Dimensionality Reduction in Transient Simulations: A Diffusion Maps Approach

A mathematically rigorous framework combining diffusion map analysis techniques with simulation data from electromagnetic transient programs is proposed to characterize the collective dynamics of transient processes. The framework can be used to compress and analyze large and complex data sets obtained from transient simulations. Through this formulation, the structures that dominate the system response, and the global measurements that contribute most to this response can be directly calculated. The resulting coordinates can be correlated with the time scales of specific motion or be effectively used to extract spatiotemporal features of high-dimensional data. The application of the method is illustrated on both, electromagnetic transient simulations and transient stability data. Simulation studies reveal that diffusion-map data-analysis techniques generate accurate estimates of modal parameters even in the presence of measurement noise.