Forecasting is pivotal in energy systems, by providing fundamentals for operation at 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.

We consider a new framework where a continuous, though bounded, random variable has unobserved bounds that vary over time. In the context of univariate time series, we look at the bounds as parameters of the distribution of the bounded random variable. We introduce an extended log-likelihood estimation and design algorithms to track the bound through online maximum likelihood estimation. Since the resulting optimization problem is not convex, we make use of recent theoretical results on stochastic quasiconvex optimization, to eventually derive an Online Normalized Gradient Descent algorithm. We illustrate and discuss the workings of our approach based on both simulation studies and a real-world wind power forecasting problem.

Energy market designs with non-merchant storage have been proposed in recent years, with the aim of achieving optimal integration of storage. In order to handle the time linking constraints that are introduced in such markets, existing works commonly make simplifying assumptions about the end-of-horizon storage level. This work analyses market properties under such assumptions, as well as in their absence. We find that, although they ensure cost recovery for all market participants, these assumptions generally lead to market inefficiencies. Therefore we consider the design of markets with non-merchant storage without such simplifying assumptions. Using an illustrative example, as well as detailed proofs, we provide conditions under which market prices in subsequent market horizons fail to reflect the value of stored energy. We show that this problem is essential to address in order to preserve market efficiency and cost recovery. Finally, we propose a method for restoring these market properties in a perfect-foresight setting.