Probabilistic real-time thermal rating forecasting for overhead lines by conditionally heteroscedastic auto-regressive models

Conventional approaches to forecasting of real-time thermal ratings (RTTRs) provide only single point estimates with no indication of the size or distribution of possible errors. This paper describes weather based methods to estimate probabilistic RTTR forecasts for overhead lines which can be used by a system operator within a chosen risk policy with respect to probability of a rating being exceeded. Predictive centres of weather conditions are estimated as a sum of residuals predicted by a suitable auto-regressive model and temporal trends fitted by Fourier series. Conditional heteroscedasticity of the predictive distribution is modelled as a linear function of recent changes in residuals within one hour for air temperature and wind speed or concentration of recent wind direction observations within two hours. A technique of minimum continuous ranked probability score estimation is used to estimate predictive distributions. Numerous RTTRs for a particular span are generated by a combination of the Monte Carlo method where weather inputs are randomly sampled from the modelled predictive distributions at a particular future moment and a thermal model of overhead conductors. Kernel density estimation is then used to smooth and estimate the percentiles of RTTR forecasts which are then compared with actual ratings and discussed alongside practical issues around use of RTTR forecasts