis, a simulation method based on non-sequential Monte Carlo sampling is used for system reliability assessment. Finally, the effectiveness of the proposed method is verified by the IEEE-33 distribution network with MV and LV flexible interconnection reliability assessment. The reliability assessment results can quantify the improvement of flexible interconnection on the reliability of distribution networks.

Multi-State Reliability Modeling and Assessment for Corrosion of Organic Coating-Substrate Structure

Abstract The organic coating-substrate structure suffers from corrosion reaction between the substrate material and water molecules during the storage stage. Digital twin is a promising tool for corrosion modeling and assessing the reliability of the organic coating-substrate structure. In this paper, a multi-state modelling method is proposed towards the digital twin and reliability modeling and analysis. Firstly, to analyze the physicochemical process involved in the corrosion of organic coating-substrate structures, a multi-physics simulation method is developed. Then, the degradation performance of the organic coating-substrate structure is discretized into several states, and a Markov model is utilized to model the degradation process of the structure to support the digital twine model construction. The transition intensities of the Markov model are estimated by using the multi-physics simulation data. In the proposed method, the multi-physics simulation method can incorporate the diffusion equation and the kinetic equation of the corrosion, allowing for the simulation of water molecule diffusion within the organic coating and the coupling simulation of the metal corrosion process. Subsequently, the reliability of the organic coating-substrate structure is analyzed under varying temperatures, humidity levels, and protective material parameters. The result shows that higher ambient temperatures and relative humidity levels contribute to an accelerated corrosion rate of the substrate, and the reliability decreases.

Reliability Analysis for Degradation-Shock Processes with State-Varying Degradation Patterns Using Approximate Bayesian Computation (ABC) for Parameter Estimation

The degradation of products is an integral part of their life-cycle, often following predictable trajectories. However, sudden, unexpected events, termed ’shocks’, can substantially alter these degradation paths. Shocks can significantly influence the pace of degradation, leading to accelerated system failure. Moreover, they may initiate changes in degradation patterns, transitioning from linear to non-linear or random trajectories. To address this challenge, we present a novel multi-state reliability model for competing failure processes that account for degradation-shock dependencies by considering the state-varying degradation pattern. The degradation process is divided into s-states, with each state treated according to its pattern based on the time-transform Wiener process. The reliability function is derived based on soft failure caused by continuous degradation involving the s-states, the sudden increase in degradation caused by random shocks, and hard failure due to some shock processes. Additionally, we performed a sensitivity analysis to determine which parameters have the most significant impact on product reliability. Due to the complexity of the likelihood function, we adopted the ABC method to estimate the model parameters. A simulation study and a practical application with micro-electro-mechanical systems (MEMS) degradation results are used to demonstrate the efficiency and effectiveness of the proposed approach.

Long-term reliability evaluation of integrated electricity and gas systems considering distributed hydrogen injections

Power-to-gas facilities consume surplus renewable electricity generation to produce alternative gases, such as green hydrogen. They can be injected into, and transported by the gas network for further use, which is a promising way toward a low-carbon energy system. However, injecting alternative gases into the gas systems can adversely affect the gas composition and the lifespan of components (e.g., gas pipelines), and may threaten the reliability of the entire integrated electricity and gas systems (IEGS) in the long term. To address this issue, this paper proposes a long-term reliability evaluation method for IEGS with distributed hydrogen injections. First, new reliability indices are proposed to evaluate both gas adequacy and gas interchangeability under uncertainties. Then, a multi-state reliability model of the pipeline is developed to characterize the corrosion evolution and hydrogen embrittlement in the long term. A contingency management scheme (CMS) is devised to minimize load curtailments and gas interchangeability deviations under component failures. Moreover, several reformulation techniques are tailored to convexify the original two-stage mixed-integer nonlinear CMS optimization problem. An analytical reliability evaluation method embedded with a system state reduction technique is designed to evaluate the long-term reliability of the IEGS more efficiently. Finally, the IEEE 24 bus Reliability Test System and the practical Belgium gas system are used to validate the proposed method. The numerical results show that the injection of alternative gas could jeopardize the reliability of the studied IEGS by 39.73% in the long term. However, we have observed a critical time window (the 8th–9th year), in which if we conduct the inline inspection and maintenance more frequently, the reliability could be improved by up to 53.31%. These results suggest that the injection of alternative gas is beneficial, but should be carefully regulated to maintain the reliability of IEGS.

