Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interpreting Frame Transformations as Diagonalization of Harmonic
  Transfer Functions   Analysis of ac electrical systems can be performed via frame transformations
in the time-domain or via harmonic transfer functions (HTFs) in the
frequency-domain. The two approaches each have unique advantages but are hard
to reconcile because the coupling effect in the frequency-domain leads to
infinite dimensional HTF matrices that need to be truncated. This paper
explores the relation between the two representations and shows that applying a
similarity transformation to an HTF matrix creates a direct equivalence to a
frame transformation on the input-output signals. Under certain conditions,
such similarity transformations have a diagonalizing effect which, essentially,
reduces the HTF matrix order from infinity to two or one, making the matrix
tractable mathematically without truncation or approximation. This theory is
applied to a droop-controlled voltage source inverter as an illustrative
example. A stability criterion is derived in the frequency-domain which agrees
with the conventional state-space model but offers greater insights into the
mechanism of instability in terms of the negative damping (non-passivity) under
droop control. The paper not only establishes a unified view in theory but also
offers an effective practical tool for stability assessment.

35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys