A distributed incremental update scheme for probability distribution of wind power forecast error

Abstract

Due to the uncertainty of distributed wind generations (DWGs), a better understanding of the probability distributions (PDs) of their wind power forecast errors (WPFEs) can help market participants (MPs) who own DWGs perform better during trading. Under the premise of an accurate PD model, considering the correlation among DWGs and absorbing the new information carried by the latest data are two ways to maintain an accurate PD. These two ways both require the historical and latest wind power and forecast data of all DWGs. Each MP, however, only has access to the data of its own DWGs and may refuse to share these data with MPs belonging to other stakeholders. Besides, because of the endless generation of new data, the PD updating burden increases sharply. Therefore, a distributed strategy is used to avoid raw data collection. In addition, the incremental learning strategy is further applied to reduce the updating burden. Finally, a distributed incremental update scheme is proposed to make each MP continually acquire the latest conditional PD of its DWGs’ WPFE. Specifically, the Gaussian-mixture-model-based (GMM-based) joint PD is first used to characterize the correlation among DWGs. Then, a distributed modified incremental GMM algorithm is proposed to enable MPs to update the parameters of the joint PD in a distributed and incremental manner. After that, a distributed derivation algorithm is further proposed to make MPs derive their conditional PD of WPFE from the joint one in a distributed way. Combining the two original algorithms, the complete distributed incremental update scheme is finally achieved, by which each MP can continually obtain its latest conditional PD of its DWGs’ WPFE via neighborhood communication and local calculation with its own data. The effectiveness, correctness, and efficiency of the proposed scheme are verified using the dataset from the NREL.