IEEE Electrification Magazine - December 2017 - 65

As the aircraft
electrical network
becomes larger and
more complex,
the multitude of
PE-based loads
can challenge
the stability of the
electrical power
system.

may be represented by dc values with
some superimposed small-ac compo-
nents. In Figure 6, the dc components
of the supply voltage, supply current,
input voltage and input current are
clearly denoted as Vg, I g, Vin, and I in,
respectively, while their correspond-
ing small-ac components are given by
vt g (t), tig (t), vt in (t), and tiin (t), respectively.
R cpl is given by Vin /I in (S. Sumsur-
ooah 2017).
The negative impedance of the PE-
based loads, under certain circum-
stances, may cause the system to
oscillate and become unstable (Mid-
dlebrook 1976). Stability assessment
is thus crucial in the design of PE sys-
tems. The system stability has to be
analyzed both at the small- and
large-signal level. Small-signal analysis investigates the
stability of an EPS when it is subject to small disturbances
(Jusoh 2004, Areerak 2009, Riccobono and Santi 2014,
Emadi et al. 2006). The analysis is performed on a linear-
ized system model about a certain operating point (Jusoh
2004, Areerak 2009, Riccobono and Santi 2014, Emadi
et  al.  2006). In contrast, large-signal stability analysis
investigates the system's behavior under large distur-
bances, including sudden large changes in loads (Che
et al. 2015, Griffo and Wang 2012, Rosado et al. 2007).
Although stability assessment of large-signal disturbanc-
es is important, this article discusses small-signal stabili-
ty analysis, which is an important concern in the reliable
operation of the system.
As PE play a key role in developing more sustainable
modes of transport, there is a dire need to address the
issue of stability. Stringent assessment techniques are
required to ensure the stability of the electrical network
for the MEA. The stability of the PM machine drive
(PMMD) ac/dc system and the dc/dc buck converter sys-
tem, being important components of the MEA, will be
discussed in the "PMMD System" and the "Buck Conver-
tor System" sections, respectively, while the stability of a
representative EPS with an ideal CPL will be assessed in
the "CPL" section.

minor loop gain T. According to the
Nyquist stability criterion, for the sys-
tem to be stable, 1 + T must not have
any roots in the right half-plane (Mid-
dlebrook 1976, Riccobono and Santi
2014). The more-than-necessary con-
dition of the Middlebrook criterion,
which is an extension of the afore-
mentioned formal requirement of the
Nyquist stability criterion, requires
that | Z o | % | Z i | for all frequencies to
ensure system stability (Middle-
brook 1976, Wildrick et al. 1995).
The classical methods treat the
physical system as a nominal model
with fixed parameter values (Franklin
et al. 1994, Dorf and Bishop 1998). The
outcome of the stability assessment is
therefore heavily dependent on the
quality of the system model. The model may be refined to
great detail by matching its response to that of the physical
system. Yet in practice, excessive model refinement is
unlikely to be viable or practical. Further, the exact values of
the system components may not be known accurately. For
instance, system parasitic elements, which are often hard to
quantify, can have a significant influence on the quality of
the model. The power supply and external filters, to be con-
nected on site, may be unknown at the design stage. This
may significantly alter the impedance of the power stage. In
addition, EPS may be exposed to large variations in their

iin(t )

Pin = Constant

Eqo(Vin,Iin)

δiin(t )

δVin(t )

Vin(t )

Stability Robustness

Cin
Rcin

Iin+iin(t )
+
Vin+vin(t )
-

"

Vg+vg(t ) +
-

Lin

"

Ig +ig(t ) Rin

"

"

Figure 5. The characteristic curve of an ideal CPL.

"

The stability of EPS is generally assessed by using classi-
cal stability analysis techniques (Franklin et al. 1994, Dorf
and Bishop 1998). These include the eigenvalue method
and impedance methods based on the Nyquist stability
criterion. An EPS can be viewed as a cascade of its source
and load components (Riccobono and Santi 2014, Rahimi
and Emadi 2009, Sudhoff and Wasynczuk 1993). As illus-
trated in Figure 4, Z o and Z i are the output and input
impedances of the source and load subsystems, respec-
tively. The impedance ratio of Z o to Z i, is known as the

-(Iin-iin(t ))
-Rcpl

Icpl = 2Iin

Pin
Figure 6. The linear model of the system with an ideal CPL.

IEEE Elec trific ation Magazine / D EC EM BE R 2 0 1 7

65



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