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• Gauss-Hermite integral based multi-point estimation method is proposed to calculate the probabilistic transient stability criterion derived through the PDSR. • To guarantee the calculation accuracy and speed at the same time, the optimal number for the sampling points is determined based on PDSR hyperplanes and improved particle swarm optimization algorithm (IPSO). • Extreme learning machine (ELM) is introduced to describe the uncertainty of practical wind power output. • Calculation accuracy of the proposed method is higher than other commonly-used point-estimation methods without much loss of computational efficiency under different wind power penetration and correlation levels. With the increasing penetration of wind power, probabilistic transient stability assessment becomes critical to deal with the uncertainties and correlations of wind power, thus improving the reliability of power system. This paper proposes an improved multi-point estimation based probabilistic transient stability assessment method. Extreme learning machine (ELM) is introduced to describe the uncertainty of practical wind power output. Gauss-Hermite integral based multi-point estimation method is proposed to calculate transient stability criterion derived through practical dynamic security region (PDSR). Optimal number of the sampling points is determined based on PDSR hyperplanes and an improved particle swarm optimization algorithm (IPSO). Test results on the New England 10-generators 39-buses system and a practical provincial power system in China show that the calculation accuracy of the proposed method is higher than that of other commonly-used point-estimation methods without much loss of computational efficiency under different wind power penetration and correlation levels. [ABSTRACT FROM AUTHOR]

• A novel CLPU model that considers the impact of outage duration with a minimal number of additional auxiliary variables is proposed. A piecewise linearization technique is developed to linearize the CLPU model as a function of outage duration so that it can be efficiently integrated into the load restoration model. • Scheduling strategies of hybrid WF-ESSs to accelerate the load restoration process are investigated. The ESS can occasionally be operated in the alarm state to accelerate load restoration at the cost of a slight sacrifice to its lifespan. • Linearization methods are developed to formulate the load restoration problem as a mixed-integer linear programming model. A rolling horizon optimization-based framework is adopted to deal with the uncertainty of wind power and reduce computational burden. A common solution to deal with the stochasticity introduced by fast-ramping wind power integration is to equip wind farms (WFs) with energy storage systems (ESSs) to formulate hybrid WF-ESSs. In addition to leveling off wind power fluctuations during normal operations, a hybrid WF-ESS can be a flexible power source to accumulate the power system restoration. In this paper, we propose a rolling optimization model for transmission network recovery and load restoration considering the contributions of WF-ESSs. The proposed model is formulated as a mixed integer linear programming problem that simultaneously optimizes the amount and location of restorable load blocks as well as the restoration lines. The cold load pickup features of interrupted loads considering the outage duration are modeled in detail. A chance-constrained method is employed to deal with the uncertainty of wind power, and a rolling horizon-based framework is adopted to reduce the influence of forecast error. Case studies are conducted on both New England 39-bus system and part of a provincial power system in China. The results show that the load restoration process can be significantly accelerated by employing the proposed method and contributions of hybrid WF-ESSs to power system restoration are validated. [ABSTRACT FROM AUTHOR]