Spatio-temporal reconciliation of solar forecasts


Tommaso Di Fonzo, Daniele Girolimetto


February 1, 2023

   Publication details

Solar Energy, 251, 13-29


In recent works by Yang et al. (2017a1,b2), and Yagli et al. (2019)3, geographical, temporal, and sequential deterministic reconciliation of hierarchical photovoltaic (PV) power generation have been considered for a simulated PV dataset in California. In the first two cases, the reconciliations were carried out in spatial and temporal domains separately. To further improve forecasting accuracy, in the third case these two reconciliation approaches were applied sequentially. During the replication of the forecasting experiment, some issues emerged about non-negativity and coherency (in space and/or in time) of the sequentially reconciled forecasts. Furthermore, while the accuracy improvement of the considered approaches over the benchmark persistence forecasts is clearly visible at any data granularity, we argue that an even better performance may be obtained by a thorough exploitation of spatio-temporal hierarchies. To this end, in this paper the spatio-temporal point forecast reconciliation approach is applied to generate non-negative, fully coherent (both in space and time) forecasts. New spatio-temporal reconciliation approaches are adopted, exploiting for the first time some relationships between two-step, iterative and simultaneous spatio-temporal reconciliation procedures. Non-negativity issues of the final reconciled forecasts are discussed and correctly dealt with in a simple and effective way. The spatio-temporal reconciliation procedures are applied to the base forecasts with forecast horizon of 1 day, of PV generated power at different time granularities (1 h to 1 day), of a geographical hierarchy consisting of 324 series along 3 levels. The normalized Root Mean Square Error (nRMSE) and the normalized Mean Bias Error are used to measure forecasting accuracy, and a statistical multiple comparison procedure is performed to rank the approaches. In addition to assuring full coherence and non-negativity of the reconciled forecasts, the results show that for the considered dataset, spatio-temporal forecast reconciliation significantly improves on the sequential procedures proposed by Yang et al. (2019), at any level of the spatial hierarchy and for any temporal granularity. For example, the forecasted hourly PV generated power by the new spatio-temporal forecast reconciliation approaches improve on the NWP 3TIER forecasts in a range from 4.7% to 18.4% in terms of nRMSE.

  • 1 Yang, D., Quan, H., Disfani, V.R., Liu, L., 2017a. Reconciling solar forecasts: Geographical hierarchy. Sol. Energy 146 (April), 276–286

  • 2 Yang, D., Quan, H., Disfani, V.R., Rodríguez-Gallegos, C.D., 2017b. Reconciling solar forecasts: Temporal hierarchy. Sol. Energy 158 (June), 332–346.

  • 3 Yagli, G.M., Yang, D., Srinivasan, D., 2019. Reconciling solar forecasts: Sequential reconciliation. Sol. Energy 179 (December 2018), 391–397