Polyhedral Predictive Regions for Power System Applications

Abstract

Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either costoptimal decisions in expectation, or decision with probabilistic guarantees. The representation of uncertainty serves as an interface between forecasting and decision-making problems, with different approaches handling various objects and their parameterization as input. Following substantial developments based on scenario-based stochastic methods, robust and chanceconstrained optimization approaches have gained increasing attention. These often rely on polyhedra as a representation of the convex envelope of uncertainty. In the work, we aim to bridge the gap between the probabilistic forecasting literature and such optimization approaches by generating forecasts in the form of polyhedra with probabilistic guarantees. For that, we see polyhedra as parameterized objects under alternative definitions (under L1 and L∞ norms), the parameters of which may be modelled and predicted. We additionally discuss assessing the predictive skill of such multivariate probabilistic forecasts. An application and related empirical investigation results allow us to verify probabilistic calibration and predictive skills of our polyhedra.

Forecasting: theory and practice

“…On the other hand, robust optimisation does not make specific assumptions on probability distributions and the uncertain parameters are assumed to belong to a deterministic uncertainty set. Hence, some authors proposed new methods to shape forecast uncertainty as polyhedral or ellipsoidal regions to enable a direct integration of forecasts in this type of optimisation problem (Bertsimas and Pachamanova, 2008;Golestaneh et al, 2019).…”

The future of forecasting for renewable energy

“…When dimension increases and decision processes become more complex, using such scenarios may not be practical, owing to the difficulty in solving the resulting optimization problems, and may not be possible at all at reasonable computational costs. This motivated various developments in stochastic optimization and control that, instead of relying on a large number of trajectories, prefer to solve problems based on multivariate forecast regions, possibly taking the form of ellipsoids (Golestaneh, Pinson, Azizipanah-Abarghooee, & Gooi, 2018) or polyhedra (Golestaneh, Pinson, & Gooi, 2019). Today, there is a general need to rethink forecasting products that are of most relevance to various forecast users and their decision problems.…”

“…The second challenge is being covered at the academic level with stochastic optimal power flow methods, which in general result in high computational times, require a full modeling of the network equations and do not include domain knowledge from human operators. As mentioned in Section 3.3, this requires new representations for forecast uncertainty, such as multivariate (i.e., modeling temporal/spatial or multivariable correlations) ellipsoids or polyhedra for robust, chance-constrained and interval optimization problems where the required uncertainty representation takes the form of prediction regions rather than scenarios (or ensembles) (Golestaneh et al, 2019).…”

Adaptive Robust Ac Optimal Power Flow Considering Intrahour Uncertainties

“…The uncertain power injections from VREs and loads are characterized by polytopic uncertainty sets that capture spatial correlations. This allows a skilled yet efficient characterization of high-dimensional uncertainty [29]. Principal component analysis (PCA) is used to enhance the numerical stability of the uncertainty characterization and reduce the computational needs [30].…”