Multi-objective Placement of TCSC for Enhancement of Steady- State Performance of Power System

16 Pages·00.901 MB·English

by  Dr. Eng. Mohamed EL-Shimy (Ain Shams University)

EL-Shimy M. Multi-objective Placement of TCSC for Enhancement of Steady-State Performance of Power System.
Scientific Bulletin - Faculty of Engineering - Ain Shams Uni. 2007;42(3):935 - 50.

Multi-objective Placement of TCSC for Enhancement of Steady-
State Performance of Power System

M. EL-SHIMY
Electric Power and Machines Department, Faculty of Engineering,
Ain Shams University, Cairo, Egypt
Email: [email protected]

Abstract
FACTS devices are considered a powerful tool for enhancing both steady-state
and dynamic performance of power systems. It is important to investigate the location
for placement of these devices because of their considerable cost and their inverse
effects on power systems if they are badly located. Locations of FACTS devices in the
power system can be obtained on the basis of static and/or dynamic performance. The
intended objective of the FACTS device will have a large impact on the placement of
the devices. A location that is the best for one objective may be less suitable for
another. This paper presents a new multi-objective placement technique of TCSC
based on sensitivity analysis for: maximum relief of network loading (or congestion),
power flow control, maximum reduction in active and reactive losses in a particular
line, and maximum reduction in active and reactive power loss of a power network.
Moreover, OPF with FACTS constraints is used to show the validity of the placement
technique to relief network congestions without load curtailment.

صخلم
يويماكيدلالاد يويتاتلااتا ااءاا نلام لاك نيسحت يلع ةيلاع ةردق تاذ يلعافتلا ضيوعتلا مظن تادعم ربتعت
يلاسلا الاهري ات يلذلاكد اهراعلااأ سالافترا نلام تادلاعملا هذهل ةمئ ملا عقاوملا ديدحت ةيمهأ جتكت .ةيبرهولا يوقلا مظكل
مظكلاب يلعالافتلا ضيولاعتلا ملاظن تادلاعمل ةلامئ ملا علاقاوملا ءدلاحتت .الاهعقاوم رالايتتا يلاا اذإ ةيبرهولا يوقلا مظن يلع
ة الالا إ نلام دلاهلا ةلاعيبي ر رلالاي .ةلايبرهولا يولاقلا مظكلال يويمالاكيء دأ / د يويتاتلالااا ااءأ يلالع االاكب ةلايبرهولا يولاقلا
هذلاهل يلالهملا علاقاوملا رلاي تت تلايث تادلاعملا هذلاهل ةلامئ ملا علاقاوملا رالايتتا يلالع ةدلاشب يلعافتلا ضيوعتلا مظن تادعم
ةرلاي تملا ةلالعافملا تادلاعمل ةلامئ ملا علاقاوملا دلايدحتل ةدلايدة يلاقيري ةلاقرولا هذلاه دلاقت .اهكم دهلا تتاب تادعملا
:يلاه ادلاهاا هذلاه د .ةلايبرهولا يولاقلا مظكلال ةيلاااسحلا سلايلحت يلالع ءالامتعتاب ةلاكمانتملا ادلاهاا نلام ءدلاع قيقحتل
يلا دلاقفلا نلام ىلاصقاا لاقلإاد ةيبرهولا تاوبشلا )مثانت دأ( سيمحت نم ىصقاا صلختلاد ةقاطلا نايرسب موحتلا
تاوبلاشلاب )ةلايلعافتلاد ةلالاعفلا( ةلاقاطلا يلا دلاقفلا نلام ىلاصقاا لاقلإا ارلايتأد نيلاعم طخب )ةيلعافتلاد ةلاعفلا( ةقاطلا
ضيولاعتلا ملاظن تادلاعم ءولايق رالابتعتا يلا ذلاتااب الامثحل سلاهماا نايرسلا ةقيري ادختاا ىلإ ة ا لإاب .ةيبرهولا
الالامثاا صيلالالقت نددلالاب الالامثاا مثانلالات نلالام صلختلالالا يلالا ادلالاهاا ءدلالاعتم سلالاهماا رالالايتاا ةلالاقء ةيلالا وتل يلعالالافتلا
.ةيبرهولا

