Energy and Power Engineering, 2013, 5, 703-707
doi:10.4236/epe.2013.54B136 Published Online July 2013 (http://www.scirp.org/journal/epe)
Study on Approach of Static Security Assessment
Accounting for Electro-thermal Coupling*
Mengxia Wang1, Hongbin Sun1, J inx in Huang2, Qiang Zhang3
1Dept. of Electrical Engineering, Tsinghua University, Beijing, China
2State Grid of China Technology College, Jinan, China
3Shandong Electric Power Dispatching and Control Center, Jinan, China
Received March, 2013
ABSTRACT
A static security assessment approach considering electro-thermal coupling of transmission lines is proposed in this
paper. Combined with the dynamic thermal rating technology and energy forecasting, the approach can track both the
electrical variables and transmission lines’ temperature varying trajectory under anticipated contingencies. Accordingly,
it identifies the serious contingencies by transmission lines’ temperature violation rather than its power flow, in this
case the time margin of temperature rising under each serious contingency can be prov ided to operators as warning in-
formation and some unnecessary security control can also be avoided. Finally, numerical simulations are carried out to
testify the validity of the proposed app roach.
Keywords: Power System; Dynamic Thermal Rating; Static Security Assessment; Transmission Line; Electro-thermal
Coupling
1. Introduction
As an indispensable technology to guarantee the security
operation of power grid, the on-line static security as-
sessment (SSA) has been being focused by both aca-
demic and engineering circles [1-3]. It takes charge of
screening the anticipated contingencies, identifying seri-
ous ones which cause voltage or thermal violation and
providing warning information to operators as the im-
portant basis for making preventive control decision for
the serious contingencies. However, thermal limit
(maximum permissible temperature) of transmission line
has been being converted into limit on power flow or
current in SSA, and the asynchronous between tempera-
ture and current of transmission line (thermal inertia) is
always ignored, this should be improved under new
situation. There are two major reasons motivate the im-
provement: (1) With the rapid increase of electric power
generation & demand, the transfer capability of power
grid is being pushed to its thermal limit, therefore, the
traditional SSA which ignores the thermal inertia tends to
impede the efficient utilization of the existing transfer
capability of power grid. (2) As the massive power gen-
erated by new energy resource integrates into power grid,
the operating state of power grid is bec omin g more com-
plication and changeful, under this case, the traditional
SSA tends to provide warning information frequently by
identifying the power flow violation, this correspond-
ingly lead to the unnecessary security control operations.
To address the issues mentioned above, it is essential
to realize to consider the electro-thermal coupling rela-
tion of transmission lin es and regards transmission lines’
temperature as their thermal limits in SSA, there are two
essential conditions for the goal: (1) Operating tempera-
ture & micro meteorological environment of transmis-
sion lines are capable of being monitored and the data
can be assembled in control center of power grid. (2) The
improved power flow calculation which considers trans-
mission lines’ temperature as state valuable should be
performed fast enough to screen the anticipated contin-
gencies and meet the need of online application. For the
first condition, dynamic thermal rating (DTR) can be
practicable, it was proposed in 1970s[4-5] and has been
widely applied in some dev eloped countries in the end of
1990s[6-7], now its monitoring data (including tempera-
ture and meteorological data) is integrated into SCADA,
but it has not been combined organically with power
system analysis and control. For the second condition,
the electro-thermal coupling power flow[8] can be util-
ized, but it must be simplified to reduce the calculation
complication and time consuming.
*This work is supported by National Key Basic Research Program o
f
China (2013CB228203), National Science Fund for Distinguished
Young Scholars (51025725) and China Postdoctoral Science Founda-
tion (2012M520271).

