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Wind profile, wake effect, and wind turbine outage create considerable impact on the energy production of a wind farm. This paper proposes a Markovian wind farm generation model that incorporates these factors. This model considers the wind farm as a generating unit with multiple generation states. The probability, frequency of occurrence, and transition rate of each state can be obtained using the collected wind profile data and wind turbine reliability parameters. The power output of each state is calculated using Jensen wake model and enumerated wind farm layouts. The proposed model is verified by a sequential Monte Carlo simulation approach using a test wind farm and recorded wind profile data from four different sites in North Dakota, USA. A state merging technique is developed to enable the application of the proposed model to adequacy assessment. The Roy Billiton Test System with a test wind farm is used to demonstrate the application of the proposed model and the procedure to adequacy assessment. Moreover, this paper investigates the influence of wake effect, peak load, seasonal wind pattern, wind turbine reliability parameters, and wind turbine type on system adequacy. [ABSTRACT FROM AUTHOR]

Many utilities in developing countries are investing in installation and renewing of Electrical Distribution System (EDS) components, such as overhead lines, cables and switching devices, to improve the EDS reliability and meet the rapid increase of load demand. In the beginning stage of investment, it is very difficult to evaluate the EDS reliability by using traditional methods due to EDS topology not being fully determined. This paper presents a comprehensive model for forecasting EDS reliability, which is built separately into two parts, i.e. the models for EDS failures and planned outages. Firstly, a three-layer Artificial Neural Network (ANN) model is proposed to forecast the EDS reliability considering EDS failures. Each neuron in the ANN input layer represents a key influencing factor of EDS failures, which are recognized by Gray Relational Analysis (GRA) method. The proposed ANN is trained using historical reliability data of an EDS. In addition, a planned outage reliability model is also built according to the magnitude of investment and type of planned outage. The priorities of improvement measures can also be obtained using the GRA to improve the EDS reliability. Case studies of practical EDSs illustrate the efficiency and applicability of the proposed techniques. [ABSTRACT FROM AUTHOR]

Abstract: The electrical energy production and reliability benefits of a wind energy conversion system (WECS) at a specific site depend on many factors, including the statistical characteristics of the site wind speed and the design characteristics of the wind turbine generator (WTG) itself, particularly the cut-in, rated and cut-out wind speed parameters. In general, the higher the degree of the wind site matching with a WECS is, the more are the energy and reliability benefits. An electrical energy production and reliability benefit index designated as the Equivalent Capacity Ratio (ECR) is introduced in this paper. This index can be used to indicate the electrical energy production, the annual equivalent utilization time and the credit of a WECS, and quantify the degree of wind site matching with a WECS. The equivalent capacity of a WECS is modeled as the expected value of the power output random variable with the probability density function of the site wind speed. The analytical formulation of the ECR is based on a mathematical derivation with high accuracy. Twelve WTG types and two test systems are used to demonstrate the effectiveness of the proposed model. The results show that the ECR provides a useful index for a WTG to evaluate the energy production and the relative reliability performance in a power system, and can be used to assist in the determination of the optimal WTG type for a specific wind site. [Copyright &y& Elsevier]

Abstract: Power system component failures can generally be classified into two categories: repairable random failures and aging failures. An essential step in power system reliability evaluation is the calculation of component unavailability. The paper presents a new model for calculating the unavailability due to aging failures using the normal distribution. It is based on the strictly mathematical derivation and can be used more easily with high accuracy compared to the traditional model. An example of seven generating units and two test systems of the RBTS and the IEEE-RTS were used to demonstrate effectiveness of the proposed model and its applications in power system reliability evaluation. [Copyright &y& Elsevier]

Abstract: Weak part analysis of a system is a key element in a system reliability quantification process. It enables the weakest areas of a system to be recognized and assists in directing remedial measures for improving the system reliability. This paper presents a novel approach to identifying the weak parts using the unreliability tracing (UT) technique and introduces the proportional sharing principle (PSP). The model for tracing the unreliability of a complex network is presented based on reliability evaluation methods using minimal cut sets (MCSs) and the PSP. The system UT sharing factors (UTSFs) are derived to easily identify the major unreliability contributions (MUCs) in a system. The method is illustrated using three cases and the UT, UTSF and the reliability impact analysis of different components are discussed. The results show that the developed technique can be applied to complex networks for UT tracing and recognizing the MUC. [Copyright &y& Elsevier]

