Study on Approach of Static Security Assessment Accounting for Electro-thermal Coupling

doi:10.4236/epe.2013.54B136

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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

Email: [email protected], linbow[email protected], [email protected]

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

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

() ,(),()

lll l

PVttTti

QVt tTti

dT t

tI t TtlL





















(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:

d() ()(()) (())

(())

lpllls cl

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

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.

(())

qTt (())

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

()

ItR

lpl

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:

1() () ()

lscr

lpl

Tqt qt qtdt

mC 

 



0

2max

()

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:

1(())

lpl

TfI

mC 



l

tdt





(5)

where，22

max

(()) ()

lll

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:



() (())

lf ll

lpl

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(())

lpl

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

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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