A Fractional Brownian Motion Model for Forecasting Lost Load and Time Interval between Power Outages

A novel idea is proposed to forecast lost load and time interval between power outages based on the similarity between the series generated by a stochastic model and the actual series. The lost load obeys a power-law distribution, which can be described as a stochastic process with long-range dependence (LRD). Fractional Brownian motion (fBm) is a stochastic model with LRD, we discretize the stochastic differential equation (SDE) driven by fBm and the difference iterative equation is constructed for forecasting. By calculating the Hurst exponent of lost load series proves that it has LRD characteristics. The stochastics series produced by fBm has a strong similarity with the actual series when the Hurst exponent is taken into fBm model. Moreover, the forecasting accuracy is enriched by considering the appropriate sample size and forecasting step size. The same process for the analysis of lost load can be applied to forecast the time interval between power outages. The efficiency of the proposed model is demonstrated by a case study of the medium voltage power grid in Shanghai compared with other approaches. Finally, the value at risk (VaR) and the conditional value at risk (CVaR) as two system-level indices for assessment of future power outages.