Increasing the wind energy penetration in a power system presents some technical challenges to the transmission expansion planning (TEP). In the first stage of TEP, the transmission bottlenecks should be determined and ranked via security assessment. The high penetration of wind energy means a large number of wind farms exist in various geographic areas. It is found that there is a correlation between the wind speed series of different farms. Therefore, integration of the correlated wind farms into security assessment is addressed in this study. Hence, a new model of wind speed prediction is presented based on the correlated autoregressive moving average time series. The copula functions are used to make the predefined correlation among wind speed series. Here a linear correlation using a Gaussian copula is implemented. Then, the risk-based security assessment is performed using the proposed sequential time simulation. The proposed process is applied to the modified IEEE 39-bus test system which comprises 15 wind farms. Then, the transmission bottlenecks are identified and ranked regarding their overload risks. Finally, the impacts of the wind farms correlation on the risk index are investigated and those contingencies which impose the highest influence on this risk are identified.

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This study aims to investigate the stagnation-ow solidi cation of vapor from saturated air. Saturated air with strain rate a impinges on a at plate and, thus, condensation occurs and an icy layer forms on the plate because the plate temperature is below the freezing temperature of water. The ice surface was modeled as an accelerated at plate that moves toward the impinging uid. The unsteady Navier-Stokes equations were subjected to a similarity transformation to obtain a single ordinary di erential equation for velocity distribution. Two methods of solution were used for the energy equation: a nitedi erence numerical technique and a numerical solution of a similarity equation. These two results were compared to determine the superior accuracy. First, freezing time increases as the far-eld temperature decreases from 0 C and, then, rapidly approaches zero as the fareld temperature approaches 0 C. Despite the expectation that condensation would begin at the substrate in a physical experiment, here, the size of the cell next to the substrate controls the time at which condensation begins. It was found that the maximum time before freezing began at an air temperature of about 5 C for 0.1 and 0.2 mm sizes. The ultimate frozen thickness for two saturated air temperatures was presented.

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