Resumo:
Time-domain simulations carried out with linear multistep integration methods,
such as the Trapezoidal Rule, are subject to an error often neglected in electromagnetic
transient (EMT) analyses, known as Frequency Warping. This thesis establishes
the frequency warping as a fundamental problem that compromises the
accuracy of EMT simulations, requiring specific approaches for its mitigation. Initially,
the manifestation of frequency warping in the combined nodal and state-space
method was investigated, demonstrating that small errors due to frequency warping
can accumulate over time, generating significant distortions even with conservative
time-step sizes. Subsequently, the modeling of frequency-dependent equivalents
through rational functions was explored, introducing Complex Vector Fitting (CVF)
in the context of power systems. The CVF methodology significantly improved accuracy,
reducing the Root Mean Square Error (RMSE) by up to eight orders of
magnitude compared to the conventional Vector Fitting approach, by relaxing the
complex conjugate constraint on model poles and residues. Differences regarding
model passivity were also observed. Two techniques were developed to reduce frequency
warping without reducing the time step size: Pole-Residue Compensation
(PRC), which adjusts poles and residues of rational models to compensate for numerical
perturbations in the discretized system eigenvalues; and Frequency-shifted Pole-
Residue Compensation (FPRC), which utilizes CVF and adds frequency translation
to the compensation. PRC enabled time steps 6.7 times larger without accuracy loss
or, for the same step size, errors up to 24 times smaller in terms of RMSE. Due to the
low computational cost and post-processing nature of the PRC, it can be easily integrated
into existing simulation routines. FPRC achieved even greater gains: steps
up to 35 times larger or RMSE reduction by a factor of up to 901 times. The results
were validated through computer simulations of electrical networks, which included
components such as transmission lines and power transformers, as well as equivalents
of electric power distribution and transmission networks. The techniques developed
in this thesis overcome limitations of conventional EMT simulations, offering flexibility
to significantly increase accuracy or substantially reduce computational.
