Interval Reliability Evaluation of a Hybrid Energy Generation System With Energy Storage

To deal with the uncertainties of wind power and load residing in the power supply reliability model, an interval reliability evaluation method is proposed by combining the wind power generation and energy storage system (ESS). Firstly, the interval power supply reliability evaluation model, which belongs to an interval mixed integer program (IMIP), is established based on the interval variables. Secondly, the IMIP model is transformed into the deterministic optimization model under two extreme circumstances by utilizing the possibility degree theory of interval numbers. The maximum power supply probability, considering the wind power interval to meet the load demand interval, is sought by optimizing outputs of the ESS and generators, i.e., the upper boundary of the load shedding is the smallest. Finally, the states of wind turbines and generators are generated based on sequential Monte Carlo simulation, and the reliability of the hybrid energy generation system is evaluated by calculating the loss of load expectation, expected energy not supplied, and maximum power supply probability, which provides a basis for establishing interval optimal allocation model of energy storage. IEEE RTS-24 test system is utilized to verify the performance of the proposed method, and the model is solved by the CPLEX 12.7 solver. The simulation results demonstrate the effectiveness and applicability of the proposed method.

Computational Method and Simulation of Reliability for Series, Parallel, and k-Out-of-n Systems with Interval Parameters

For series, parallel, and k-out-of-n voting system reliability calculation methods, the six σ principles have been proposed in this study to derive the interchange relationship between interval parameters and random parameters. The interval reliability index can be expressed in the function of the random reliability index. The interval reliability index can then be transformed into a random reliability index. The computational method of the reliability for series, parallel, and k-out-of-n voting systems with interval parameters is established. Finally, it has been shown that the proposed method is rational, practical, and applicable with two engineering practical simulations.

Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

In this paper, a new reliability measure, named sequential interval reliability, is introduced for homogeneous semi-Markov repairable systems in discrete time. This measure is the probability that the system is working in a given sequence of non-overlapping time intervals. Many reliability measures are particular cases of this new reliability measure that we propose; this is the case for the interval reliability, the reliability function and the availability function. A recurrent-type formula is established for the calculation in the transient case and an asymptotic result determines its limiting behaviour. The results are illustrated by means of a numerical example which illustrates the possible application of the measure to real systems.

On the Computation of Some Interval Reliability Indicators for Semi-Markov Systems

In this paper, we computed general interval indicators of availability and reliability for systems modelled by time non-homogeneous semi-Markov chains. First, we considered duration-dependent extensions of the Interval Reliability and then, we determined an explicit formula for the availability with a given window and containing a given point. To make the computation of the window availability, an explicit formula was derived involving duration-dependent transition probabilities and the interval reliability function. Both interval reliability and availability functions were evaluated considering the local behavior of the system through the recurrence time processes. The results are illustrated through a numerical example. They show that the considered indicators can describe the duration effects and the age of the multi-state system and be useful in real-life problems.

A Sensitivity-Based Approach for Reliability Analysis of Randomly Excited Structures With Interval Axial Stiffness

Reliability assessment of linear discretized structures with interval parameters subjected to stationary Gaussian multicorrelated random excitation is addressed. The interval reliability function for the extreme value stress process is evaluated under the Poisson assumption of independent up-crossing of a critical threshold. Within the interval framework, the range of stress-related quantities may be significantly overestimated as a consequence of the so-called dependency phenomenon, which arises due to the inability of the classical interval analysis to treat multiple occurrences of the same interval variables as dependent ones. To limit undesirable conservatism in the context of interval reliability analysis, a novel sensitivity-based procedure relying on a combination of the interval rational series expansion and the improved interval analysis via extra unitary interval is proposed. This procedure allows us to detect suitable combinations of the endpoints of the uncertain parameters which yield accurate estimates of the lower bound and upper bound of the interval reliability function for the extreme value stress process. Furthermore, sensitivity analysis enables to identify the most influential parameters on structural reliability. A numerical application is presented to demonstrate the accuracy and efficiency of the proposed method as well as its usefulness in view of decision-making in engineering practice.