Probabilistic power flow methodology for the modeling of horizontally-operated power systems

Stochastic generation is expected to take a large share of the energy production in future power systems. Two basic features of this type of generation distinguish it from the traditional centralized, conventional generation: it is highly distributed (large number of small-scale generators) and non-dispatchable (use of an uncontrolled prime mover). The incorporation of such power sources in the lower system levels leads to a new horizontal structure of the power system, where the distribution networks contain both uncertain stochastic generation and load. For the analysis of such systems, the use of a probabilistic approach is necessary. There are two basic problems with the probabilistic formulation of this problem: the large number of random variables involved in the analysis and the presence of complex dependencies between the system inputs. In this contribution, a two-step method is presented for the stochastic modeling of the system: first, clusters of positively correlated variables are defined and modeled based on the concepts of perfect correlation (comonotonicity), and then the exact correlations between these clusters are modeled based on a new proposed technique, the joint normal transform methodology. This powerful computational method can be easily applied to large systems with a high number of stochastic generators. The proposed method has been implemented and applied for the 5-bus/7-branch test system (Hale network) with a high penetration of wind generation. The results are presented in the paper.