Reliability modeling of wave energy converters based on pelamis technology

Wave generators, as renewable sources, are increasingly applied for power generation in developed electric networks. With the development of wave generator technologies, large-scale devices such as oscillating water columns, pelamis, wave-dragon, oyster, buoy, sea wave slot cone converter, and tapchan have been invented to extract electrical power from wave energies. The output of wave generators relies on the height and period of waves, and because of the wide variation in these quantities, the produced power from them changes widely. Therefore, in electric networks incorporating large wave generators, reliability is influenced and should be analyzed. In this paper, for the first time, the reliability modeling of pelamis, as a kind of commercial-scale wave generator, is executed. In the proposed multi-state reliability model of pelamis, failures of composed components and changes in the production of power are addressed. To obtain the optimal number of power states in the model, the XB factor is computed. Then, to reduce the number of power states in the model, the fuzzy c-means clustering methodology is applied. The obtained model is used to examine the adequacy assessment of an electric network containing a pelamis farm. Numerical results show that wave converters can improve the reliability performance of electric systems. However, wave period and height affect the reliability indices of the power system. The effectiveness of the proposed method is validated by comparing the outcomes obtained by the analytical and Sequential Monte Carlo Simulation methods.

Impact of system parameters and geospatial variables on the reliability of residential systems with PV and energy storage

A reliable power supply is the foundation of modern society, enabling technologies used to function within a society. Residential systems are places where the end users directly consume power, enabling technologies to sustain life. With the emergence of behind-the-meter resources, the end-users have some control over power supply reliability. The intermittency and variability of these resources impact residential system reliability. In this work, we study the reliability performance of a grid-supplemented residential system with behind-the-meter Distributed Energy Resources(DER) subject to various system parameters and geospatial variables. We propose a multistate reliability model for the behind-the-meter microinverter-based Photo Voltaic (PV) system and integrated inverter-based energy storage (ES) system. A sequential Monte Carlo method is then presented to evaluate the reliability indices for the residential system with behind-the-meter DERs as the main supply and the grid as the backup. The sequential Monte Carlo method is used to analyze the reliability performance of the residential model at the top 100 populous counties of the United States, where actual load and solar irradiance data at the counties is used. In the analysis, the sensitivity of indices to system parameters such as DER size and the sensitivity of the indices to climate zone and gross horizontal irradiation (GHI), which affects the load conditions and the PV output of the residential system, is performed. The analysis results show that the system parameters and the geospatial variables significantly impact the residential system’s reliability. The insights from this analysis will be of immense value to the distribution system planners to provide zone-specific guidelines for DER system sizing and toward the evolution of utility business models. The methodology developed can be used to extend the analysis to other locations.

Multi-state reliability modeling method for Tianwen-1 high-resolution camera

Multi-state reliability modeling method for Tianwen-1 high-resolution camera

Reliability analysis of an active distribution network integrated with solar, wind and tidal energy sources

The global trends toward increasing clean and sustainable power generation have brought significant changes and developments in electrical distribution networks. The existing passive networks are being restructured to facilitate renewable distributed generations to ensure high degree of reliability of power supply to customers. A distribution system reliability assessment (DSRA) is crucial to analyze the risk and cost associated with power interruptions and take necessary preventive and corrective actions. This paper presents an approach to DSRA and carries out a comprehensive reliability assessment of an active distribution network (ADN) connected with solar, wind, and tidal energy sources. A multi-state reliability model is developed, combining the Markov and well-being frameworks to determine the reliability of a network energized by multiple renewable energy sources (RESs). The load point reliability and worth-oriented indices, namely SAIDI, SAIFI, CAIDI, AENS, EENS, ECOST and IEAR, are evaluated to analyze the impacts of the three RESs on the reliability of the ADN. The paper also proposes two new metrics to estimate the benefits of adding RESs from the reliability worth and cost perspectives. The analyses have been carried out on the Roy Billinton Test System. The results show that the maximum reliability worth and cost benefits can be extracted from a combined operation of multiple RESs. A combination of solar-wind-tidal energy sources, therefore, can be an effective solution for countries having long coastlines to fulfill not only the sustainable energy goals but also to improve the grid's reliability and reduce the monetary losses incurred due to customer interruptions.

