Analytical Methods in Reliability Analysis

This paper reviews three main methods in reliability analysis for power systems and applies them to a micro-grid with significant clean energy penetration. The approaches used are Reliability Block Diagrams (RBD), Fault Tree Analysis (FTA) and Markov Reliability Modeling (MRM). Each method is introduced and applied to a simple system to illustrate its application procedure. Reliability parameters such as the system's mean time to failure (MTTF), component structure importance, and reliability function are evaluated using simulation models. All three methods are then used to find the reliability measures of a real micro-grid which is characterized by significant clean energy penetration using solar photovoltaic panels and a fuel cell.

This paper presents a general mechanical system reliability modeling and analysis method, which consider the correlations of failure modes. Firstly, the performance functions which mathematically represent the failure modes are linearized based on FORM (First Order Reliability Methods), and the correlation coefficient matrix of those functions is calculated. Then, the PFTA (Probabilistic Fault Tree Analysis) method is adopted to establish the system reliability model which can take the correlations into account. Finally, effective algorithms such as G-FOMN (General First Order Multinormal Method) are used to quantify the system reliability, and the sensitivities of the system reliability index with respect to each failure mode, as well as the mean value and standard deviation of each random variable are also calculated. An engineering example demonstrates the applicability of the proposed method.

A self-anchored suspension bridge contains many interrelated and acting components. The damage of any component under load may affect the service function of the bridge. The reliability index of a single element often overestimates the safety state of the bridge. To evaluate the overall reliability of a self-anchored suspension bridge, a reliability analysis method for a self-anchored suspension bridge system based on the integral dimension reduction (IDR) method is established, which avoids the calculation of high-dimensional integral and greatly improves the analysis efficiency. Firstly, the reliability indexes and checkpoints of each potential failure element are analyzed. Secondly, the sensitivity of random variable reliability is analyzed and the corresponding safety margin equation is established. Finally, the IDR method is used to reduce the dimension of high-dimensional integral and transform it into the product of equivalent linear failure mode failure probability, which improves the analysis efficiency. Using this analysis method, the static system reliability of a three-tower self-anchored suspension bridge is analyzed, which provides a method of system reliability analysis of this kind of bridge.

System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding method

Generally, overvoltages trigger the protection aspects of the inverter to disconnect from the grid, resulting in islanding operation of the PV system. This further contributes to abrupt voltage fluctuations, load shedding and sudden changes in power flow. Therefore, the distribution networks associated with high penetration PV generation have a risk of power outages and in turn increased maintenance costs. This necessitated the tools and methodologies to quantify reliability of the grid-connected PV systems. These reliability analysis tools and methods serve to evaluate the performance of PV systems and generate reliability indices, which further aid in achieving efficient design at the planning stage and determining the reduced cost and improved benefits at the operational phase. A systematic way to evaluate the reliability of grid-connected PV inverters is then presented in this chapter. The reliability analysis is carried out at the 2.2 MW grid-connected rooftop PV system installed in Jamia Millia Islamia (JMI), New Delhi, India, considering the variations of input power and failure rates of PV system components under ambient conditions. The reliability analysis is carried out for inverters at both string level and central level with the site data as a benchmark. A basic reliability indices computation method is adapted to realize the operation of both inverter system for several risk metrices and quantify their impact on system operation.

According to the piezoelectric material damage theory and the fracture criterion based on damage theory, which has been established by Yang etc., reliability analysis is carried through about a damaged piezoelectric truss. Taken the mechanical damage extension force, electric damage extension force and cross-section area of bar element as stochastic variables, the expression of safety margins of bar element has been proposed. Based on those, the SFEM and PNET method are introduced to solve the reliability index of the structural system. The result indicates positive applied and negative applied electric field have great effect on the reliability of the system, which provides the basis to control the reliability of structural system. Finally, a calculation example is carried out under the conditions of positive applied electric field, negative applied electric field and no electric field. Meantime, the quantification results of the reliability index under three conditions are compared with each other.