• The proposed multi-state model prevents the underestimation of reliability level caused by two-state failure model. • The proposed model can accurately evaluate the reliability index, which better reflects the multiple operation states. • Different TES strategies will lead to different operation decisions and reliability results of CSP plants. • The SF size and the TES capacity are positively correlated with the system reliability level. But the system reliability index tends to be stable when the SF size and the TES capacity are large. This paper proposes a multi-state reliability evaluation model for the concentrated solar power (CSP) plant considering partial function failure. Firstly, the component functions and components' consequences of random failure of CSP plants are analyzed. Core components affecting the output of CSP plants are selected. The CSP plant is divided into three subsystems: the heat collection, the heat exchange, and the power generation subsystems, according to the component function. Each subsystem is equivalent to a two-state component. Thus, an 8-state Markov model of CSP plant is established. The CSP plant can be operated in a partial function failure state as thermal energy storage (TES) or generation, depending on the functions of solar-heat and heat-electricity conversion. On this basis, the 8-state model can be simplified to a 4-state model by combining the partial function failure states of the same effect. Finally, the 4-state model is applied to the sequential Monte Carlo simulation for the reliability evaluation of power systems containing CSP plants. Two TES strategies are considered in the simulation: One is based on solar field (SF) average output, another is designed to satisfy the load preferentially. The proposed model is tested on the modified RBTS/IEEE RTS systems to verify the effectiveness. [ABSTRACT FROM AUTHOR]

• A novel sparse density estimator named GCE is presented for dependence modeling. • A CE method using GCE is developed to get the IS-PDF of correlated RVs (CRVs) • Composite system reliability evaluation is greatly accelerated using IS-PDF of CRVs. Multivariate kernel density estimation (KDE) is powerful for dependence modeling, but producing a non-sparse probability density estimation model. To address this issue, a sparse density estimation technique termed as generalized cross-entropy (GCE) density estimator, is proposed to estimate the joint probability density function (PDF) of correlated random variables (RVs). Moreover, to effectively accelerate the composite systems reliability evaluation, a unified cross-entropy based importance sampling (CEIS) method accommodating both GCE and KDE density estimators is presented, and a creative CE optimization approach is also developed based on the composition sampling algorithm, through which the analytical updating rules of IS-PDF parameters can be derived even though GCE and KDE estimators do not belong to the exponential distribution family (EF). Compared to the KDE estimator, the GCE estimator encounters much less dimensionality difficulty in CE optimization due to the model sparsity merit, and consequently achieves more accurate IS-PDF parameters and better CEIS efficiency. The superiority of GCE estimator over KDE estimator in correlation modeling and CEIS is verified by several numerical tests. [ABSTRACT FROM AUTHOR]

• The cross-entropy (CE) method addressing high-dimensional dependencies is explored. • A CE method termed as CE-DRDM is developed from dimension reduced dependence model. • An improved hierarchical disaggregate structure is proposed to enhance CE-DRDM. • A novel CE optimization is used to derive the analytic formula of IS-PDF parameter. • A novel sparse density estimator is used to reduce the number of IS-PDF parameter. Cross-entropy (CE) based importance sampling (IS) accelerates the reliability evaluation of power system greatly, but is mainly focused on the CEIS of independent random variables (RVs) or low-dimensional correlated RVs (CRVs). To extend the CE method to high-dimensional CRVs while avoiding the "curse of dimensionality" in optimizing a high-dimensional IS probability density function (IS-PDF), an efficient CE method termed as CE-DRDM, is developed from a dimension-reduced dependence model (DRDM). First, based on the DRDM's original hierarchical disaggregate structure (HDS), the CE-DRDM which conducts the CEIS for a single aggregate RV rather than the high-dimensional CRVs is proposed. Second, to solve the issue that the performance of CE-DRDM may degrade in the case of high penetration of renewable energy, the CE-DRDM is enhanced by improving the DRDM's HDS, and then a novel CE optimization method is proposed, through which the analytical updating formulas of IS-PDF parameters can be derived. Thirdly, the CE-DRDM is further enhanced by using a sparse density estimator, based on which the number of IS-PDF parameters needed to be optimized in the CE optimization reduces greatly, and consequently the optimization accuracy improves accordingly. Finally, the validity of CE-DRDM is verified by several numerical cases with high-dimensional dependencies. [ABSTRACT FROM AUTHOR]

