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As inverter-based resources (IBRs) penetrate power systems, the dynamics become more complex, exhibiting multiple timescales, including electromagnetic transient (EMT) dynamics of power electronic controllers and electromechanical dynamics of synchronous generators. Consequently, the power system model becomes highly stiff, posing a challenge for efficient simulation using existing methods that focus on dynamics within a single timescale. This paper proposes a Heterogeneous Multiscale Method for highly efficient multi-timescale simulation of a power system represented by its EMT model. The new method alternates between the microscopic EMT model of the system and an automatically reduced macroscopic model, varying the step size accordingly to achieve significant acceleration while maintaining accuracy in both fast and slow dynamics of interests. It also incorporates a semi-analytical solution method to enable a more adaptive variable-step mechanism. The new simulation method is illustrated using a two-area system and is then tested on a detailed EMT model of the IEEE 39-bus system. 

Power engineers rely on computer-based simulation tools to assess grid performance and ensure security. At the core of these tools are solvers for sparse linear equations. When transformed into a bordered block-diagonal (BBD) structure, part of the sparse linear equation solving can be parallelized. This work focuses on using the Schur-complement-based method for LU factorization on BBD matrices, specifically, Jacobian matrices from large-scale systems. Our findings show that the natural ordering method outperforms the default ordering method in computational performance for each block of the BBD matrix. This observation is validated using synthetic 25k-bus and 70k-bus cases, showing a speedup of up to 38% when using natural ordering without permutation. Additionally, the impact of the number of partitions is studied, and the result shows that computational performance improves with more, smaller partitions in the BBD matrices. 

This paper proposes a semi-analytical approach for efficient and accurate electromagnetic transient (EMT) simulation of a power grid. The approach first derives a high-order semi-analytical solution (SAS) of the grid’s state-space EMT model using the differential transformation (DT), and then evaluates the solution over enlarged, variable time steps to significantly accelerate the simulations while maintaining its high accuracy on detailed fast EMT dynamics. The approach also addresses switches during large time steps by using a limit violation detection algorithm with a binary search-enhanced quadratic interpolation. Case studies are conducted on EMT models of the IEEE 39-bus system and large-scale systems to demonstrate the merits of the new simulation approach against traditional numerical methods.