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In this paper, a reliability evaluation model and a bilevel unreliability allocation model for the ±500-kV HVdc transmission system with the double-circuit lines on the same tower (DCLST) are proposed. The reliability evaluation indices associated with this DCLST HVdc system are also defined. The reliability model is based on the characteristics of common starting point and terminal point structure and double-circuit HVdc coordination operation. And it is developed by integrating HVdc subsystem reliability models together. A multistate Markov model for the dc line (DCL) subsystem is built by considering the common-cause outage of four DCLs on the same tower. The reliability evaluation model of the ac filter (ACF) subsystem is constructed by considering the derated capacity operation state caused by ACF failures. On the other hand, a bilevel unreliability allocation model is constructed based on the proportion-allocation criterion. The allocation model is embedded into the reliability evaluation model so that all reliability indices can be allocated to each component after only one reliability evaluation calculation. As a result, the impact of each component on the system reliability and weak components of the system can be explicitly and unambiguously identified. An actual ±500-kV HVdc transmission project with the DCLST is used for case study to validate the effectiveness of the proposed models and indices. [ABSTRACT FROM PUBLISHER]

In this paper, an optimal reliability allocation (ORA) model of ±800 kV ultra-high voltage direct current (HVDC) transmission system is proposed. The model intends to provide the means to determine the availability requirements of components in the bidding process of ±800 kV ultra HVDC transmission projects. In this model, the component availability is optimized based on the prespecified system reliability. The objective function is composed of the component investment cost and the operation and maintenance cost. The ORA is formulated as a constrained nonlinear programming problem, and the genetic algorithm (GA) is used to find its solution. An improved dagger sampling (IDS) method is proposed to evaluate the reliability of ultra HVDC systems, and a bisection method is used to generate the initial population of the GA. An actual ultra HVDC project is used to conduct the case study. Results show that the proposed ORA model can minimize the component investment, operation, and maintenance costs, while achieving optimal allocation of the system reliability index to obtain the availability of components. In addition, the impact of the component spare on the ORA result is investigated. Performance comparison on the sampling efficiency of the IDS method and the direct Monte Carlo sampling method is also presented. [ABSTRACT FROM AUTHOR]

Energy production of a wind farm is greatly affected by the wake-effect. In wind farm planning, it is essential to optimize the layout of wind turbine generators (WTGs) to alleviate the impact of wake-effect. This paper presents a new wind farm layout optimization model with an objective function to maximizing equivalent power of the wind farm. The proposed model incorporates the discrete joint probability distribution and characteristics of the wind, wind energy model, and the wake-effect. A particle swarm optimization algorithm is used to solve the optimization problem. In the optimization process, geometric analysis is conducted to determine the upstream WTGs and to calculate the horizontal and deviating distances among WTGs along the wind direction. An effective look-up table is constructed to directly determine the upstream/downstream WTGs. Then the optimal layout of a wind farm can be obtained. The proposed technique is applied to the wind farm layout optimization and the modified Roy Billinton Test System and IEEE Reliability Test System for reliability analysis of a generating system containing a wind farm. Simulation results demonstrate the validity and flexibility of the proposed technique in the layout optimization of WTGs in a wind farm. [ABSTRACT FROM AUTHOR]

Double 12-pulse ultra HVDC transmission systems of \pm 800 kV and \pm 660 kV have larger transmission capacities, more complicated configurations, more complex operation modes, and more components, in comparison to \pm 500 kV or less HVDC transmission systems. Hence, the reliability evaluation of the ultra HVDC transmission system is more complicated than that of the HVDC system. To thoroughly describe different operating modes, this paper presents two new reliability measures for ultra HVDC transmission systems, that is, partial monopole forced outage times and partial bipole-forced outage times. Reliability evaluation models for individual subsystems, including converter transformers (CT), ac filters, converter valve groups, and smoothing reactors have been built considering operation modes and configuration characteristics. In particular, the reliability model of the CT subsystem was built by considering the type and the number of standby CTs, and that of the ac filter subsystem was built by considering the capacity state table of filters. A reliability evaluation model for ultra HVDC transmission systems was proposed by combining reliability logic relationships among subsystems and using the state enumeration method. Case studies of practical ultra HVDC transmission systems illustrate the correctness of indices and the proposed models. In addition, sensitivity analysis and standby analysis of major components were also conducted. [ABSTRACT FROM PUBLISHER]

Wind turbine power converter system (WTPCS) is a crucial device in a wind energy conversion system. This paper presents the new failure rate models and a reliability evaluation technique for the (WTPCS) considering effects of wind speeds, which can be named by the multistate probability analysis method. The case studies on the WTPCS of a 2 MW wind turbine with a permanent magnet synchronous generator are conducted using wind speed data at Lauwersoog and Valkenburg wind sites in Holland. The results indicate that reliability of the WTPCS is affected significantly by variations of wind speed and the rated wind speed of wind turbine. The effectiveness of the proposed method is demonstrated by examples. [ABSTRACT FROM AUTHOR]

