  Energy forecasting is pivotal in energy systems, by providing fundamentals
for operation, with different horizons and resolutions. Though energy
forecasting has been widely studied for capturing temporal information, very
few works concentrate on the frequency information provided by forecasts. They
are consequently often limited to single-resolution applications (e.g.,
hourly). Here, we propose a unified energy forecasting framework based on
Laplace transform in the multi-resolution context. The forecasts can be
seamlessly produced at different desired resolutions without re-training or
post-processing. Case studies on both energy demand and supply data show that
the forecasts from our proposed method can provide accurate information in both
time and frequency domains. Across the resolutions, the forecasts also
demonstrate high consistency. More importantly, we explore the operational
effects of our produced forecasts in the day-ahead and intra-day energy
scheduling. The relationship between (i) errors in both time and frequency
domains and (ii) operational value of the forecasts is analysed. Significant
operational benefits are obtained.