Introduction
Most power systems contain elements that help regulate power flow such as
phase changers, series compensation, and shunt compensation, but historically these
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EL-Shimy M. Multi-objective Placement of TCSC for Enhancement of Steady-State Performance of Power System.
Scientific Bulletin - Faculty of Engineering - Ain Shams Uni. 2007;42(3):935 - 50.
devices were mechanically switched and may not be capable of reacting fast enough to
prevent cascading failures. The need for better high-speed control of power flow led to
an initiative at the Electric Power Research Institute (EPRI) [1] to develop power-
electronic based devices, employing high speed, high power semi-conductor
technology, to help better regulate power flow. All these devices are collectively
known as Flexible AC Transmission System (FACTS) devices. The family of FACTS
devices includes high speed versions of traditional devices like phase changers, and
series and shunt compensators, as well as devices based on a new technology, the
voltage source converter (VSC) [2].
An alternative to increasing transmission capacity is to make more efficient use
of the existing power grid. This can be accomplished through increased control. One
of the most promising recent decentralized network controllers is the family of
(FACTS) devices [3-5]. FACTS devices have been shown to be effective in
controlling power flow and damping power system oscillations. By controlling power
flow on an individual line, power can be redirected to/from various parts of the power
grid. Redirecting power flow allows for utilization of power lines that physics of
power flow alone would not allow. The variable series compensation is highly
effective in both controlling power flow in the line and in improving stability. With
series compensation the overall effective series transmission impedance from the
sending end to the receiving end can be arbitrarily decreased thereby influencing the
power flow. This capability to control power flow can effectively be used to increase
the transient stability limit and to provide power oscillation damping [5-8].
Locations of FACTS devices in the power system can be obtained on the basis
of static and/or dynamic performance. The intended objective of the FACTS device
will have a large impact on the optimal location of the devices [9-14].
An accurate method for computation of sensitivities that incorporates the actual
power system condition is useful for analysis of power flow control with controllable
devices [15-20]. The linearization of the load flow equations around the nominal
operating point yields such sensitivities.
The location of a Thyristor Controlled Series Capacitor (TCSC) can be
evaluated based on a sensitivity analysis in order to control power flow in the system,
or based on a residue approach in order to influence the damping behavior of the
system [14, 20, 21]. Sensitivity analysis determines the influence on each variable due
to the changes in the system. It is a direct measure of the controllability of the active
power flow in specified line by the TCSC located in the same, or in another line. On
the other hand, the residue method gives very effective approach to determine the
location of TCSC, due to the fact that a larger residue results in a larger change of the
corresponding oscillatory mode.
The basic objectives of this paper is to quantify the effect of controllable series
reactances on power systems and to find a simple, but accurate method for multi-
objective placement of TCSC based on sensitivity analysis for enhancing static
performance of power systems. The problem formulation can be considered as an
extension and a modification of the work presented in [12, 14, 18]. This paper presents
a new multi-objective placement technique of TCSC based on sensitivity analysis for:
maximum relief of network loading (or congestion), power flow control, maximum
reduction in active and reactive losses in a particular line, and maximum reduction in
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EL-Shimy M. Multi-objective Placement of TCSC for Enhancement of Steady-State Performance of Power System.
Scientific Bulletin - Faculty of Engineering - Ain Shams Uni. 2007;42(3):935 - 50.
active and reactive power loss of a power network. Moreover, OPF with FACTS
constraints is used to show the validity of the placement technique to relief network
congestions.

TCSC Placement Problem
The preliminary mathematical modeling of a system with TCSC, and a general
form of static-sensitivity analysis are shown in Appendix 1, and Appendix 2
respectively. The mathematical symbols used is this section are defined in these
appendices. The selection of input and output variable depends on the study being
carried. Consider an N-bus system with win n-lines such that a TCSCs are placed on
l
all lines and let the vector X be the vector of TCSC reactances. where:
cl

 
XT UT  x  x  x (1)
cl cl1 clm cln
l

The output vector W takes the form:

 
WT  |P |  |P | |Q |  |Q | P  P Q  Q P Q
l1 ln l1 ln Ll1 Lln Ll1 Lln L L
l l l l
(2)

