An asymmetric bisquare regression for mixed cyberattack-resilient load forecasting

Load forecasting can effectively reduce the operating costs of the power industry, while attacks on the load can lead to inaccurate forecasts. In the existing reports, the robust regression method can potentially alleviate the interference of the attack for load forecasting. However, most current existing methods can handle the data under symmetric attacks, which are not effective in data under asymmetric attacks. In this paper, an asymmetric robust regression method (asymmetric bisquare regression) is proposed for mixed cyberattack-resilient load forecasting. Instead of the symmetric bisquare loss function, in the asymmetric bisquare loss function, two tuning parameters are introduced to control the impacts from negative and positive attacks, respectively. Particularly, the two tuning parameters can be adaptively estimated according to the proportion of attack type. Finally, we demonstrate that the asymmetric robust regression method is superior to all considered robust statistical regression methods through a comparative study of mixed cyberattack-resilient load forecasting.