Reliability Analysis of Flexible Multiple State Switch Based on Bayesian Network Method

In order to accurately establish the reliability model of flexible multiple state(FMSS) switch and excavate the weaknesses of component reliability, a method of reliability modeling of FMSS based on Bayesian network is proposed in this paper. Firstly, a multi-state reliability model is established by Markov process. Then, the Bayesian network of MMC is established. The correctness of the model is verified by examples. The reliability of SM, MMC and FMSS is calculated. The influence of submodule redundancy on FMSS is analyzed. The weak link of FMSS is analyzed. The research results in this paper can provide support for the application of FMSS in distribution network.

Spinning reserve scheduling in power systems containing wind and solar generations

Wind and solar as two renewable energy resources are largely used to generate clean and sustainable energy in the power systems. To integrate these renewable energies in the power system, different aspects of the power system such as reliability and operation are affected that must be investigated. It is due to the variation in the generated power of these resources that are arisen from the variation in the wind speed and solar radiation. To model the uncertainty nature of large-scale wind and photovoltaic farms in the operation studies of the power system, an appropriate multistate reliability model is developed for the wind and photovoltaic farms considering both failure of main components and variation in the wind speed and solar radiation. To determine the optimum number of states in the reliability model of wind and photovoltaic farms, XB index is calculated and based on the fuzzy c-means clustering technique the transition rates among different states are obtained. To calculate the transition rates among different states, the fuzzy numbers are used that results in the accurate and reduced reliability model for wind and photovoltaic farms. To determine the probability of different states in the reliability model of wind and photovoltaic farms in the operation studies, matrix multiplication technique is utilized to determine important indices of the power system such as the unit commitment risk. In this paper, the amount of required spinning reserve of a power system containing wind and solar generation units can be determined based on the reliability criterion. The proposed technique is applied to the two reliability test systems including RBTS and IEEE-RTS and the reliability-based operation indices of these systems are calculated to present the effectiveness of the proposed analytical method.

Reliability evaluation for multi-state manufacturing systems with quality-reliability dependency

As multi-state reliability models and the dependency theory can characterize the polymorphism of manufacturing systems during degradation, they have been discussed in depth over the past few decades. However, most studies on the dependence of manufacturing systems ignored the dynamic characteristics (the production rhythm). Therefore, a reliability evaluation method that considers quality-reliability (Q-R) dependency of a multi-state manufacturing system is proposed in this paper. Q-R dependency contains two main characteristics: quality deviation and production rhythm. The stochastic-flow manufacturing network (SFMN) model is constructed to describe the interaction among machines, products, and buffers in a manufacturing system. Moreover, the quality state-space model and the usage of buffers are used to quantify the quality deviation and the production rhythm, respectively. Reliability evaluation method for multi-state manufacturing systems with Q-R dependency is proposed. Finally, an illustrative example is presented to demonstrate the effectiveness of the proposed method.

Reliability Assessment Framework for the Distribution System Including Distributed Energy Resources

This paper introduces a new framework for the reliability assessment of the distribution systems. The framework proposes three levels to include the effects of distributed generation (DG), energy storage (ES) systems connected to the distribution system and as behind the meter at the customer premises, coordination of resources, and cyber-physical systems. Methodology for level 2 reliability assessment that includes behind the meter DG and ES systems of the distribution system is proposed. A multi-state reliability model for behind the meter PV systems is developed along with the model for the ES system. The developed methodology is demonstrated on the RBTS bus 4 test distribution system with behind the meter PV and ES systems.

