A methodology to correlate river inflows in state sampling Monte Carlo simulation

Abstract

This paper proposes a methodology to sample inflow states of run-of-the-river hydropower plants that are spatially correlated, preserving the statistical dependence among them, in Non-Sequential Monte Carlo Simulation (MCS). The technique used to correlate the inflows of hydro plants in the Brazilian synthetic series generation model, which is based on the correlation matrix and Cholesky Decomposition, is adapted to be used in the sampling stage. Nataf transformation is used for addressing non-normality of the inflow data. The solution method is such that no assumption about the data probability distribution is necessary. Although the methodology is applied to inflows in this paper, it can be applied to any other quantity, such as winds. A case study is proposed to evaluate the correlation of the sampled inflows and the impact on the reliability indices. Besides, it is investigated the effect when inflows states are clustered to reduce the number of states in the system for better computational efficiency. Case study shows that the reliability indices obtained with the proposed methodology are within the confidence interval of the indices calculated by the Sequential MCS with an execution time as fast as the Non-Sequential one, while the non-consideration of correlation causes very significant errors. Simulation with 50 clusters produces equally good results with a reduction of 75 % of the execution time. Sensitivity analysis showed that halving the number of clusters maintains the accuracy of the results, while 10 clusters results in overestimating system reliability. Different degrees of correlation have been simulated, showing that the higher the correlation among the hydro plants, the less reliable the system becomes.