The modulus of line active and reactive power flow is taken to avoid error and
misunderstanding of the sensitivity results. For example, if the modulus is not taken
and the sensitivity of power flow on line m’ due to placement of a TCSC on line m is
negative, this will give one of the following meanings: (i) the effects of the TCSC is to
reduce the flow on line m’, or (ii) the flow on line m’ is increased in opposite direction
i.e. from bus j to bus i if the sensitivity is calculated for flow on line m’ from bus i to
bus j. As the modulus of line active and reactive power flow is taken, a negative
sensitivity will only mean that the flow on line m’ is reduced due to placement of
TCSC on line m, and this flow is increased with positive sensitivity.
The output-to-input static-sensitivity is obtained using the general form (A2-14)
where the matrices required in the calculation of the output-to-input static-sensitivity
matrix K are explained in the following. The Jacobian matrix F is the Newton-
UW X
Raphson power flow standard Jacobian matrix and takes the form [22]:

P 
 
 F (3)
  X  
Q V
   

The Jacobian matrix F takes the form:
U

P
  
 F X
  U l
Q
 
(4)
P X 
cl  
 X
  cl
Q X
 cl

A general element in the P/X matrix (and similarly Q/X ) takes the form
cl cl
P/x . The derivatives P/x and Q/x are obtained by differentiating
i clm i clm i clm
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EL-Shimy M. Multi-objective Placement of TCSC for Enhancement of Steady-State Performance of Power System.
Scientific Bulletin - Faculty of Engineering - Ain Shams Uni. 2007;42(3):935 - 50.
equations (A1-1) and (A1-2) after modifying them due to the existence of the TCSC as
described in Appendix 1. These derivatives takes the form:

 
 V2 VV cos  VV sin
P  lm i i j ij lm i j ij
i   for i  slack, and m K(i) (5)
X
clm 
0 Otherwise


 
 V2 VV cos  VV sin
Q  lm i i j ij lm i j ij
i   for i  K(PQ), and m K(i) (6)
X
clm 
0 Otherwise


where
K(PQ) is the set of all PQ-buses.

g 2r (x  x )
  lm  lm lm clm
lm x (r2 (x  x )2)2
clm lm lm clm

b r2 -(x  x )2
  lm  lm lm clm
lm x (r2 (x  x )2)2
clm lm lm clm

z  r  jx
lm lm lm

The vectors  and  takes the form:  W X and W Uwhere
X U X U
the input vector U is defined in equation (1), the output vector W is defined in equation
(2), and the state vector X is defined in equation (A2-9). Theses derivatives can be
easily found by direct differentiation similar to that performed in equations (5), and
(6).
With series compensation the overall effective series transmission impedance
from the sending end to the receiving end can be arbitrarily decreased thereby
influencing the power flow on the entire lines causing redistribution of the power flow
allover the network. A basic constraint on placement of TCSC is that such placement
will not cause transmission congestion (line overload) a situation that can initiate a
cascaded failure event (reducing system security and reliability), reduction in the
competition opportunity in deregulated electricity markets, load shedding, …, and
finally system collapse. One way to avoid such situation is to use the sensitivity of line
real power flow performance index PPI to line power flow as restraining factor on
placement of TCSC on electrical networks [12]. The PPI itself can be used to describe
the severity of system loading during normal and contingency conditions [23]. This
PPI is given by:

n 2n
l   P 
PPI  m1 2lnm Pllmmmaox (7)

where
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EL-Shimy M. Multi-objective Placement of TCSC for Enhancement of Steady-State Performance of Power System.
Scientific Bulletin - Faculty of Engineering - Ain Shams Uni. 2007;42(3):935 - 50.
P max is the rated continuous capacity of line m.
lm
n is an exponent.
 is a real non-negative weighting factor which may be used to reflect
lm
importance of line m.
P is the base-case power flow on line m.
lmo

The value of PPI is small when all network lines normally loaded, and its value
increases as the network lines loading increases, and its values becomes high when
there is a single major congestion or a number of small line loading violations. The
inability to discriminate between a single major congestion and a number of small line
loading violations is called masking effect. Because a single major congestion may
have severe effect on system security as compared to a large number of small
violations, the masking effect should be omitted. This is can be achieved through
proper selection of the exponent n. A value of n > 1 may be a solution leading to
reduction of the probability of occurrence of the masking effect. Herein, n is taken
equals to 2, and  is taken equals to unity for all lines (equal importance).
lm
The sensitivity of line real power flow performance index PPI to line power
flow as affected by placement of TCSC on line m’ is represented by the index P
lcm’
which is given by:

n 4
P  PPI l |P3 | 1  Plm     
lcm' x lmo Pmax x
cl' xcl'0 m1  lm  clm'

