Joint Planning and Operations of Wind Power under Decision-dependent Uncertainty

TL;DR

This paper develops a decision-dependent robust optimization model for wind farm planning that accounts for the smoothing effect of dispersed wind farms, providing a probabilistic performance guarantee and an efficient solution method.

Contribution

It introduces a novel decision-dependent Wasserstein ambiguity set in a two-stage robust optimization model for wind power planning, with a reformulation as a mixed-integer second-order cone program.

Findings

The proposed model outperforms traditional methods in numerical tests.

The solution framework accelerates computation by hundreds of times.

The model provides probabilistic guarantees on out-of-sample performance.

Abstract

We study a joint wind farm planning and operational scheduling problem under decision-dependent uncertainty. The objective is to determine the optimal number of wind turbines at each location to minimize total cost, including both investment and operational expenses. Due to the stochastic nature and geographical heterogeneity of wind power, fluctuations across dispersed wind farms can partially offset one another, thereby influencing the distribution of aggregated wind power generation-a phenomenon known as the smoothing effect. Effectively harnessing this effect requires strategic capacity allocation, which introduces decision-dependent uncertainty into the planning process. To address this challenge, we propose a two-stage distributionally robust optimization model with a decision-dependent Wasserstein ambiguity set, in which both the distribution and the radius are modeled as functions of the planning decisions, reflecting the statistical characteristics of wind power resources. Then, we reformulate the model as a mixed-integer second-order cone program, and the optimal objective value provides a probabilistic guarantee on the out-of-sample performance. To improve computational efficiency, we develop a constraint generation based solution framework that accelerates the solution procedure by hundreds of times. Numerical experiments using different datasets validate the effectiveness of the solution framework and demonstrate the superior performance of the proposed model.