Analyzing Performance and Scalability of Benders Decomposition for Generation and Transmission Expansion Planning Models

TL;DR

This paper evaluates strategies to improve Benders Decomposition performance for large-scale Generation and Transmission Expansion Planning models, achieving faster solutions with high accuracy.

Contribution

It introduces an alternative approach for handling bilinear constraints and tests various acceleration strategies on large GTEP models.

Findings

Accelerated Benders Decomposition methods solve large GTEP problems within 5 hours.

Regularization combined with hot-starting and relaxations improves convergence.

Selected strategies reduce problem gap to under 1% intractable cases.

Abstract

Generation and Transmission Expansion Planning (GTEP) problems co-optimize generation and transmission expansion, enabling them to provide better planning decisions than traditional Generation Expansion Planning or Transmission Expansion Planning problems, but GTEPs can be computationally complex or intractable. Benders Decomposition (BD) has been applied to expansion planning problems, with various methods applied to accelerate convergence. In this work, we test strategies for improving the performance of BD on GTEP models with nodal resolution and DCOPF constraints. We also present an alternative approach for handling the bilinear constraints that can result in these problems. These tests included combinations of using generalized Benders decomposition (GBD), hot-starting via a transport constrained model, using linear relaxations of the master problem, and using regularization. We test these methods on mixed-integer linear programming GTEP models with up to 146 buses (10 million continuous variables and 400 mixed-integer decisions). With selected accelerated Benders decomposition approaches, the problems can be solved to under a 1\% gap in as little as 5 hours where they were otherwise intractable. Results also suggest that using regularization on these initial hot-starting and relaxation steps and turning it off after they are complete was generally the best combination of strategies.