Model niezawodności oparty na wydajności przesyłu energii i jego zastosowanie do oceny lotniczego układu hydrauliki siłowej

The power transfer systems (PTS) has special reliability properties, including multiple states and fault dependence. Consequently, traditional binary-state reliability modeling methods cannot accurately evaluate the reliability of PTS. In order to resolve the contradiction between terminal energy demand and power transfer capability of PTS, this paper proposes a novel multi-state reliability model based on power transfer efficiency (PTE) for reliability evaluation of PTS. The multi-state model caused by performance degradation based on PTE is considered in this paper. In addition, the failure correlation in virtue of the system structure and energy allocation mechanism is analyzed in the proposed model, and the corresponding reliability evaluation result is obtained under different terminal energy requirements. The approach is verified on the example of a dual hydraulic actuation system (DHAS), in which the stochastic model based on the generalized stochastic Petri nets (GSPNs) is established and combined with the power transfer capability via universal generating function (UGF). Though changing flow rate to face the degradation rate of hydraulic pump, the reliability assessment of DHAS based on the proposed reliability model is effective and accurate.

Reliability assessment of multi-state reconfiguration pipeline system with failure interaction based on Cloud inference

Traditional reliability theory cannot objectively describe the multi-state of the pipeline system with reliability analysis. In addition, studies on reliability modeling of the multi-state pipeline system assume that the states of each pipeline unit are independent. In this work, an efficient method was proposed to identify the performance relationship. Specifically, a model of a multi-state reconstruction system containing the decaying process and the repairing process was established. Also, a multi-state reliability modeling method was developed based on the performance degradation process of the pipeline system considering the failure interaction. Further, the Markov model of the degradation process was built to determine the relationship between the occurrence probability of each state and the decay path. The cloud generalization function was established using cloud inference combined with the general generation function. The pipeline system can be dynamically divided by the analytic hierarchy process according to different factors affecting the degradation of pipeline performance. A numerical example was used to demonstrate the efficiency and applicability of the proposed method by comparing it with existing methods. The proposed approaches are found to be sufficient to improve risk decision and reliability analysis of the pipeline system, which better supports the reliability-informed integrity management for the whole system.

Degradation-Based State Reliability Modeling for Components or Systems With Multiple Monitoring Positions

Engineering components or systems may have multiple monitoring positions for the degradation observations of single or multiple performance characteristics. For the reliability analysis with multiple degradation processes, the existing works are generally based on the binary-state degradation model and the Copula method, where the component or system survives only if every single monitoring position survives. This article develops a degradation-based continuous multistate reliability model through the definition of the state function, where the component or system state is determined by the states of all the monitoring positions. Furthermore, two reliability analysis frameworks of components or systems with multiple monitoring positions are given: $ k$ -out-of- $ n$ reliability framework and importance reliability framework. The proposed method not only casts off the binary-state constraint for the degradation modeling, but also gives a new way to analyze the component or system reliability in the case of multiple degradation processes, which are monitored in multiple monitoring positions. A numerical case and a practical case about the train wheel tread are given to demonstrate the availability and the possible advantages of the proposed model.

Reliability Modeling of Reservoir-Based Tidal Power Plants for Determination of Spinning Reserve in Renewable Energy-based Power Systems

The penetration level of renewable and sustainable energy resources such as geothermal, wind, solar energies and ocean in power generation systems has been increasing. One of the important renewable energy resources is tidal power plants which makes use of rising and falling sea water level. Because of the uncertain nature of the generated power arisen from the variation in the water level in flood and ebb situations, integration of large-scale reservoir-based tidal power plants to power systems can involve numerous types of challenges. Thus, large-scale tidal power plants can be effectively used in operation studies of power systems. For this purpose, a probabilistic approach is introduced in this paper based on the modified PJM technique for integrating the large-scale tidal plant into operation studies of the power system. In this regard, a multi-state reliability model considering both the failure rate of composed components and the variation in the tide levels is developed and used in the operation studies. For evaluation of the impact of the tidal power plant on operation studies of a power system, numerical examples are put forward in which important indices such as unit commitment risk, required spinning reserve and peak load carrying capability can be calculated.

