IEEE Power & Energy Magazine - May/June 2018 - 61

equal area criterion (eac), which has a clear, concise, and
intuitive physical meaning that explains the mechanism of
power system stability and is able to address the stability
problem from a causality-reasoning perspective rather than
by using numerical statistics analysis. however, the eac is
only applicable to single-machine/infinite-bus (sMib) systems and does not consider energy dissipation or control
strategies during the fault event.
researchers seek to expand the applicability of analytical
methods because of their advantage in the analysis and control
of power systems. however, the real power system is too complex to use analytical methods because the large scale of the
power system is essentially a very high-dimensional problem
that the analytical method is unable to solve. big data thinking
provides a possible solution. the extended eac (eeac) uses
the idea of dimension reduction to extend the applicability of
the eac to complex power systems.
figure 6 shows the logic flow of the eeac. it first conducts the simulation of the postdisturbance trajectory based
on the full model of the power system (namely, R n space
models) using numerical integration algorithms. next, we

can transform the obtained high-dimensional trajectory into
a set of orthogonal (independent) sMib trajectories using
a linear-stability-preserving, dimension-reduction mapping.
the stability analysis can then be analytically carried out
using eac theory, where there exists a dominant mode of
oscillation that lies on R 1 or R 2 space. (the transformed trajectory can be analyzed in R 1 space if the dominant mode of
oscillation is one or several generators swinging away from
other majority generators. it can be analyzed in R 2 space if
the dominant mode of oscillation is two groups of generators
swinging with each other.) the stability margin or parameter margin can be quantitatively evaluated through causality reasoning rather than numerical statistical analysis. the
stability control strategy can then be optimized.
in this way, the eeac upgrades the numerical statistics
analysis of large power system stability into causal reasoning analysis. it is applicable to many complex power systems
with strong nonlinearity and time variance as well as complicated contingency scenarios.
the eeac theory can be viewed as a deep knowledge
extraction technique from massive simulation data or phasor

Numerical Integration
n

R Power System

300
250
200
150
100
50
0
-50
-100
-150

t
Original Trajectory in R n Space

Dimension
Reduction

Inverse
Transformation

5

P

PE′ (δ′ )
Parameterization

P0

0

6

1

4

2
δ′0

π /2

t
δ′

3
Stability Margin

Theoretical Analyses

Independent Trajectory
in n × R 2 Spaces
Causal Reasoning

figure 6. The logic flow for studying power system stability.
may/june 2018

ieee power & energy magazine

61



Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - May/June 2018

Contents
IEEE Power & Energy Magazine - May/June 2018 - Cover1
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IEEE Power & Energy Magazine - May/June 2018 - Cover3
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