Optimal reconciliation of hierarchical wind power forecasts of correlated wind farms

Abstract

Wind power forecasts of widely distributed wind farms in a spatial hierarchy are required at different hierarchical levels of power system architecture for various operational decisions. Accurate hierarchical forecasts necessitate aggregation consistency across hierarchy i.e. lower-level forecasts summate precisely to higher-level forecasts. Aggregation consistency substantially improves through optimal reconciliation of forecasts. Reconciliation can further improve forecast accuracy by incorporating spatial correlation among wind farms in the hierarchy. However, covariance matrix formed in reconciliation observes matrix order to increase manifold while including correlation. Estimation of such high-dimensional matrix is computationally complex. Additionally, aggregation of estimation errors leads to poor estimation accuracy. Moreover, in this reconciliation process, covariance matrix based on the observed data is non-invertible as the number of predictors usually happens to be larger than sample size. This work proposes MinT(Shrink) estimator for covariance matrix estimation for such systems. This estimator captures correlation among wind farms while shrinks off-diagonal elements of covariance matrix toward zero to alleviate computational complexity of high-dimensional matrix. It also provides invertible covariance matrix by employing shrinkage parameter λ. Case study presents efficacy of considering spatial correlation in hierarchical wind power forecasts in terms of improved forecast accuracy at all hierarchy levels and time horizons.