DAE Index Reduction for Electromagnetic Transient Models

TL;DR

This paper introduces modular index-reduced subsystem models for electromagnetic transient (EMT) systems, enabling efficient numerical integration without approximations or symbolic algorithms, significantly improving computational performance.

Contribution

It develops two novel modular index-reduction methods for EMT models that simplify large network simulations and outperform symbolic algorithms in efficiency.

Findings

Custom subsystem models reduce memory and runtime by orders of magnitude.

Performance tests on models with up to 1152 buses show significant efficiency gains.

The approach shifts computational bottleneck from model construction to integration.

Abstract

Electromagnetic transient (EMT) models are index-2 differential-algebraic equations when they include certain topologies and are formulated with modified nodal analysis. Such systems are difficult to numerically integrate, a challenge that is currently addressed by applying model approximations or reformulating with index-reduction algorithms. These algorithms exist in general-purpose software tools, but their reliance on symbolic representation makes them computationally prohibitive for large network-wide EMT models. This paper derives and presents two modular index-reduced subsystem models that allow EMT models to be integrated with standard solvers, without approximations or symbolic algorithms. Both subsystems include a transformer, one isolated and one machine-coupled. We measure the computational performance of constructing EMT models with up to 1152 buses using the custom subsystem models and the symbolic algorithms. The custom approach reduces memory usage and runtime of model construction by several orders of magnitude compared to the general approach, shifting the bottleneck from construction to integration.