Modeling Complex Dependencies In Wind Power And Uncertainties In Both Wind Power And Loads For Probabilistic Small Signal Stability Analysis

In recent years,probabilistic approaches have become very popular in the analysis of modern power systems.With increasing integration of stochastic power sources such as wind power and the uncertainty arising from the uncertain nature of power system loads,probabilistic methods are well suited to account for these uncertainties.Wind power is characterised by complex dependencies especially when multiple wind power sources are considered.Several dependence modeling methods have been proposed for probabilistic small signal stability analysis but due to homogeneity,they are limiting in nature and lack flexibility in capturing the complex dependencies existing between multiple wind power sources.Hence in this study,a dynamic Pair Copula-PEM approach is proposed that allows for the complex dependencies existing between multiple wind power sources and the stochastic nature existing in both wind power and loads to be effectively captured during probabilistic small signal stability analysis.The proposed approach is adopted to probabilistically analyse the small signal stability of the IEEE 39-bus test system at three different wind power penetration levels concurrently considering light and heavy loading conditions.The approach is implemented under the Power System Analysis Toolbox(PSAT)environment in conjunction with Matlab.Increasing wind power penetration,uncertainties in both wind power and loads and the complex dependencies between wind power sources are probabilistically established to adversely affect the system's small signal stability.The highest likelihoods of instability occur when the complex dependencies and uncertainties are cumulatively considered alongside heavy loading and high wind power penetration.Hence increasing penetration of uncertain and strongly dependent wind power sources and the uncertainty existing in power system loads should be intensively studied as they present risks towards a power system's small signal stability.