Due to the lack of feeder corridors, the Chinese utility companies frequently choose the technique of putting multiple overhead feeders on a same tower (MFST) to meet the load demand in a heavy load area. In many situations, the distance among the feeders of MFST in an electrical distribution network (EDN) is usually too small to meet the requirements of safety regulation for repairing and maintenance. Therefore, when a fault occurs on a feeder of MFST, the other feeders have to be in a triggered passive outage (TPO) state to assist the repairing of the failed feeder. This paper presents a reliability evaluation algorithm for EDNs containing MFST using the section technique. The definition of TPO and the equivalent TPO rate and TPO duration are also proposed. Based on the TPO parameters and the section technique, the reliability evaluation algorithm containing the MFST can be obtained. Case studies on the modified RBTS-BUS6 and the EDNs of three districts in Dongguan city, China, show that the MFST has a significant impact on the EDN reliability and should be considered in the reliability evaluation. The results also show the effectiveness and applicability of the proposed approach. [ABSTRACT FROM PUBLISHER]

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: Wind power is a very useful renewable energy source that is attracting consideration around the world due to its non-exhaustive nature and its environmental and social benefits. The correlation between multiple wind sites has a significant impact on the reliability of power systems containing wind energy conversion systems (WECS). Conventional methods cannot be directly applied to evaluate the reliability of WECS in the absence of comprehensive modeling techniques that recognize the correlation of the wind speeds at different wind farm locations. This paper proposes a model for power system reliability assessment that can consider the wind speed correlation and preserve the statistical characteristics of wind speeds, such as the mean and deviation of the wind speed time series (WSTS). A time-shifting technique is used to produce a new WSTS for a given correlation between two wind sites. The optimal shifted time at the two sites is determined using a linear interpolation technique. The probability distributions of the generated power and the system reliability indices with different degrees of correlation between the two sites are compared using two reliability test systems, i.e. the RBTS and the IEEE-RTS. The results show that the proposed method is useful in evaluating the reliability of WECS with correlation between two wind sites. [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]

The cross-entropy (CE) method can accelerate power system reliability evaluation effectively. An importance sampling (IS) based iterative parameter updating algorithm is usually used in CE optimization. However, the efficiency in capturing the concerned samples for parameter updating may be unsatisfactory, especially for a system with intrinsic nature of rare failure events. Besides, the stopping criterion of this iterative algorithm is usually determined subjectively, incurring insufficient or excessive parameter updating and a resultant higher computational burden of the entire simulation. To address the above two problems, a CE method based on subset simulation and minimum computational burden criterion is proposed. In CE optimization, the subset simulation combined with M-H sampling is adopted as an alternative to IS to effectively improve the efficiency of capturing desired samples for parameter updating at each iteration. Moreover, a novel quantitative stopping criterion is presented in such a way that the computational burden for the entire simulation is estimated and compared after each parameter updating iteration, and the optimal parameters corresponding to the minimum computational burden can be determined. The computational performance of the proposed method is validated by comparing the proposed approach with existing methods under several numerical tests including a realistic power system. [ABSTRACT FROM AUTHOR]

In integrated cyber-physical power systems (CPPS), the malfunctions of cyber system deeply affect the dispatcher's remedial action scheme, and thus have a significant impact on the reliability of the physical power system. The random failures of electrical devices in physical power system and the random outages of measurement and remote control in cyber system are both considered for the CPPS reliability evaluation in this paper. Firstly, the component outage models in physical, access, backbone and application layers are presented. Then, a linearized DC state estimation (SE) model is introduced and the SE errors incurred by measurement failures, i.e. bad and lost measurements, are interpreted. Moreover, the impact of SE errors and remote control failures on the corrective action scheme of the control center during the fault recovery process is simulated by a novel modification of the classical optimal load shedding (OLS) model. Finally, to verify the effectiveness and validity of the proposed CPPS reliability evaluation method, the communication network topologies of the cyber system for the RBTS and IEEE-RTS96 are designed, and then the reliability evaluation based on the presented component outage models and the novel modified OLS model are conducted by the non-sequential Monte Carlo simulation (NMCS). [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]

• High nonlinearities are modeled in the integrated energy systems risk evaluation. • The chronological characteristics of gas storages and pipelines are incorporated. • A novel adaptive energy flow algorithm based on a relaxation idea is proposed. • Several new risk indices related to wind power curtailments are presented. The interconnection and coordinated operation of electricity-gas integrated energy system (EGIES) is becoming a trend. The flexible energy conversion achieved by gas-fired power generation (GPG) and power to gas (P2G) has brought a new opportunity for improving the reliability of both electricity and gas systems in EGIES and enhancing the ability in absorbing fluctuant renewable energy. In this paper, a reliability evaluation framework for EGIES with the high nonlinearities of gas system components and the assessment of wind power absorption is proposed. To capture the practical operation behaviors of gas system, the highly nonlinear characteristics of gas system components are accurately modeled and incorporated into the proposed sequential simulation process. To address the convergence difficulties caused by the high nonlinearity of energy flow equations, an improved energy flow calculation algorithm based on a relaxation idea is presented, achieving an effective convergence acceleration in the reliability evaluation of EGIES. The validity and performance of the proposed method are verified by using the RBTS integrated with a gas network. [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]