Adequacy studies of power systems with barrage‐type tidal power plants

Tidal as renewable energy is increasingly utilised for power generation in many countries. Integration of tidal plants into the power system requires considering the intermittent nature of the generated power caused by variable tide levels. Thus, the reliability studies of power systems including high tidal generation affected by the uncertain nature resulting from the variable water levels are investigated. The reliability model of a tidal power plant on a barrage is proposed. In the proposed model, the failure rates of the composed components (especially the hydro pump and gate) and the effect of tidal height variation on the components failure rate are considered. Also, the reliability model with numerous states resulting from the variability of the generated power through the fuzzy C-means clustering technique and Xie-Beni index is reduced to a multi-state reliability model. The resulting reliability model is utilised for the generation adequacy studies of a power system containing large-scale tidal power plants. Moreover, different reliability indices are calculated for future generation expansion planning. The proposed technique is applied to the two-test systems, and sensitivity analysis is performed. Besides, the effects of the hydro pump, maintenance, ageing of the components and peak load are investigated.

Multi-state operating reserve model of aggregate thermostatically-controlled-loads for power system short-term reliability evaluation

Thermostatically-controlled-loads (TCLs) have been regarded as a good candidate for maintaining the power system reliability by providing operating reserve. The short-term reliability evaluation of power systems, which is essential for power system operators in decision making to secure the system real time balancing, calls for the accurate modelling of operating reserve provided by TCLs. However, the particular characteristics of TCLs make their dynamic response different from the traditional generating units, resulting in difficulties to accurately represent the reliability of operating reserve provided by TCLs with conventional reliability model. This paper proposes a novel multi-state reliability model of operating reserve provided by TCLs considering their dynamic response during the reserve deployment process. An analytical model for characterizing dynamics of operating reserve provided by TCLs is firstly developed based on the migration of TCLs’ room temperature within the temperature hysteresis band. Then, considering the stochastic consumers’ behaviour and ambient temperature, the probability distribution functions of reserve capacity provided by TCLs are obtained by cumulants. On this basis, the states of reserve capacity and the corresponding probabilities at each time instant are obtained for representing the reliability of operating reserve provided by TCLs in the LZ-transform approach. Case studies are conducted to validate the proposed technique.

Switching-Algebraic Analysis of Multi-State System Reliability

Multi-State systems are systems whose outputs are multi-valued (due to multiple levels of capacity or performance) and (possibly) whose inputs are also multi-valued (due to multiple performance levels or multiple modes of failure). These systems are a generalization of binary or dichotomous systems that have binary or two-valued outputs and inputs. The multi-state reliability model generalizes and adapts many of the concepts and techniques of the binary reliability model, and naturally ends up with sophisticated concepts and techniques of its own. This paper explores the possibility of simply analyzing a multi-state system by reformulating or encoding its inputs in terms of binary inputs and evaluating each of its multiple output levels as an individual binary output of these alternative inputs. This means that we dispense with multiple-valued logic in the analysis of a multi-state system, since this system is now analyzed solely via switching algebra (two-valued Boolean algebra). The wealth of tools and techniques of switching algebra are now used (without any modification or adaptation) in the analysis of the multi-state system (at the cost of an expanded input domain). The paper makes its point though the analysis of a standard commodity-supply system, whose multi-valued inputs are expressed in terms of physically-meaningfully binary inputs. The analysis is made possible through the use of advanced techniques for deriving probability–ready expressions together with the employment of large-size Karnaugh maps and utilization of multiplication tables, symmetric switching functions, and Boolean quotients. Though the system studied involves twelve binary input variables, its manual analysis is completed successfully herein, yielding results that exactly agree with those obtained earlier via automated methods, and are possibly less prone to the notorious effects of round-off errors.

Reliability and Safety Analysis on Multi-state System of EMUs with Degraded Components

Aiming at the restrictions of the conventional reliability analysis based on binary logic on the systems with degraded components, a multi-state reliability analysis modeling method is proposed. The components and systems are classified into different states in this model according to different failure levels. Then a multi-state logic relation is established among units and systems as per the systematic block diagram, and the reliability analysis model for multi-state system is constructed, in which multi-level system reliability is realized and the major hazards resulted from neglecting potential faults in the binary system are avoided. Meanwhile, in line with the temporal distribution of system reaching ultimate limit state in safety, a system risk function is formulated. Therefore, the safety analysis model for a multi-state system is constructed. The examples of reliability analysis on EMU traction system indicate the effectiveness and advantages in evaluating reliability and safety of a complex system with multi-state reliability and safety analysis model.