M. X. WANG ET AL.
704
In this paper, combined with DTR technology, an on-
line security analysis frame considering electro-thermal
coupling is firstly formulated to present the precondition
& purpose of online security assessment considering
electro-thermal coupling. Then the approach is proposed
to realize the fast screening of anticipated contingencies
with temperature variation calculation.
2. Framework of On-line Electro-thermal
Coupling Security Analysis
In this section, a preliminary exploration is performed to
combine the DTR technology with power system security
analysis, and the framework of electro-thermal coupling
security analysis is proposed as Figure 1 based on the
classical security analysis which presented by Dyliyacco
in 1970s.
In Figure 1, extended state estimation (Block ①) is
the foundation for on-line operation of the security anal-
ysis considering electro-thermal coupling, it takes ad-
vantage data measured by DTR, can not only estimate
traditional electric state (such as node voltage amplitude
and phase angle) but also the temperature and parameters
of HBE[9] (Heat Balance Equation) of transmission lines.
As the preliminary research, reference [10] has proposed
an extended state estimation based on existing SCADA.
The electro-thermal coupling power flow (Block②)
technique[8] can be used to simulate the temperature
variation trajectory of tran smission lines in research time
horizon based on the load forecast data. If voltage or
temperature violations are found (Block ③), processing
corrective control (Block ④) will be activated to elimi-
nate the temperature and electric v iolations. If initial state
is secure (no violation in initial state), the security as-
sessment considering electro-thermal coupling will be
activated, it screens every contingency in anticipated
contingency set (Block ⑤), picks out serious ones
Figure 1. Framework of static state security analysis con-
sidering electro-thermal coupling.
which cause voltage or temperature violation, and pro-
vides warning information to operators. According to the
information, operators of power system will start the
correspondingly preventive control (Block ⑥) to im-
prove the security operation of power system.
From above description, the purpose & precond ition of
online security assessment considering electro-thermal
coupling is clarified: (1) It realizes fast calculation of the
temperature variation and considering temperature as
transmission lines’ thermal limit to identify serious acci-
dents. (2) The initial te mperature and parameters of HBE
which are needed to perform the security assessment
considering electro-thermal coupling can be obtained by
means of extended state estimation. Based on this frame-
work, the approach of security assessment considering
electro-thermal coupling is proposed in next section.
3. Approach of Security Assessment
Considering Electro-thermal Coupling
To track the temperature trajectory under anticipated
accident, the electro-thermal coupling power flow tech-
nique proposed in [8] is available. The model is as fol-
lows:




(),(),()0 N
(),(),()0 N
() ,(),()
il
il
lll l
PVttTti
QVt tTti
dT t
H
tI t TtlL
dt













(1)
where, t represents the time of temperature dynamics,
V(t), θ(t) respectively represent the altitude and phase
angle vector of voltage, Tl(t) represents the temperature
of transmission line l, Il (t) is the current of transmission
line l. The first two equations in equation set (1) repre-
sent node power balance equations. Because of the cou-
pling relationship between transmission lines’ resistance
and temperature, these two equations are not only the
functions of voltage but also the function of temperature.
The last differential equation represents HBE, it is the
function of Il and T l when other parameters (such as wind
speed, direction, etc) are given by extended state estima-
tion. It can be expressed in detail as follows:
2
d() ()(()) (())
d
(())
l
lpllls cl
rl
Tt
mCItRTtqqTt
tqTt


(2)
where, lpl is the product of the weight per unit
length of transmission line l and its specific heat capacity.
The first item on right side of equation (2 ) represents the
resistance heating per unit length of transmission line l. It
is the function relates to temperature of lines. qs repre-
sents the heat that produced by the solar heating per unit
mC

M. X. WANG ET AL. 705
length. , represent the heat losses per
unit length produced by convection and radiation respec-
tively. They are all the functions relate to temperature of
line l.
(())
cl
qTt (())
rl
qTt
Obviously, model (1) detailedly considers the elec-
tro-thermal coupling relationship in power flow, however,
it will cost much time for solving differential-algebraic
equations for every anticipated contingency which may
not appropriate for online application. Fortunately, the
coupling between resistance and power flow is weak, that
is why the PQ decouple method is effective to the power
flow calculation. Meanwhile, the resistance-temperature
coefficient is small (always < 0.01). So the coupling be-
tween temperature and power flow is weaker. Based on
this characteristic, there are two ways to simplify the
calculation of temperature dynamics. For one thing, the
influence of transmission lines’ temperature on power
flow can be ignored. For another, the functions that relate
to temperature in HBE can be treated approximately
through setting a fixed and seemly temperature value.
Therefore, the equation (2) can be re-described as fol-
lows:
2max
()
l
ItR
d(
d
l
lpl
Tt
mC t
)() () ()
l scr
qtqtqt (3)
Where, the Rmaxl is the resistance under the maximum
permissible temperature (maxl
T) of transmission line l.
note that items on the r ight side of equation (3) no longer
relate to temperature. There are two approximations for
this expression. Firstly, the influence of changing tem-
perature of transmission line on power flow is ignored,
which makes the current quadratic term unrelated to
temperature. Secondly, the resistance of transmission line
is set as a conservative constant value (the resistance
under the maximum permissible temperature). For the
cooling items, the same approximation is implemented,
using the conservative constant temperature value
max 20ll
TT
to ensure the relatively conservative outcome, where the
T0l represents the initial temperatu re of tran smission line l,
it can be obtained by DTR or extended stat estimation .
After the above approximate treatment, the meteorol-
ogy-related items in HBE, qs, qc and qr are all constants
under a certain meteorological condition. Then make
definite integral over t0-tf to both sides of equation (3),
and obtain:
0
1() () ()
f
ft
t
lscr tt
lpl
Tqt qt qtdt
mC 
 

