November 2021
Intermediate
416 pages
12h 42m
English
book
Harmonic Modeling of Voltage Source Converters using Basic Numerical Methods
by Ryan Kuo-Lung Lian, Ramadhani Kurniawan Subroto, Victor Andrean, Bing Hao Lin
Content preview from Harmonic Modeling of Voltage Source Converters using Basic Numerical Methods
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4Matrix Exponential
“No problem can be solved from the same level of consciousness that created it.”
– Albert Einstein
If one chooses to model a power converter in time‐domain, one needs to be familiar with basic numerical methods for evaluating integration and matrix exponentials. This chapter is mainly devoted to matrix exponentials. In fact, it has been shown by Van Loan in [43] that the exponential of a certain block triangular matrix can replace the need for computing the integrals.
It is proved in [43] that if a block triangular matrix, 
is defined as
(4.1)
then for 
,
(4.2)
where
(4.3)
(4.4)
(4.5)
Hence, one can avoid evaluating the convolution integral when obtaining ...
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