IEEE Electrification Magazine - December 2019 - 88

eigenvalues. Considerable work has been done to enhance
the traditional droop method by increasing its damping
on operation points to improve the transient-behavior
performance, which includes adaptively adjusting the
droop coefficients, estimating the grid impedance, adding
feedforward components, and modifying the transfer
function by adding proportional, integral, and deriva-
tive elements.
The dynamic phasor is another important sensitivity
factor. As mentioned previously, the microgrid is a high-
coupling distributed system with a low inertia stiffness. It
contains multiple electric elements and control loops that
have different slow and fast dynamics, so the phasor
dynamic highly impacts the system and stability margin.
Although it is more accurate to develop a microgrid model
that includes the phasor dynamics, doing so will lead to
difficulties during stability simulations and while design-
ing the controller parameters. Therefore, depending on the
research topic, reduction can be considered. For example,
both of Coelho's famous models, which were proposed in
2002 and 2012, considered the angular frequency, ~, as a
constant value, not a dynamic one, in the nodal-admit-
tance-network equation to achieve the frequency regula-
tion and power sharing. The simulation and experimental
results matched perfectly.
Participation analysis can identify the impacts of differ-
ent sensitivity parameters, such as electrical elements,
controllers, sampling time, and communication. Through
that method, it is possible to clearly know which factor
has the highest impact, based on the research require-
ments. A reduced-order model can then be developed by
ignoring some of the state variables that are not related to
the specific stability problem.

Conclusions
The growth of the rapidly developing global microgrid
market will inevitably lead to new developments. Advanc-
es in network, communication, and control technologies
have enabled microgrids to become increasingly hierarchi-
cal, distributed, flexible, and intelligent through the inte-
gration of more complicated controllers. To understand
the complex dynamic behavior of microgrids that have a
hieratical structure and reveal the interactions of various
components, accurate mathematical models are neces-
sary for stability analysis and designing effective con-
trol strategies.
In this article, we summarized and analyzed the most
challenging topics in microgrid-modeling research and
explained the small-signal modeling method's populari-
ty. To better understand small-signal modeling's devel-
opment status, we reviewed its history and listed the
methods that are used for microgrids, including the
names of researchers and dates. The challenges of and
solutions to small-signal modeling methods for ac

88

I E E E E l e c t r i f i cati o n M agaz ine / DECEMBER 2019

microgrids that have hierarchical structures were
ex plored. Information was provided that could be
regarded as a guide for those who are interested in this
research field.

Acknowledgments
This article was supported by the National Natural Sci-
ence Foundation of China (grants 51707158 and 61802301),
Scientific and Technological Projects of Shaanxi Province
(grant 2015GY102), Natural Science Foundation of Shaanxi
Province (grants 2018JQ6006 and 2019JQ-056), and China
Scholarship Council (grant 201808610075).

For Further Reading
S. Sen and V. Kumar, "Microgrid modelling: A comprehensive
survey," Annu. Rev. Control, vol. 46, pp. 216-250, Oct. 2018.
J. He and X. Wu, "Small-signal stability analysis and opti-
mal parameters design of microgrid clusters," IEEE Access,
vol. 7, pp. 36,896-36,909, Feb. 2019.
G. Diaz, C. Gonzalez-Moran, J. Gomez-Aleixandre, and A.
Diez, "Complex-valued state matrices for simple representa-
tion of large autonomous microgrids supplied by PQ and VF
generation," IEEE Trans. Power Electron, vol. 24, no. 4, pp. 1720-
1730, 2009.
N. Pogaku, M. Prodanovic, and T. C. Green, "Modelling,
analysis and testing of autonomous operation of an inverter-
based microgrid," IEEE Trans. Power Electron, vol. 22, no. 2,
pp. 613-625, 2007.
P. Benner, M. Ohlberger, A. Patera, G. Rozza, and K.
Urban, Model Reduction of Parametrized Systems. New York:
Springer, 2017.
I. Y. Chung, W. Liu, D. A. Cartes, E. G. Collins, Jr, and S. I.
Moon, "Control methods of inverter-interfaced distributed
generators in a microgrid system," IEEE Trans. Ind. App, vol. 46,
no. 3, pp. 1078-1088, 2001.
M. Rasheduzzaman, "Small signal modeling and analysis
of microgrid systems," Dissertation, Missouri Univ. of Sci-
ence and Technology, Rolla, MO, 2015.
E. A. A. Coelho, P. C. Cortizo, and P. F. D. Garcia, "Small sig-
nal stability for parallel-connected inverters in standalone ac
supply systems," IEEE Trans. Ind. Appl, vol. 38, no. 2, pp. 533-
542, 2002.
E. A. A. Coelho et al., "Small-signal analysis of the mi-
crogrid secondary control considering a communication
time delay," IEEE Trans. Ind. Electron, vol. 63, no. 10, pp. 6257-
6269, 2016.

Biographies
Ying Wu (wuyg1226@hotmail.com) is with the School of
Computer Science, Xi'an Shiyou University, China.
Yanpeng Wu ( ywu@et.aau.dk) is with the Department
of Energy Technology, Aalborg University, Denmark.
Josep M. Guerrero ( joz@et.aau.dk) is with the Depart-
ment of Energy Technology, Aalborg University, Denmark.
Juan C. Vasquez ( juq@et.aau.dk) is with the Depart-
ment of Energy Technology, Aalborg University, Denmark.
Jiao Li ( lijiao@xsyu.edu.cn) is with the School of Com-
puter Science, Xi'an Shiyou University, China.
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