Sequence operation theory and its application in power system reliability evaluation

A new unequal-weighted sampling method for efficient reliability analysis

In this study, long term component reliability analysis of PV system is performed using Markov method. Four major components for evaluation of the system are considered with 16 different states to evaluate a PV system as a package with one reliability index. The probability analysis for each state shows that although at very first years the states of combination of multiple failures are negligible, after several years of operation, all states are effective in the reliability of the system. Based on Markov modeling given in the study and actual failure and repair rates of components, the reliability analysis shows that the reliability of the system decreases from 0.99 to 0.81 in 20 years. The initial condition for each year is gained from the final condition of the previous year. The annual value of the reliability of PV system makes the designers plan major maintenance and switching based on cost and load. 1

Aiming at the limitation of traditional trans-scale safety and arming device reliability analysis method, this paper presents a reliability calculation method for trans-scale safety and arming device about failure mechanism, failure process and failure mode correlation. The problem which the trans-scale safety and arming device is easy to be affected by technology, structure, gap, material and so on, the failure mechanism is complex, the reliability data is short and the reliability is difficult to predict is solved. This article estimates the system reliability of (the reliability is 0.992725), analyzes the key failure modes and influencing parameters that affect system reliability, and establishes an optimization design model based on the key reliability impact parameters, which improves the system reliability index (reliability is 0.99905) and verifies the accuracy and rationality of the reliability analysis method.

A combination method for modeling wind power plants in power systems reliability evaluation

Electrical systems have evolved toward greater complexity, demanding dynamic methods to assess their reliability. Traditional reliability analysis methods often fail to account for operational changes that a system undergoes over time, which affects the importance and criticality of its components. Variability in component reliability and failure probabilities can alter a system's internal structure, changing the relevance of certain components at different times. This study proposes an integrated methodology based on importance measures to evaluate reliability in systems with dependent components. Given that conventional Reliability Block Diagram (RBD) models are typically static and do not consider standby redundancy, importance measures were incorporated into the reliability analysis. This approach enabled the identification of critical components and the prioritization of maintenance strategies. The measures used include the Birnbaum importance index, improvement potential, risk reduction, and criticality. The methodology allows modeling the survival signature of components and the complete system at a given time, incorporating a Monte Carlo algorithm to analyze system reliability while accounting for dependencies between elements. This method was applied to a hydroelectric power plant, facilitating informed maintenance decision-making.

Reliability block diagram (RBD) is an effective tool for modeling and evaluating system reliability. During operation, a system’s reliability may decrease significantly due to the failure of certain critical nodes and thus should be reconfigured. This paper presents a framework for system reliability evaluation and dynamic optimization based on RBD, designed from the perspective of system users. First, we improve the classic RBD model with a new encoding scheme and develop an accurate RBD computation algorithm that is easily recognized by computers and highly efficient. Second, we create an optimization algorithm based on Tabu Search to reconfigure the system after node failure, striking a balance between system reliability recovery and RBD variation amplitude. Finally, we provide some numerical examples and a computational experiment based on a practical instance from a navy fleet to demonstrate the correctness and effectiveness of our proposed methods.

This paper reviews some of the analytical methods developed in our laboratory for reliability evaluation of large scale power systems including renewable energy sources like photovoltaic units and wind farms. The methods presented here successfully reflect the correlations existing between the hourly load and the fluctuating energy outputs of unconventional generating units. Three different approaches, each an improvement over its predecessor, are presented for computing reliability indices like Loss of Load Expectation (LOLE) and Expected Unserved Energy (EUE). In the first approach, all the generation system models are combined hourly by means of an efficient algorithm for calculating the relevant reliability indices. The second approach uses a clustering algorithm for identifying a set of system states, such that the reliability indices are calculated for each state and then aggregated to yield overall values. The third approach introduces the concept of mean capacity outage tables for efficiently calculating EUE,

In this paper, a new method is developed that can be applied efficiently in reliability analysis and design verification of structures under random vibration. This method is based on singular value decomposition of modal coordinates cross covariance matrix. Computational algorithm and relative flow chart for this method is developed and compatible reliability criterion with this algorithm has been extracted. In order to results verification, we use Miles relation and Monte Carlo simulation -that are two well known methods in reliability analysis- and all of these methods are applied to a simple finite element model. Results show that new algorithm is more efficient for reliability analysis of structures under random vibration.