📝 SummarXiv

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.