IEEE Electrification Magazine - December 2017 - 70

In practice, nominal
system models are
bound to contain
uncertainties.

nominal value of 0.3 X, while the
variation in the resistive load is as
described in case study 1.1. From n
analysis, it has been found that if
both the uncertain load and line
resistance are kept within 80.3% of
their respective nominal values, the
system under study can be ensured
to be stable for an output power of up
to 17.3 W. For case 1.2, the robust stability margin increas-
es as the line resistance R in, set in the range of [150 mX,
450 mX], provides more damping to the resonant LC input
filter with respect to case 1.1, when R in is set at a constant
value of 160 mX. Therefore, for case 1.2, n analysis finds
new uncertainty sets of [1.5 X, 3.5 X] and [180 mX, 420 mX]
for the resistive load and line resistance, respectively, and
the system is robustly stable for R 2 1.5 X and R in 2 180 mX
and for an output power of up to 17.3 W.
Temperature is one of the main factors that can intro-
duce uncertainties in multiple system parameters. In
case study 2.2, the buck converter system is considered to
be working in an environment where temperature may
vary between - 40 and 80 °C with a reference value of
20 °C. The temperature variation influences the values of
the resistive components of the buck converter, such as
the equivalent series resistance of the capacitors and
inductors of the input and output filters, the line resis-
tance, and the switch on resistance of the metal-oxide-
semiconductor field-effect transistor (MOSFET). The load
is assumed to vary, as in case 1.1. Case study 2.2 was then
repeated with the same condition as case 2.1 but with
temperature being fixed at its nominal value. Further to n
analysis, the robust stability margin of the buck converter
has been found to be 50.5% when uncertainties in tem-
perature are included as shown in case study 2.1, as com-
pared to 74.5% when uncertainties in temperature are not
included in case study 2.2. The important difference in
the robust stability margin in these two case studies
emphasizes the necessity of incorporating operating tem-
perature uncertainty for more reliable stability analysis of
a system.
In practice, it is neither viable nor time efficient to cre-
ate highly refined system models to represent actual sys-
tems. Hence, approximate system models, with a good
tradeoff between accuracy and simplicity, are often used
for design. The nominal values of their system compo-
nents are generally based on known data such as
nameplate information. Case studies 3.1-3.3 aim to dem-
onstrate how model uncertainties, which may be known
to a different level of accuracy, can be incorporated in the
robust stability analysis without compromising the reli-
ability of the results. In addition, it examines the effect of
model uncertainties on the robust stability margin. In case
study 3.1, n analysis has predicted the critical out-
put power of the considered buck converter to be 15.0 W
with a robust stability margin of 61.4% when model

70

I E E E E l e c t r i f i cati o n M a gaz ine / DECEMBER 2017

uncertainties are neglected and the
model is assumed to be completely
accurate. On the other hand, the criti-
cal output power has been deter-
mined as 11.6 W in case study 3.2,
when uncertainties are included,
while its value increased to 12.2 W
when the given uncertainties are
defined within a relatively narrower
range in case study 3.3. With model uncertainties incorpo-
rated in the analysis, the robust stability margin is 0.210
and 0.288 for cases 3.2 and 3.3, respectively. Although the
results for cases 3.2 and 3.3  seem to be conservative in
comparison to case 3.1, they are more reliable. This is
because the analyses consider uncertainties of the system
model, and therefore include worst-case scenarios.
The findings in these studies confirm that uncertain-
ties have a significant impact on the stability robustness,
and must be duly incorporated during design process,
particularly for safety-critical applications.

Conclusions
PE is the enabling technology that is paving the way
toward more sustainable aviation. There is a pressing
need for design engineers to address the issues, such as
power system stability, that could slow down the transi-
tion toward the MEA. In doing so, design engineers may
need to think beyond classical techniques and adopt
novel analysis tools that can provide more effective
solutions to the current issues associated in the devel-
opment of the future electric aircraft. This article has
demonstrated the n-based SSV as one possible tech-
nique to analyze and ensure the stability robustness of
the MEA electrical network.

Acknowledgment
We gratefully acknowledge the support for this work from
the European Union (EU) as part of the Clean Sky project,
part of the EU FP7 program.

For Further Reading
International Energy Agency. Transport Energy and CO2: Moving
Towards Sustainability. OECD Publishing, Paris, France, 2009.
Working Group III Technical Support Unit, "Climate
Change 2014: Mitigation of Climate Change," presented at
the Intergovernmental Panel on Climate Change, New York,
2014.
K. J. Karimi. (2007). "Future aircraft power systems-integra-
tion challenges (slides)." The Boeing Company. [Online]. Avail-
able: http://eng.umd.edu/~austin/ense622.d/lecture-resources/
Boeing787-MoreElectricAircraft.pdf
P. Wheeler and S. Bozhko, "The more electric aircraft: Tech-
nology and challenges," IEEE Electrific. Mag., vol. 2, pp. 6-12,
Dec. 2014.
A. Boglietti, A. Cavagnino, A. Tenconi, S. Vaschetto, and P.
di Torino, "The safety critical electric machines and drives
in the more electric aircraft: A survey," in Proc. 35th Annu.
Conf. IEEE Industrial Electronics, Porto, Portugal, Nov. 2009, pp.
2587-2594.
http://eng.umd.edu/~austin/ense622.d/lecture-resources/
Table of Contents for the Digital Edition of IEEE Electrification Magazine - December 2017
