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An Efficient Hybrid Heuristic for the Transmission Expansion Planning under Uncertainties

Yure Rocha, Teobaldo Bulhões, Anand Subramanian, Joaquim Dias Garcia

TL;DR

Addresses the stochastic transmission expansion planning problem under uncertainties in renewables and demand. Proposes a hybrid solution combining Progressive Hedging for scenario decomposition with an integrated framework consisting of destroy-and-repair, beam search, and a MIP solver. Key contributions include a novel destroy-and-repair operator guided by residual flows, an iterative beam search to explore multiple feasible replacements, and a PH-based decomposition that scales to networks with up to 10,000 buses; tested on adapted PGLib-OPF and California test system scenarios (up to 96 hourly scenarios), achieving an average improvement in optimality gap of 16.23% on stochastic instances and substantial improvements in deterministic subproblems. The approach demonstrates scalable, high-quality solutions for large-scale STEP and offers practical guidance for planning under uncertainty.

Abstract

We address the stochastic transmission expansion planning (STEP) problem considering uncertainties in renewable generation capacity and demand. STEP's objective is to minimize the total investment cost of new transmission lines and generation cost. To tackle the computational challenges of large-scale systems, we propose a heuristic approach that combines the progressive hedging (PH) algorithm for scenario-wise decomposition with an integrated framework for solving the resulting subproblems. The latter combines a destroy-and-repair operator, a beam search procedure, and a mixed-integer programming approach. The proposed framework is evaluated on large-scale systems from the literature, containing up to 10000 nodes, adapted to multiple scenarios based on parameters from the California test system (CATS). Compared with a non-trivial baseline algorithm that includes the integrated MIP and heuristics, the proposed PH-based framework consistently improved solution quality for the six systems considered (including CATS), achieving an average optimality gap reduction of 16.23% within a 2-hour time limit.

An Efficient Hybrid Heuristic for the Transmission Expansion Planning under Uncertainties

TL;DR

Addresses the stochastic transmission expansion planning problem under uncertainties in renewables and demand. Proposes a hybrid solution combining Progressive Hedging for scenario decomposition with an integrated framework consisting of destroy-and-repair, beam search, and a MIP solver. Key contributions include a novel destroy-and-repair operator guided by residual flows, an iterative beam search to explore multiple feasible replacements, and a PH-based decomposition that scales to networks with up to 10,000 buses; tested on adapted PGLib-OPF and California test system scenarios (up to 96 hourly scenarios), achieving an average improvement in optimality gap of 16.23% on stochastic instances and substantial improvements in deterministic subproblems. The approach demonstrates scalable, high-quality solutions for large-scale STEP and offers practical guidance for planning under uncertainty.

Abstract

We address the stochastic transmission expansion planning (STEP) problem considering uncertainties in renewable generation capacity and demand. STEP's objective is to minimize the total investment cost of new transmission lines and generation cost. To tackle the computational challenges of large-scale systems, we propose a heuristic approach that combines the progressive hedging (PH) algorithm for scenario-wise decomposition with an integrated framework for solving the resulting subproblems. The latter combines a destroy-and-repair operator, a beam search procedure, and a mixed-integer programming approach. The proposed framework is evaluated on large-scale systems from the literature, containing up to 10000 nodes, adapted to multiple scenarios based on parameters from the California test system (CATS). Compared with a non-trivial baseline algorithm that includes the integrated MIP and heuristics, the proposed PH-based framework consistently improved solution quality for the six systems considered (including CATS), achieving an average optimality gap reduction of 16.23% within a 2-hour time limit.
Paper Structure (13 sections, 4 equations, 1 figure, 2 tables, 3 algorithms)

This paper contains 13 sections, 4 equations, 1 figure, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Mathematical formulation
  4. Solution approach
  5. Progressive hedging algorithm
  6. Destroy-and-repair procedure
  7. Beam search heuristic
  8. Computational experiments
  9. Benchmark instances
  10. Parameter tuning
  11. Integrated approach performance for the deterministic systems
  12. Comparison against a baseline approach
  13. Concluding remarks and future work

Figures (1)

  • Figure 1: Partial BS execution for an instance with 5 buses, 6 existing lines and 12 candidate circuits.