Using Quadratic Programming to Optimally Adjust Hierarchical Load Forecasting

Electric load is hierarchically organized based on geography, which requires hierarchical forecasts covering all levels to support decision makings of power system operations. A trivial way to implement hierarchical forecasts is to independently generate load forecasts at each level using state-of-the-art techniques. However, these independently-generated forecasts may not satisfy hierarchical structures, i.e., the sum of lower-level forecasts cannot add up exactly to upper-level forecasts. To deal with this problem, this letter presents a quadratic programming (QP) model to optimally adjust load forecasts independently generated at each level of a hierarchy. The proposed model obtains the “best” forecasts as close as possible to base forecasts but also satisfy the aggregate consistency defined by hierarchical structures. Numerical results using real-world data validate the effectiveness of the proposed approach in two application scenarios (i.e., bulk power systems and power distribution networks). The accuracy improvement of the proposed approach over either base forecasts or bottom-up forecasts can be observed at all levels of the hierarchy.