The value of P is anticipated as follows: a positive value of P indicates that the
network loading increases with the considered location of the TCSC, a negative value
of P indicates that the network loading decreases with the considered location of the
TCSC. Hence, for maximization of network loading relief (or maximization of
network congestion relief) TCSC should be placed on the location corresponding to
the most negative value of P. Although calculation of P is initiated to represent a
basic constraint on the placement of TCSC on electrical networks, the most negative
value of P itself satisfy the objective of maximization of network congestion relief.
This can be proven using a network with a severs network congestions such that the
traditional optimal power flow OPF algorithms can not relief this congestion without
load curtailment. Then, the optimal placement of TCSC is implemented on the system
based on the most negative P-criteria and a modified OPF algorithm incorporating
FACS devices with power flow control constraints [24] is utilized to show the effect of
TCSC to relief severe network congestions.
By inspecting equation (7) that was extensively in reliability, security, and
stability publications, it is clear that the line loading is represented by its maximum
(rated) active power flow which is far away from reality as the actual limits of a line is
given as either rated current flow (I max), or rated apparent power flow (S max). Hence,
lm lm
for sack of accuracy an apparent power performance index (SPI) is used instead of the
PPI. The SPI is given by:

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EL-Shimy M. Multi-objective Placement of TCSC for Enhancement of Steady-State Performance of Power System.
Scientific Bulletin - Faculty of Engineering - Ain Shams Uni. 2007;42(3):935 - 50.

2n
SPI nl lm Slmo 2n nl lm Pl2moQl2mo  (9)
 2n Smax  2n  Smax 
m1 lm m1  lm 

The sensitivity of line apparent power flow performance index SPI to line
power flow as affected by placement of TCSC on line m’ is represented by the index
S which is given by (for n = 2, and  = 1):
lcm’ lm

n 4
S  SPI l S2  1  |P | Plm |Q | Qlm  
lcm' xcl' xcl'0 m1 lmoSlmmax  lmo xclm' lmo xclm' 

The outcome from the value of S is treated in the same manner of treating the
value of P. In this paper both S and P are used and compared, in doing so in the
calculation P the line active power limit is taken equals to its apparent power limits as
widely used based on the assumption that the line power flow is mostly active power.
But this justification is not general.
The following objectives for TCSC placement are: maximum relief of network
loading (or congestion), power flow control, maximum reduction in active and reactive
losses in a particular line, and maximum reduction in active and reactive power loss of
a power network. The proposed procedure to solve a placement problem is to construct
a set of placement solutions that satisfy each of the objectives and then an overlapping
placement solution is found that is satisfying all the objectives. This procedure will be
illustrated in the results section.

Study System
The multi-objective placement and sensitivity analysis are performed on the
six-bus system shown in Fig. 1. The system consists of 6-buses, 4-generators, and 7-
lines. Line indexes m are shown within a circle. The system bus-data and base-case
AC power flow, line-data, base-case line power flow and loses, and generator-cost
functions and generator limits are shown in Table 1, 2, 3, and 4 respectively, all in p.u
on 100-MVA, 138-kV base. A TCSC is assumed to be placed on all lines such that
-0.7x  x  0 to avoid overcompensation.
lm clm