• Introduce the risk masking effect for contingency analysis of transmission system. • Propose a screening model for top incremental risk events. • Perform case studies to illustrate the advantage of screening with incremental risk. Screening of severe contingency event is vital in transmission system operation and planning. This study investigates the reliability issue of load loss with static analysis of contingency events of the transmission system. As not all high-risk events provide a more critical impact than its sub-events, the risk index is not always efficient for contingency screening. In this context, this paper proposes a contingency screening model with incremental risk for transmission system. Firstly, the significance of both the risk and the incremental risk of contingency events is analyzed. We show that the use of incremental risk can avoid the "risk masking effect", which is defined as the situation that high-risk events with weak reference value may mask the events with valuable information about more critical cases. Secondly, the optimization objective of contingency screening is set to maximize the incremental risk of contingency event. The purpose is to directly identify the events that describe a more critical impact than its sub-events and to improve the screening efficiency over that by the risk assessment. Finally, a recursive screening algorithm is designed to identify the set of N − k events with high incremental risk. Case studies on the IEEE-RTS and a provincial grid in China were carried out to show that the events with incremental risk only account for a small proportion of the total high-risk events. Thus, identification of N − k events with more critical impact than sub-events is achieved for system risk analysis in that enumeration of all the high-risk events is not required. [ABSTRACT FROM AUTHOR]

The uncertainties in reliability evaluation model are fundamentally classified into aleatory and epistemic types. Aleatory uncertainty arises from the intrinsic randomness associated with a physical system, such as components stochastic failure and repair process. Epistemic uncertainty, on the other hand, results from an incomplete or inaccurate scientific understanding of the underlying process, such as component reliability parameters uncertainty. It’s significant for risk based decision to distinguish the two kinds of uncertainties and quantify their impacts on reliability analysis. In literatures, most of papers focused on aleatory uncertainty, and only a few of them discussed the epistemic uncertainty. This paper is aimed to address uncertainty analysis of reliability indices considering the randomness of reliability parameters. Two goals are achieved in this paper. Firstly, the reliability indices are approximated through Taylor series with high efficiency after component parameters change, and its accuracy is compared with rerunning reliability evaluation. Secondly, to uncover the uncertainty propagation from input reliability parameters level to reliability evaluation output level, two methods, i.e. Taylor series Approximation and Monte Carlo simulation combined with nonparametric probability density estimation are proposed. Results obtained for the RBTS and IEEE-RTS79 power systems are presented and the validity of the proposed methods is verified. [ABSTRACT FROM AUTHOR]

• A nonparametric pair-copula construction is used to model multivariate correlation. • A uniform framework of nonparametric kernel density estimation is constructed. • A probability density function transformation method is proposed. • The conditional sampling method to generate correlated samples is depicted. • Reliability evaluation procedure considering multivariate dependence is detailed. The correlated variation of bus loads, wind powers, etc., has a significant impact on the power system operation risk. The construction of the accurate dependence model becomes vital in the field of power system reliability evaluation. Most currently used methods in estimating the multivariate joint probability density function (PDF) may encounter obstacles such as modeling accuracy and the curse of dimensionality, especially in the high-dimensional case. To address such problems, a nonparametric pair-copula construction (NPCC), which decomposes the joint PDF into a product of marginal PDFs and a set of bivariate copula (also called pair-copula) densities based on graph theoretic algorithm, is used in this paper to achieve an accurate modeling of the multivariate correlation. To construct a unified framework of nonparametric estimation, the marginal PDFs and the bivariate copula densities are both estimated in a data-driven mode. Moreover, a PDF transformation method is also proposed in estimating the bivariate copula densities, aiming to avoid the problem that the distribution range of the transformed variables in the pair-copula densities exceeds its feasible domain. The performance of the proposed NPCC is verified by a modified version of IEEE-RTS79 with complex correlation among bus loads and wind powers. [ABSTRACT FROM AUTHOR]