Wind speed follows the Weibull probability distribution and wind power can have a significant influence on power system voltage stability. In order to research the influence of wind plant correlation on power system voltage stability, in this paper, the stochastic response surface method (SRSM) is applied to voltage stability analysis to establish the polynomial relationship between the random input and the output response. The Kendall rank correlation coefficient is selected to measure the correlation between wind farms, and the joint probability distribution of wind farms is calculated by Copula function. A dynamic system that includes system node voltages is established. The composite matrix spectral radius of the dynamic system is used as the output of the SRSM, whereas the wind speed is used as the input based on wind farm correlation. The proposed method is compared with the traditional Monte Carlo (MC) method, and the effectiveness and accuracy of the proposed approach is verified using the IEEE 24-bus system and the EPRI 36-bus system. The simulation results also indicate that the consideration of wind farm correlation can more accurately reflect the system stability.

In order to study in depth the influence of the uncertainty factors on power system stability and to obtain the probability of instability under different levels, an evaluation method of power system stability based on monomial cubature rules (MCRs) is proposed. In this paper, the wind speed and the matrix spectral radius are considered as the uncertainty parameter and the output response, respectively. The relationship between the wind speed and the matrix spectral radius is found with MCRs to assess power system dynamic stability, and linear regression is used to solve chaotic polynomial coefficients. The comparison of the calculation results of the MCRs and Monte Carlo simulations on the IEEE 30-bus system indicates that the MCRs require a smaller number of computations and give high accuracy.

A novel meshless scheme is proposed for inverse source identification problems of Helmholtz-type equations. It is formulated by the non-singular general solutions of the Helmholtz-type equations augmented with radial basis functions. Under this meshless scheme, we can determine smooth source terms from partially accessible boundary measurements with accurate results. Numerical examples are presented to verify validity and accuracy of the present scheme. It is demonstrated that the present scheme is simple, accurate, stable and computationally efficient for inverse smooth source identification problems.

The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurate and stable numerical solution, while the shape parameter values are almost independent. In this paper, we give a quasi-optimal conical spline which can improve the numerical results. Besides, we consider the collocation points in the Chebyshev-type which improves solution accuracy of the method with no additional computational cost.