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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 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]

• 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]