Results
First of all some of the lines will be rejected from placement list based on the
values of  in equation (8) or (10). The calculation of P requires the calculation of line
active power flow sensitivity to TCSC location and the calculation of S requires the
calculation of both line active power flow and line reactive power flow sensitivities to
TCSC location.
The line active power flow sensitivity matrix is shown in Table 5 and can be
used as a guide for TCSC placement for line active power flow control this shown in
Table 6. The priority locations in Table 6 for placement of TCSC are arranged in
priority sets for TCSC placement i.e. from the most effective locations to the least
effective locations for placement of TCSC for line active power flow. The diagonal
elements of the sensitivity matrix of Table 5 represents the self-sensitivity to active
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EL-Shimy M. Multi-objective Placement of TCSC for Enhancement of Steady-State Performance of Power System.
Scientific Bulletin - Faculty of Engineering - Ain Shams Uni. 2007;42(3):935 - 50.
power flow i.e. sensitivity of line active power flow as a result of placement of a
TCSC on that line, while the off-diagonal values represent the mutual-sensitivity i.e.
i.e. sensitivity of line active power flow as a result of placement of a TCSC on another
line.
It is clear from Table 5 that the active power flow on a line can be increased, or
decreased, or not affected significantly by placement of TCSC on a specified line. For
example, the most effective TCSC location for reduction of active power flow on line
1 is placement of TCSC on line 6 as the value of sensitivity is the most negative index
while placement of TCSC on line 1 results on the maximum increase of active power
flow on line 1 as affected by the TCSC as the value of sensitivity is the most positive
index. It is also shown that placement of TCSC on line 4 has no significant effect on
the active power flow on line 1. An interesting situation appear with placement of
TCSC, for example, on line 3, the active power flow sensitivity on line 3 as affected
by TCSC on that line results in active power flow reduction (this verified through full
AC power flow). Hence, it is not a general rule that placement of a series capacitor on
a line within a network increases the active power flow on that line, actually the full
AC power flow shows that the reactive power flow on line 3 increases by placing a
TCSC on that line, this is clarify the importance of using the most negative S-criteria
instead of most negative P-criteria as a constraint explained earlier to enhance system
security. Moreover, the full AC power flow show that the placement of TCSC has
insignificant effect on bus voltage magnitudes.
The value of P as affected by TCSC location is shown in Table 7 which shows
that placement of TCSC either on line 5 or line 6 increases network loading (P > 0)
with maximum increase associated with placement of TCSC on line 5. Therefore, both
lines are rejected from the TCSC placement set. The optimal placement of TCSC for
network loading relief based on the most-negative P-criteria is a TCSC placed on line
7. The effectiveness of placement of TCSC on other lines for network loading relief is
arranged as a priority list as shown in Table 7. Hence, one of these location (i.e.
placement on lines 1, 2, 3, 4, 7) will be the selected location if it satisfy all the desired
objectives. The effectiveness of this location rejection for TCSC placement will be
verified by calculation the performance index SPI for separate placement of TCSC on
line 7 and line 5 and simulating the changes in SPI through multiple loadflow as the
TCSC reactance changes all over its range. Fig. 2 shows theses changes in the SPI, it is
clear from that figure that placement of a TCSC on line 7 decreases the PPI allover the
range of variation of the TCSC and the opposite occurs with placement of TCSC on
line 5.
The line reactive power flow sensitivity matrix is shown in Table 8 and can be
used as a guide for TCSC placement for line reactive power flow control this shown in
Table 9 arranged in priority sets for TCSC placement i.e. from the most effective
locations to the least effective locations for placement of TCSC for line active power
flow.
Based on the values of the line active- and line reactive- power flow sensitivity
matrices, the sensitivity of line apparent power flow performance index SPI to line
power flow as affected by placement of TCSC on line m’ is calculated based on
equation (10) and these values along with TCSC placement priority are shown in
Table 10. Based on the most-negative S criteria an additional line is rejected from
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EL-Shimy M. Multi-objective Placement of TCSC for Enhancement of Steady-State Performance of Power System.
Scientific Bulletin - Faculty of Engineering - Ain Shams Uni. 2007;42(3):935 - 50.
TCSC placement list which is line 3. It is logical that the results obtained from S
criteria are more accurate than those obtained from P criteria. Therefore, the final
TCSC placement list consists of 4 locations on lines {7, 1, 4, 2} arranged according to
their effectiveness in relieving network overloads (congestions). Based on that, the
rejected locations are identified in Table 6 and Table 7 by non-bold numbers. Also,
from this point the rejected locations will not be mentioned in the following placement
lists.
The line- active power loss and reactive power loss sensitivity matrices are
shown in Table 11 and Table 12 respectively. Those matrices can be used as a guide
for TCSC placement for line active and reactive power loss reduction as shown in
Table 13. Hence, the overlapping placement decisions of active and reactive power
loss reduction represent the candidate locations of TCSC for line apparent power
reduction.
The network active, and reactive power loss sensitivity matrices are shown in
Table 14. Those matrices can be used as a guide for TCSC placement for network
power loss reduction as shown in Table 14. Hence, the overlapping placement
decisions of active and reactive power loss reduction represent the candidate locations
of TCSC for line apparent power reduction.
Based on Tables 10 and 14, the optimal placement of TCSC network loading
relief maximization and network apparent loss minimization is a TCSC is placed on
line 7. Tables 6 and 9 gives a priority list for TCSC placement for line active and
reactive power flow control which is very valuable, especially, in deregulated
electricity markets where controllable power flow paths are an important requirements
for maximization of electricity markets deregulation. Although, placement of TCSC on
line 7 minimize the overall network power loss, Table 13 lists a priority sets for
placement of TCSC for power loss reduction on a particular line.
To evaluate the proposed technique in the congestion relief reduction, the load
parameters of Table 1 are doubled and a traditional OPF algorithm (with no load
curtailment option) is applied to solve the system with no TCSC installed. The results
in this case is that the OPF could not get an acceptable operating point for the system
because line 5 is congested and the system operating cost is 6371.1 $/hr. To solve this
problem a TCSC is placed on two locations separately, the first location on line 7 (the
optimal location) and on line 3 (the rejected location with lowest positive S, Table
10). The OPF algorithm of [24] is applied and the results show that with a TCSC
placed on line 7, an acceptable operating point is obtained with no congestions and the
–0.033 p.u and the system operating cost is 6368.58 $/hr. With a TCSC placed on line
3, the congested line remains congested. By forcing the reactance of the TCSC on line
3 to a value of -0.1x , additional congestion is occurred on line 6 and the system
l3
violations increases. This is prove that the optimal placement of TCSC is on line 7 and
also prove the accuracy of the most-negative S-criteria over the most-negative P-
criteria.

