A novel importance sampling method of power system reliability assessment considering multi-state units and correlation between wind speed and load

Data-driven Operation Risk Assessment of Wind-integrated Power Systems via Mixture Models and Importance Sampling

“…In addition, K needs to be set. Popular techniques for determining K include the splitand-merge method [16], cross-validation, and Akaike information criterion (AIC) [17]. For a given K, the remaining GMM parameters can then be estimated by maximizing the log-likelihood of ( 14) [25].…”

“…where r k = ∑ i r ik ; g i =[g wt -1i g wti ] T ; α k is the scalar parameter of Dirichlet distribution; m 0 , v 0 , κ 0 , S 0 are the parameters of the Normal-Inverse-Wishart distribution, m 0 is a D×1 vector parameter, v 0 and κ 0 are scalar parameters, and S 0 is a D× D matrix parameter, D is the number of dimensions in the data. Equation (17) represents the E-step, and ( 18)-( 22) correspond to the M-step. These two steps are conducted iteratively.…”

“…MMs are semi-parametric probabilistic models that can represent arbitrarily complex PDFs with great flexibility. Gaussian MMs (GMMs) have been used to model spatial correlation of wind speed in long-term reliability evaluation [16], [17]. Researchers have also employed GMMs to model the forecast error of wind power [18] and represent the uncertainty of wind power in probabilistic optimal power flow (OPF) [19].…”

“…Researchers have also employed GMMs to model the forecast error of wind power [18] and represent the uncertainty of wind power in probabilistic optimal power flow (OPF) [19]. In contrast to [16] and [17], this paper adopts GMMs to construct time-dependent PDFs of wind power for specific hours in order to render them suitable for short-term reliability evaluation. The drawback of using wind speed data is thus avoided.…”

An Efficient Framework for Adequacy Evaluation through Extraction of Rare Load Curtailment Events in Composite Power Systems

“…Hence, there are two research tracks for the purpose of overcoming the MCS computational burden. A first research track is to develop high performance programming paradigms [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] for the purpose of reducing the computation time of state evaluation. A second track could be to derive more efficient sampling techniques [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] for reducing the number of the states needed to be evaluated through concentrating the sampling effort in the regions of interest.…”