Value of forecasts in planning under uncertainty: Extended version

TL;DR

This paper presents a convex optimization framework for incorporating forecasts into planning under uncertainty, demonstrating how forecast informativeness influences decision utility, with applications to renewable energy management.

Contribution

It introduces a novel convex reformulation of planning under uncertainty with forecast constraints, enabling evaluation and refinement of forecast utility for improved decision-making.

Findings

Convex reformulation allows efficient robust planning under forecast constraints.

Forecast informativeness significantly impacts the optimal utility achieved.

Numerical example demonstrates practical application in wind energy trading.

Abstract

In environments with increasing uncertainty, such as smart grid applications based on renewable energy, planning can benefit from incorporating forecasts about the uncertainty and from systematically evaluating the utility of the forecast information. We consider these issues in a planning framework in which forecasts are interpreted as constraints on the possible probability distributions that the uncertain quantity of interest may have. The planning goal is to robustly maximize the expected value of a given utility function, integrated with respect to the worst-case distribution consistent with the forecasts. Under mild technical assumptions we show that the problem can be reformulated into convex optimization. We exploit this reformulation to evaluate how informative the forecasts are in determining the optimal planning decision, as well as to guide how forecasts can be appropriately refined to obtain higher utility values. A numerical example of wind energy trading in electricity markets illustrates our results.