Conclusion
This paper presents a new simple multi-objective placement technique for
placement of TCSC for power system steady-state performance enhancement. Several
developments are done to the previously published techniques for single-objective
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EL-Shimy M. Multi-objective Placement of TCSC for Enhancement of Steady-State Performance of Power System.
Scientific Bulletin - Faculty of Engineering - Ain Shams Uni. 2007;42(3):935 - 50.
placement of TCSC in power systems to enhance the TCSC placement problem. The
use of the most-negative S-criteria instead of the traditionally used the most-negative
P-criteria enhances power systems security and reduces the cascaded outage
probability of power systems through accurate rejection of TCSC candidate locations
that increase the network loading and can lead to network congestion. Several
evaluations and verifications are done to prove the capability of the proposed
technique to accurately place TCSC for multi-objectives.

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Appendix 1: Preliminary Mathematical Modeling
The power system AC power flow model can be found in any power system analysis text book for
example [22] and is based on the system section shown in Fig. A1-1. Where:

bsi: Susceptance of all shunt devices connected to bus i (e.g. capacitor or inductor
banks)
y = 1/z = y = g + j b : series admittance of line m connecting bus i and bus j.
ij ij ji ij ij
y = y = g + j b : shunt admittance of line m.
sij sji sij sij
V: bus voltage magnitude of bus i.
i
: bus voltage phase angle of bus i.
i
m: line index.
S : apparent power generated at bus i = P + jQ .
Gi Gi Gi
S : apparent power demanded from bus i = P + jQ .
Di Di Di

Then the active and reactive power injected to i are given by:

P P P V2g V V g cos b sin  (A1-1)
i Gi Di i ii i j ij ij ij ij
jK(i)

Q Q Q V2b V V g sin b cos  (A1-2)
i Gi Di i ii i j ij ij ij ij
jK(i)

where
K(i): Set of all buses connected to bus i.
 =  - 
ij i j

g  g g
ii sij ij
jK(i)

b  (b b )b 
ii sij ij si
jK(i)

The active and reactive power flow on line m from bus i to bus j are given by:

P P V2g g VV cos bVV sin (A1-3)
lm ij i ij ij i j ij ij i j ij

Q Q V2(b b )bVV cos g VV sin (A1-4)
lm ij i sij ij ij i j ij ij i j ij

The active and reactive power losses on line m are given by:

P P P g (V2 V2)2g VV cos (A1-5)
Lm ij ji ij i j ij i j ij

11