DAE Index Reduction for Electromagnetic Transient Models
This addresses a computational bottleneck for engineers simulating large network-wide EMT models, offering a practical improvement over existing symbolic methods.
The paper tackled the challenge of numerically integrating electromagnetic transient (EMT) models, which are index-2 differential-algebraic equations, by deriving two modular index-reduced subsystem models that avoid approximations or symbolic algorithms. The result showed that the custom approach reduced memory usage and runtime of model construction by several orders of magnitude for models with up to 1152 buses, shifting the bottleneck from construction to integration.
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.