Candidate bus selection for dynamic VAR planning towards voltage stability enhancement considering copula‐based correlation of wind and load uncertainties

Abstract

As a critical step of VAR planning, candidate bus selection can significantly reduce the scale of the planning problem without impairing the optimality of the planning decisions. A novel candidate bus selection method is proposed considering not only the capacity sensitivity of candidate buses, but also the correlation among uncertainties of wind power generation and load demands. First, two metrics are proposed for different sensitivity analysis purposes to evaluate voltage performance in the post-contingency stage comprehensively, considering the extent of the voltage deviation and voltage recovery time simultaneously. Then, D-vine copulas are constructed systematically and employed to generated correlated operational scenarios for the dependent variable sensitivity analysis based on Kucherenko indices. Morris screening method is used for the independent capacity sensitivity analysis of the candidate buses. Finally, a 2-dimensional candidate bus selection process is proposed for the decision-makers to determine the candidate buses flexibly. The proposed method is tested on a modified Nordic 74-bus system with an industry-standard complex load model. Simulation results verify the effectiveness and accuracy of the proposed method.

Two-stage Stochastic Programming for Coordinated Operation of Distributed Energy Resources in Unbalanced Active Distribution Networks with Diverse Correlated Uncertainties

“…The copula is a multivariate cumulative distribution with uniform marginals of each variable on the interval [0, 1] [26]. According to Sklar's theorem [27], [28], the foundation of copula theory defines that any K-dimensional random input variables {x 1 x 2 x K } with marginals {F 1 (x 1 ), F 2 (x 2 )F K (x K )} link by a copula c to express their joint cumulative distribution function F K , as shown in (45).…”

“…Formulas ( 24) and ( 25) are the operation constraints for DEs to ensure the power boundary and ramping rate within the allowed range; (26) denotes that the RES generation cannot exceed the available resources; (27) shows the reactive power limits of RES units; ( 28)-( 32) are the operation constraints for ESS; (28) and (29) denote that the charging and discharging power should be within the capacity boundary; meanwhile, the charging and discharging events of the ESS cannot happen at the same time; (30) denotes the ESS energy capacity limits and (31) builds the relationship of the energy stored in ESS and its charging/discharging power; (32) ensures the same ESS scheduling flexibility of each dispatch period where the starting energy should be equal to the ending energy [11]; (33) and ( 34) are the constraints of threephase power unbalance, indicating the root branch unbalance at each time interval and the overall power unbalance should be within the pre-defined limits; (35) denotes that the root branch apparent power should be within the power limit of substation; (36) -(39) are the constraints related to VVC scheme [10]; (36) denotes that the voltage of the reference bus is defined based on the tap position of OLTC; (37) indicates the tap position limits of OLTC; (38) indicates the reactive output from CB units, which is discreetly relying on its tap position; (39) shows the reactive output limits of CB units; and (40) limits the bus voltage of each phase within the safety range [3].…”

Data‐driven look‐ahead voltage stability assessment of power system with correlated variables

“…Therefore, vine copula has been emerged as a powerful tool for modelling multivariate dependence structure with asymmetric tail dependence. Vine copula has been recently used for assessing power system stability [13][14][15]. A crucial step for constructing vine copulas is to select appropriate copula family for each bivariate copula, especially when there are no sufficient data for judging which data set belongs to which class of parametric distribution functions [13][14][15].…”

“…Vine copula has been recently used for assessing power system stability [13][14][15]. A crucial step for constructing vine copulas is to select appropriate copula family for each bivariate copula, especially when there are no sufficient data for judging which data set belongs to which class of parametric distribution functions [13][14][15]. Thus, several nonparametric methods such as checkerboard copula and kernel copula have been utilized for estimating the bivariate copula functions.…”

“…Thus, this study develops a dimension reduction based on the GSA for determining the so-called effective dimension [18], which can reduce the dimension of the original problem. Sensitivity analysis methods can be classified into three groups: Local [17], screening [1,8,13], and global methods [6,[9][10][11]. A comprehensive comparison between different sensitivity analysis methods is presented in [19].…”