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Uncertainty-Aware Grid Planning in the Real World: A Method Enabling Large-Scale, Two-Stage Adaptive Robust Optimization for Capacity Expansion Planning

Gabriel Mantegna, Emil Dimanchev, Filippo Pecci, Neha Patankar, Jesse Jenkins

TL;DR

This paper introduces a method for endogenizing uncertainty into capacity expansion models, a variant of adaptive robust optimization, that addresses this gap and performs similarly to the traditional method in terms of outcomes, while significantly reducing computational complexity, making it scalable to real-world planning problems.

Abstract

Capacity expansion models are frequently used to inform multi-billion dollar grid infrastructure decisions, a context in which there is significant uncertainty surrounding the future need for and performance of such infrastructure. However, despite much academic literature on the topic, virtually no grid planning processes use capacity expansion models that endogenously consider uncertainty, an oversight which frequently leads to short-sighted infrastructure decisions. This is partially due to a technology transfer gap, but it is also due to a lack of methods that work at large scale. In this paper we introduce a method for endogenizing uncertainty into capacity expansion models, a variant of adaptive robust optimization, that addresses this gap. We apply the method to a real-world capacity expansion planning problem, that of the State of California, and compare its performance to that of traditional adaptive robust optimization. We find that both the traditional method and our method identify increased transmission investment as a key lever for increasing robustness and adaptability, while helping to avoid downside risks that current deterministic planning processes may be exposing ratepayers to. Our method performs similarly to the traditional method in terms of outcomes, while significantly reducing computational complexity, making it scalable to real-world planning problems.

Uncertainty-Aware Grid Planning in the Real World: A Method Enabling Large-Scale, Two-Stage Adaptive Robust Optimization for Capacity Expansion Planning

TL;DR

This paper introduces a method for endogenizing uncertainty into capacity expansion models, a variant of adaptive robust optimization, that addresses this gap and performs similarly to the traditional method in terms of outcomes, while significantly reducing computational complexity, making it scalable to real-world planning problems.

Abstract

Capacity expansion models are frequently used to inform multi-billion dollar grid infrastructure decisions, a context in which there is significant uncertainty surrounding the future need for and performance of such infrastructure. However, despite much academic literature on the topic, virtually no grid planning processes use capacity expansion models that endogenously consider uncertainty, an oversight which frequently leads to short-sighted infrastructure decisions. This is partially due to a technology transfer gap, but it is also due to a lack of methods that work at large scale. In this paper we introduce a method for endogenizing uncertainty into capacity expansion models, a variant of adaptive robust optimization, that addresses this gap. We apply the method to a real-world capacity expansion planning problem, that of the State of California, and compare its performance to that of traditional adaptive robust optimization. We find that both the traditional method and our method identify increased transmission investment as a key lever for increasing robustness and adaptability, while helping to avoid downside risks that current deterministic planning processes may be exposing ratepayers to. Our method performs similarly to the traditional method in terms of outcomes, while significantly reducing computational complexity, making it scalable to real-world planning problems.
Paper Structure (14 sections, 4 theorems, 19 equations)

This paper contains 14 sections, 4 theorems, 19 equations.

Key Result

Lemma 1

If the only uncertain parameters in a linear two-stage adaptive robust optimization model with full recourse are objective function coefficients (costs), the model can be converted to a single-stage model and solved as an LP.

Theorems & Definitions (11)

  • Lemma 1: LP reformulation of two-stage ARO for cost-based uncertainties
  • proof
  • Lemma 2: LP reformulation of two-stage ARO via scenarios
  • proof
  • Remark 1
  • Theorem 1: LP-representation of split-budget formulation
  • proof
  • Remark 2
  • Theorem 2: Convex relaxation of two-stage ARO
  • proof
  • ...and 1 more