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CANOPI: Contingency-Aware Nodal Optimal Power Investments with High Temporal Resolution

Thomas Lee, Andy Sun

TL;DR

CANOPI addresses the challenge of large-scale capacity expansion with endogenous transmission contingencies by formulating a security-constrained nodal DC power-flow model that includes impedance-feedback. It combines a linear approximation with a fixed-point correction for the nonlinear impedance effects, and introduces a novel level-bundle optimization framework with interleaved contingency constraint generation, plus a minimal cycle-basis IP to sparsify DC constraints. The paper also provides a fast cycle-based DCOPF algorithm and a transmission-correction mechanism to ensure impedance-consistent upgrades. Demonstrated on a 1493-bus Western Interconnection with 52 hourly scenarios and up to 20 billion contingency constraints, CANOPI yields meaningful reliability and economic benefits while achieving substantial computational speedups. The work bridges macro-energy planning with detailed transmission physics, enabling scalable, nodal-contingency-aware planning on realistic grids.

Abstract

We present CANOPI, a novel algorithmic framework, for solving the Contingency-Aware Nodal Power Investments problem, a large-scale nonlinear optimization problem that jointly optimizes generation, storage, and transmission expansion. The underlying problem is nonlinear due to the impact of transmission upgrades on impedances, and the problem's large scale arises from the confluence of spatial and temporal resolutions. We propose algorithmic approaches to address these computational challenges. We pose a linear approximation of the overall nonlinear model, and develop a fixed-point algorithm to adjust for the nonlinear impedance feedback effect. We solve the large-scale linear expansion model with a specialized level-bundle method leveraging a novel interleaved approach to contingency constraint generation. We introduce a minimal cycle basis algorithm that improves the numerical sparsity of cycle-based DC power flow formulations, accelerating solve times for the operational subproblems. CANOPI is demonstrated on a 1493-bus Western Interconnection test system built from realistic-geography network data, with hourly operations spanning 52 week-long scenarios and a total possible set of 20 billion individual transmission contingency constraints. Numerical results quantify the reliability and economic benefits of fully incorporating transmission contingencies in integrated planning models and highlight the computational advantages of the proposed methods.

CANOPI: Contingency-Aware Nodal Optimal Power Investments with High Temporal Resolution

TL;DR

CANOPI addresses the challenge of large-scale capacity expansion with endogenous transmission contingencies by formulating a security-constrained nodal DC power-flow model that includes impedance-feedback. It combines a linear approximation with a fixed-point correction for the nonlinear impedance effects, and introduces a novel level-bundle optimization framework with interleaved contingency constraint generation, plus a minimal cycle-basis IP to sparsify DC constraints. The paper also provides a fast cycle-based DCOPF algorithm and a transmission-correction mechanism to ensure impedance-consistent upgrades. Demonstrated on a 1493-bus Western Interconnection with 52 hourly scenarios and up to 20 billion contingency constraints, CANOPI yields meaningful reliability and economic benefits while achieving substantial computational speedups. The work bridges macro-energy planning with detailed transmission physics, enabling scalable, nodal-contingency-aware planning on realistic grids.

Abstract

We present CANOPI, a novel algorithmic framework, for solving the Contingency-Aware Nodal Power Investments problem, a large-scale nonlinear optimization problem that jointly optimizes generation, storage, and transmission expansion. The underlying problem is nonlinear due to the impact of transmission upgrades on impedances, and the problem's large scale arises from the confluence of spatial and temporal resolutions. We propose algorithmic approaches to address these computational challenges. We pose a linear approximation of the overall nonlinear model, and develop a fixed-point algorithm to adjust for the nonlinear impedance feedback effect. We solve the large-scale linear expansion model with a specialized level-bundle method leveraging a novel interleaved approach to contingency constraint generation. We introduce a minimal cycle basis algorithm that improves the numerical sparsity of cycle-based DC power flow formulations, accelerating solve times for the operational subproblems. CANOPI is demonstrated on a 1493-bus Western Interconnection test system built from realistic-geography network data, with hourly operations spanning 52 week-long scenarios and a total possible set of 20 billion individual transmission contingency constraints. Numerical results quantify the reliability and economic benefits of fully incorporating transmission contingencies in integrated planning models and highlight the computational advantages of the proposed methods.

Paper Structure

This paper contains 24 sections, 6 theorems, 25 equations, 1 figure, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Literature review
  3. Contributions
  4. Model
  5. Capacity expansion problem
  6. Detailed operational problem
  7. Generation and Storage Constraints
  8. Cycle-based DC Power Flow
  9. Impedance Feedback
  10. Transmission Contingencies
  11. Overall Operational Subproblem
  12. Algorithms
  13. Approximate operational subproblem
  14. Contingency constraint-generation oracle
  15. Bundle method with interleaved constraint generation
  16. ...and 9 more sections

Key Result

Proposition 1

(Lower and upper bounds). For any impedance-defining capacity $\hat{x}^\mathrm{br}$, scenario $\xi_\omega$, and a subset of contingencies $\mathcal{J}\subseteq\mathcal{J}^\mathrm{full}$, consider the following quantities computed at two capacity decisions $x, z\in\mathcal{X}$ Then, $(\theta^{*z}, g^*)$ and $(\theta^{*x}, \sigma^\mathrm{c})$ provide valid lower and upper bounds on the $\mathcal{J}^

Figures (1)

  • Figure 1: Iterative procedure CORR to re-optimize a consistent $\hat{x}^\mathrm{br} = \tilde{x}^\mathrm{br}$. Note the non-transmission $(x^\mathrm{non\text{-}br}_*, y^\mathrm{non\text{-}br}_*)$ inputs are fixed across all iterations of RTEP, while $\hat{x}^\mathrm{br}$ is updated iteratively.

Theorems & Definitions (12)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • Proposition 5
  • proof
  • ...and 2 more