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Regularized Benders Decomposition for High Performance Capacity Expansion Models

Filippo Pecci, Jesse D. Jenkins

TL;DR

The paper tackles the scalability challenge of high-resolution electricity capacity expansion models (CEMs) by developing a tailored regularized Benders decomposition framework that partitions full-year operational problems into parallel sub-problems. A two-stage approach leverages interior-point level-set regularization to generate high-quality planning cuts while handling mixed-integer decision variables, enabling efficient solution of multi-period CEMs with multi-day energy storage and reservoir hydropower. Computational experiments on large CONUS systems and a Brazil case demonstrate substantial speedups over monolithic solvers and traditional Benders methods, achieving MILP solutions with sub-0.1% optimality gaps in hours rather than days. The work provides a scalable pathway to incorporate detailed operational constraints, stochastic scenarios, and discrete investments in planning, with broad potential for extension to multi-energy systems and network-decomposition strategies.

Abstract

We consider electricity capacity expansion models, which optimize investment and retirement decisions by minimizing both investment and operation costs. In order to provide credible support for planning and policy decisions, these models need to include detailed operations and time-coupling constraints, consider multiple possible realizations of weather-related parameters and demand data, and allow modeling of discrete investment and retirement decisions. Such requirements result in large-scale mixed-integer optimization problems that are intractable with off-the-shelf solvers. Hence, practical solution approaches often rely on carefully designed abstraction techniques to find the best compromise between reduced computational burden and model accuracy. Benders decomposition offers scalable approaches to leverage distributed computing resources and enable models with both high resolution and computational performance. In this study, we implement a tailored Benders decomposition method for large-scale capacity expansion models with multiple planning periods, stochastic operational scenarios, time-coupling policy constraints, and multi-day energy storage and reservoir hydro resources. Using multiple case studies, we also evaluate several level-set regularization schemes to accelerate convergence. We find that a regularization scheme that selects planning decisions in the interior of the feasible set shows superior performance compared to previously published methods, enabling high-resolution, mixed-integer planning problems with unprecedented computational performance.

Regularized Benders Decomposition for High Performance Capacity Expansion Models

TL;DR

The paper tackles the scalability challenge of high-resolution electricity capacity expansion models (CEMs) by developing a tailored regularized Benders decomposition framework that partitions full-year operational problems into parallel sub-problems. A two-stage approach leverages interior-point level-set regularization to generate high-quality planning cuts while handling mixed-integer decision variables, enabling efficient solution of multi-period CEMs with multi-day energy storage and reservoir hydropower. Computational experiments on large CONUS systems and a Brazil case demonstrate substantial speedups over monolithic solvers and traditional Benders methods, achieving MILP solutions with sub-0.1% optimality gaps in hours rather than days. The work provides a scalable pathway to incorporate detailed operational constraints, stochastic scenarios, and discrete investments in planning, with broad potential for extension to multi-energy systems and network-decomposition strategies.

Abstract

We consider electricity capacity expansion models, which optimize investment and retirement decisions by minimizing both investment and operation costs. In order to provide credible support for planning and policy decisions, these models need to include detailed operations and time-coupling constraints, consider multiple possible realizations of weather-related parameters and demand data, and allow modeling of discrete investment and retirement decisions. Such requirements result in large-scale mixed-integer optimization problems that are intractable with off-the-shelf solvers. Hence, practical solution approaches often rely on carefully designed abstraction techniques to find the best compromise between reduced computational burden and model accuracy. Benders decomposition offers scalable approaches to leverage distributed computing resources and enable models with both high resolution and computational performance. In this study, we implement a tailored Benders decomposition method for large-scale capacity expansion models with multiple planning periods, stochastic operational scenarios, time-coupling policy constraints, and multi-day energy storage and reservoir hydro resources. Using multiple case studies, we also evaluate several level-set regularization schemes to accelerate convergence. We find that a regularization scheme that selects planning decisions in the interior of the feasible set shows superior performance compared to previously published methods, enabling high-resolution, mixed-integer planning problems with unprecedented computational performance.
Paper Structure (8 sections, 11 equations, 3 figures, 2 tables, 3 algorithms)

This paper contains 8 sections, 11 equations, 3 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Multi-period capacity expansion models with stochastic operational scenarios
  3. Benders Decomposition
  4. Regularized Benders Decomposition
  5. Results
  6. Multi-period capacity expansion with discrete decisions
  7. Single-period capacity planning with multiple operational scenarios.
  8. Conclusions

Figures (3)

  • Figure 1: Illustrative example of the planning decision process with 3 planning years, each corresponding to 5 operational weeks and 2 stochastic scenarios. The operational weeks consist of 168 hours.
  • Figure 2: Test systems from the Continental United States (CONUS).
  • Figure 3: Convergence of Algorithm \ref{['alg:reg_benders_int']}, where Stage 1 solves the continuous relaxation, while Stage 2 enforces the integrality constraints on investment and retirement decisions. Note that the y-axis uses a $\log_{10}$ scale.