5594 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 33, NO. 5, SEPTEMBER 2018
A Hybrid Fault Cluster and Th´ evenin Equivalent
Based Framework for Rotor Angle
Stability Prediction
Seyed Mahdi Mazhari , Member, IEEE, Nima Safari , Student Member, IEEE,
C. Y. Chung , Fellow, IEEE, and Innocent Kamwa , Fellow, IEEE
Abstract—This paper addresses a novel approach for rotor angle
stability prediction in power systems. In the proposed framework,
a fault cluster (FC) concept is introduced to divide an electrical
network into several disparate zones. FCs are determined in accor-
dance with the installed PMU locations so that the well-developed
wide-area fault detection modules can estimate the origin of any
fault in the network among FCs. The proposed framework assigns
a stability prediction model to each FC. Parameters of the Th´ evenin
equivalent network (TEN) seen from some generators, selected via
a feature selection process, are calculated both in steady-state and
during fault. The adopted TEN parameters are then applied as
inputs to an ensemble decision tree-based prediction models. The
proposed method benefits from parallel computation in the train-
ing process and does not require post-fault data. The performance
of the proposed framework is validated on several IEEE test sys-
tems, followed by a discussion of results.
Index Terms—Decision tree, fault cluster (FC), feature selection,
phasor measurement unit (PMU), Th´ evenin equivalent, transient
stability.
I. INTRODUCTION
P
OWER systems are usually confronted with various
weather conditions and fortuitous events that may lead
to incidents causing partial or complete instability of the net-
work. Transient stability refers to the ability of the system to
maintain synchronism of generators and bring itself back to a
stable steady-state following a large disturbance [1]. Transient
instability is among the most infrequent, yet most severe, events
in power systems and can bring about unintended islanding,
cascading outages, and widespread blackouts.
Conventionally, power system operating limits are conser-
vatively set to prevent system instability; therefore, optimal
Manuscript received September 15, 2017; revised January 19, 2018; accepted
March 31, 2018. Date of publication April 5, 2018; date of current version Au-
gust 22, 2018. This work was supported in part by the Natural Sciences and
Engineering Research Council of Canada and in part by the Saskatchewan Power
Corporation (SaskPower). Paper no. TPWRS-01425-2017. (Corresponding
author: Seyed Mahdi Mazhari.)
S. M. Mazhari, N. Safari, and C.Y. Chung are with the Department of Electri-
cal and Computer Engineering, University of Saskatchewan, Saskatoon, SK S7N
5A9, Canada (e-mail:, s.m.mazhari@usask.ca; n.safari@usask.ca; c.y.chung@
usask.ca).
I. Kamwa is with the Department of Power System and Mathematics, Hydro-
Qu´ ebec/IREQ, Varennes, QC J3X 1S1, Canada (e-mail:, kamwa.innocent@
ireq.ca).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPWRS.2018.2823690
exploitation of the existing facilities is confined [2]. However,
rapid development of phasor measurement units (PMUs), as
part of the wide-area measurement system, paved the way for
network operation closer to stability limits. Early prediction of
rotor angle stability based on PMU data can trigger sets of emer-
gency control strategies that can prevent or reduce destructive
impacts of large disturbances [3].
Several methods and algorithms have been developed for rotor
angle stability prediction in recent years. Time-domain analysis
of an identified event with respect to the system parameters is the
most conventional and accurate approach to tackle this problem
[4], [5]; however, unaffordable computational burden hinders its
application to online prediction [6]. Transient-energy-function
based algorithms form another group of techniques in which
variations of kinetic and potential energies against reference
values are employed as criteria for stability assessment [7],
[8]. Nonetheless, calculating levels of these energies follow-
ing certain contingencies is challenging in real-life power
systems [9].
Data-driven approaches offer an alternative framework for
online stability prediction; these methods engage sophisticated
artificial intelligence (AI) techniques to find a prediction model
over a large set of training data obtained by offline analysis.
Notably, data-driven based algorithms (DDA) have garnered in-
terest in recent years due to their advantages in real-time applica-
tions [10]–[17]. Various techniques have been developed based
on this approach for either pre- or post-fault system variables; it
should be mentioned that in the stability context, post-fault refers
to the system after fault clearing time. In [10], post-fault rotor
angles of generators are preprocessed and then fed into a hybrid
classifier composed of probabilistic neural networks (NNs). Ap-
plication of adaptive artificial NNs is also investigated in [11] in
which a pre-disturbance operating point is employed to predict
system stability. Performance of a support vector machine is
evaluated in [12], [13]; in both papers, post-fault rotor angles
are used as inputs to the prediction model, though [12] also uses
generator speeds and voltages in the training process. Signifi-
cant success with robustness of decision tree (DT) [13]–[15],
core vector machine [16], and extreme learning machine [17]
have been reported; furthermore, new indices have been intro-
duced for feature extraction in [14], [15] and a feature selection
process employed by [16] and applied to a wide array of pre-
and post-disturbance parameters in the specialized literature.
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