Abstract
A high level of stochastic dependence (or correlation) exists between different uncertainties (i.e., loads and renewable generation), which is nonlinear and non-Gaussian and it affects power system stability. Accurate modeling of stochastic dependence becomes more important and influential as the penetration of correlated uncertainties (such as renewable generation) increases in the network. The stochastic dependence between uncertainties can be modeled using 1) copula theory and 2) joint probability distributions. These methods have been implemented in this paper and their performances have been compared in assessing the small-disturbance stability of a power system. The value of modeling stochastic dependence with increased renewables has been assessed. Subsequently, the critical uncertainties that most affect the damping of the most critical oscillatory mode have been identified and ranked in terms of their influence using advanced global sensitivity analysis techniques. This has enabled the quantification and identification of the impact of modeling stochastic dependence on the raking of critical uncertainties. The results suggest that multivariate Gaussian copula is the most suitable approach for modeling correlation as it shows consistently low error even at higher levels of renewable energy penetration into the power system.
Highlights
I NCREASED proportions of renewable energy sources (RES) lessen the flexibility of power system operation due to the intermittent nature and spatiotemporal dependence among the RES sources
This section discusses the simulation results obtained by a multi-level approach consisting of the correlation modelling, optimal power flow, modal analysis, and subsequent sensitivity analysis
The analysis of uncertainty ranking further confirms the previously obtained results with respect to the Inherent intra-dependence and interdependence among input parameters have been incorporated within the probabilistic modal analysis and priority ranking of uncertainties
Summary
I NCREASED proportions of renewable energy sources (RES) lessen the flexibility of power system operation due to the intermittent nature and spatiotemporal dependence among the RES sources. The stochastic dependence within load, wind, and PV has been previously modelled through bivariate methods, using Clayton [7], [9], Frank [7], [9], and Gumbel [7], [9], [10] copulas Multivariate methods such as Gaussian [2], [7], [9], [11] and Student’s t [7] copulas have been applied to power systems studies. There is no work in the existing literature which models stochastic dependence of load-wind-PV (through copula theory and joint distribution) to assess their impact on power system stability. Following the modelling of stochastic dependence during the sampling procedure, the priority ranking of critical uncertainties to identify those having the greatest impact on small-disturbance stability has been completed using the global Sobol sensitivity analysis technique [19]. This paper makes the following novel contributions: 1) A clear demonstration of modelling stochastic dependence among system uncertainties using six different techniques to explicitly capture correlation. 2) A comparison of the accuracy of stochastic dependence modelling through bi-variate and multi-variate copula and joint normal distribution. 3) Assessment of the significance of modelling stochastic dependence for variable levels of RES penetration and identification of appropriate modelling tools. 4) The evaluation of critical uncertainties through power system stability indicators considering the impact of stochastic dependence. 5) Identification of the most appropriate method for modelling stochastic dependence for small-disturbance stability studies based on thorough error analysis against realistic data
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