Methods for acceleration, and stability assessment of single-rate and multi-rate electromagnetic transient simulations
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Date
2023-03-29
Authors
Sinkar, Ajinkya
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Abstract
This thesis aims to investigate methods for speeding single-rate EMT simulations of large power networks as well as develop a rigorous analytical approach for assessing the stability of multi-rate EMT simulations.
Firstly, an alternative method for formulating the equations of a network for EMT simulations is presented. It uses descriptor state-space equations (DSE) to represent the dynamical equations of a circuit. A procedure for interfacing a DSE-based formulation with a companion circuits-based EMT simulator is also developed. This procedure enables the interfacing of arbitrary power networks with any commercial CC-based EMT simulation package and can also be used to speed up the simulation using parallel processing.
Subsequently, two of the commonly used sparse matrix-based parallelization methods are adapted and used for speeding-up DSE-based simulations, and their computational performance is compared. The first method transforms a sparse matrix into Block Diagonal (BD) form whereas, the second one transforms it into a Bordered Block Diagonal (BBD) form.
Next, a novel universally passive delay-based interface is developed that uses existing inductors in the circuit to partition the network in EMT simulations. It allows for simulation speed up when the solution of the partitioned network is computed on a parallel computing platform. It is shown that the proposed interface has superior accuracy compared to other existing inductor-based partitioning approaches and is guaranteed to be passive thus benefiting the numerical stability of the simulation.
Finally, a novel approach for the stability assessment of multi-rate EMT simulations of linear time-invariant (LTI) circuits is developed. Firstly, it is demonstrated that multi-rate EMT simulations can produce unstable results for stable continuous-time LTI circuits even when the well-known A-stable trapezoidal integration method is used. Further, it is shown that such simulations always yield a periodically varying system in the discrete-time domain. By exploiting this property and applying the well-known technique of `lifting', a sampled data time-invariant representation for the simulated discrete-time system is obtained. This can then be used for assessing the numerical stability of the simulation using eigenvalue analysis. The proposed method is useful for assessing the stability of multi-rate EMT simulations even before running them.
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Keywords
Electromagnetic Transient (EMT) Simulations, Parallel Processing, Multi-rate Simulations, Stability