0
2max
()
ll
I tR (4)
Supposing that the environmental parameters are con-
stant during the whole research time hor izon, then the qs,
qc and qr are all constant in equation (4), and equation (4)
can be expressed as:
00
2
1(())
f
ft
t
l tt
lpl
TfI
mC 

l
tdt


(5)
where，22
max
(()) ()
lll
f
It ItRC

 C=qs-qc-qr
Equation (5) indicates that the v ariation of temperature
of transmission lines during t0-tf can be expressed by an
integrating function of current qu adratic term. Supposing
that t0-tf is divided into n time period with
△ t time step,
equation (5) ca n be di screti z ed as followed:

2
01
() (())
n
lf ll
t
lpl
t
TtTtfI t
mC 

 (6)
Therefore, if power flow at t=1…n are calculated then
substitute the Il (t) into equation (6), th e temperature var-
iation value from t0 to tf can be fast obtained. If the tem-
perature difference meet the followed equation, the
transmission line is identified to be safe under certain
contingency.
2max 0
1(())
n
ll
t
lpl
tl
f
It TT
mC 

 (7)
If detailed temperature trajectory is required during
t0-tf, equation (6) can be calculated after every power
flow calculation at t=1…n without solving differential-
algebraic equations. Moreover, the resistance, HBE pa-
rameters of transmission lines can also be updated under
new temperature value, the calculation accuracy will be
improved.
4. Case Study
To demonstrate the validity of proposed security assess-
ment approach in this paper, the modified six-node pow-
er system is adopted as the test system. Its structure is
shown in Figure 2, and the electric power grid parame-
ters are shown in Table 1. In Table 1, the transmission
lines’ initial temperature is obtained by solving a
1
4
2
5
3
6
Figure 2. Six nodes power system.

