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

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.

Figures (7)

• Figure 1: A visualization of the RTS and expanded RTS. Black lines indicate existing corridors while red lines indicate new corridors, with the size of the line corresponding to the capacity of the line(s) on the corridor.
• Figure 2: Results of GBD and BD applied to the RTS and expanded RTS with no speedup strategies. The solution of a transport constrained model is shown in black, with the gap between the best solution of the algorithm and the transport constrained model annotated on the right-hand side. "Loose Big M" uses a value of $M_\ell = 10 \overline{f}$.
• Figure 3: Comparison of the six speedup strategies (Table \ref{['tab:strategies']}) for GBD and BD on the RTS. Gaps reported on the right-hand side are compared to the solution of the transport constrained model. "Reg" is not shown because it performed worse than alternatives ($>$1% gap). Lines begin after any hot-starting and LP relaxation procedures finish.
• Figure 4: Comparison of the six speedup strategies (Table \ref{['tab:strategies']}) for GBD and BD on the expanded RTS. Gaps reported on the right-hand side are compared to the solution of the transport constrained model. "LP" and "Reg" are not shown because the LP relaxation did not finish in the given time, and the regularization alone never got below a 5% gap. Lines begin after any hot-starting and LP relaxation procedures finish.
• Figure 5: Results of the expanded RTS system with three different random samplings of available lines for new line construction.