M. X. WANG ET AL.
706
static HBE, whose differential item is set to be zero un-
der initial operating state and under a normal meteoro-
logical condition described by [8]. Under online operat-
ing circumstance, it also can be obtained by extended
state estimation. The thermal ratings are also calculated
under the environmental parameters given by [8], and
transmission lines’ maximum permissible temperature is
70℃. They are regarded as the thermal limit of transmis-
sion lines in conventional static security assessment.
In followed two scenes, suppose that transmission
lines’ maximum permissible temperature are 70℃, the
initial time point(t0) is 0, research time horizon is 30 mi-
nutes (tf = 30) and the time step is 5 minutes, so the
whole research horizon is divided into 6 time periods.
The initial nodes’ input power is given in Table 2.
4.1. Scene 1
Under the given condition above, suppose that the an-
ticipated accident set includes the outage of all transmis-
sion lines in Figure 2, and occur at t0. The traditional
static security assessment has been firstly carried out, and
the outage of transmission line 1-4 which caused line
2-4’s current (1.00 p.u) over its thermal rating (0.98 p.u)
is screened out as serious contin gency. According to this
result, corresponding preventive control have to be acti-
vated to answer this con tingency.
Table 1. Paramete r s of electic power grid.
Node number of
transmission line Rl p.u Xl p.u Bl/2 p.u mlcpl J/kg ℃
Initial
temperature
℃
Thermal
rating
p.u
1 4 0.065 0.2 0.01711.3 39.6 1.22
1 5 0.08 0.3 0.016 853 36.5 1.31
2 3 0.05 0.25 0.014 1127 33.6 1.60
2 4 0.05 0.1 0.005 444.5 47.4 0.98
2 5 0.1 0.3 0.016 711.3 35.4 1.20
2 6 0.07 0.2 0.011 711.3 34.9 1.22
3 5 0.12 0.26 0.012 1127 37.9 0.97
3 6 0.02 0.1 0.005 1127 39.1 1.55
4 5 0.2 0.4 0.02444.5 33.6 0.98
5 6 0.1 0.3 0.016 711.3 33.9 1.20
Table 2. Initial active power of nodes (p.u).
Node Active power
1 0.88
2 1
3 1
4 -1.05
5 -1.08
6 -0.7
For the approach proposed in this paper, this scene
supposes load node 4 and corresponding generator node
power variation during t0-tf are given in Table 3.The
power of generator nodes are obtained by the participa-
tion fact ors whic h decided b y economic dispat c h.
As seen in Table 3, load node 4’s power tends to in-
crease. The warning information provided by the pro-
posed approach is given in Table 4. With the proposed
approach, temperature is considered to be thermal limit
of transmission lin es, and the temperature of line 2-4 will
violate 70℃ between 10min and 15min after the outage
of line 1-4. It can be seen that the proposed approach
screened out the outage of line 1-4 as serious contin-
gency, meanwhile, the detailed temperature trajectory
can be tracked and the time margin (> 10 min, < 15 min)
before the temperature violation can also be provided to
operators for t he p r eventive control d e c i s i on.
4.2. Scene 2
In this scene, the load node 4 and corresponding genera-
tor node power variation during t0-tf is given in Table 5.
Conversely, the load power of node 4 tends to decrease.
Under this case, the temperature violation is avoided
because of the downtrend of power generation and load
after the outage of 1-4, so the initial state of power sys-
tem is identified to be security by the proposed security
assessment approach and the superfluous preventive con-
trol can be avoided.
The temperature and current trajectory of line 2-4 un-
der the outage of line 1-4 a re given as Table 6.
Table 3. Active power of node 1-4 (p.u).
Time period Node 4 Node 1 Node 2 Node 3
1 -1.07 0.885 1.010 1.005
2 -1.09 0.890 1.020 1.010
3 -1.11 0.895 1.030 1.015
4 -1.13 0.901 1.040 1.020
5 -1.15 0.907 1.050 1.025
6 -1.17 0.914 1.060 1.030
Table 4. Result of static security assessment (p.u).
Serious
accident Time periodTemperature of line 2-4 Current of line 2-4
1 62.7 1.00
2 69.6 1.02
3 72.9 1.04
4 75.1 1.05
5 76.8 1.07
Outage of
line 1-4
6 78.5 1.09
Time margin >10 min, <15 min

M. X. WANG ET AL.
707
Table 5. Active power of node 1-4 (p.u).
Time period Node 4 Node 1 Node 2 Node 3
1 -1.03 0.875 0.990 0.995
2 -1.01 0.870 0.980 0.990
3 -0.99 0.865 0.970 0.985
4 -0.97 0.860 0.960 0.980
5 -0.95 0.855 0.950 0.975
6 -0.93 0.850 0.940 0.970
Table 6. Result of static security assessment (p.u).
Time period Temperature of line 2-4 Current of line 2- 4
1 62.7 1.00
2 67.8 0.99
3 68.8 0.97
4 68.2 0.95
5 67.2 0.94
6 66.1 0.92
5. Conclusions
In this paper, the framework of on-line static security
analysis considering electro-ther mal coupling is presented,
and the corresponding security assessment approach is
further proposed. The conclusions are as follows:
1) The proposed framework of on-line static security
analysis is the organic combination of DTR technology
and static security analysis.
2) The proposed security assessment approach is a
kind of simplified electro-thermal coupling power flow,
it is capable of calculating the temperature dynamics of
transmission lines after contingency with less computa-
tion amount.
3) The proposed security assessment approach consid-
ers temperature as transmission lines’ thermal limit
which can make the security assessment more actually.
Moreover, the time margin can be provided as warning
information and some unnecessary preventive control
can also be avoided.
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