Download Identification of Unified Power Flow Controller Location under Line

International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011
Identification of Unified Power Flow Controller
Location underLine Outage Contingencies
Dr. Shobha Shankar1, Dr. T. Ananthapadmanabha2,
The increase in power flows and environmental constraints
have forced electric utilities to install new equipment to
enhance networkoperation.The continuous and fast
improvement of power electronicstechnology has made
flexible AC transmission systems (FACTS) a promising
concept for power system applications. The IEEE definition
of FACTS is “Alternating Current transmission system
incorporating power electronic-based and other static
controllers to enhance controllability and increase power
transfer capability”.With the application of FACTS
technology, power flow along transmission line can be more
flexibly controlled. Among a variety of FACTS controllers,
UPFC is one of the most interesting and potentially the most
versatile. It can provide simultaneous and independent control
of important power system parameters: line active power flow,
line reactive power flow, impedance and voltage. It offers the
necessary functional flexibility for the combined application
of phase angle control with controlled series and shunt
compensation.
From the literature, it is clear that most of the work on
UPFC belongs to two areas namely i)UPFC modeling and
integration into power flow solutions and ii) control actions
for effective operation of UPFC [1]-[10]. Because of the
considerable costs of the FACTS device, it is important to
ascertain the location for placement of these devices suitable
for various network contingencies.
Many static models are proposed and incorporated into the
existing load flow model in the literature.The sending and
receiving ends of the UPFC are decoupled. The former is
transformed into a PQ bus while the latter is transformed into
a PV bus. The active and reactive power loads in the PQ bus
and the voltage magnitude at the PV bus are set at the values
to be controlled by the UPFC. The method is simple but works
only if the UPFC is used to control voltage magnitude, active
power and reactive power simultaneously [11]. The UPFC is
modelled as a series reactance together with a set of active and
reactive nodal power injections at each end of the series
reactance. The UPFC injection model is implemented into a
full Newton-Raphson program by adding the UPFC power
injections and their derivatives with respect to the AC network
state variables, i.e. nodal voltage magnitude and angles, at the
appropriate locations in the mismatch vector and Jacobian
matrix. The original dimensions of the mismatch vector and
Jacobian matrix are not altered at all. The series voltage source
parameters voltage magnitude and angle are adjusted manually
in order to achieve a power flow solution [12]. The UPFC
Abstract:With the increased loading of existing power transmission
system and the tendency towards maximizing economic benefits has
led power system utilities to run close to the limits of stable
operation. The increase in power flows and environmental constraints
have forced electric utilities to install new equipment to enhance
network operation. This paper presents an approach for identifying
optimal location of Unified Power Flow Controller under line outage
contingencies. Fuzzy approach is used to combine the effect of
voltage stability margin indicated by Minimum Singular Value of
load flow Jacobian matrix (MSV) and voltage change to identify the
optimal location. With unified power flow controller at optimal
location, the voltage stability margin of the system is enhancedand
voltage profiles are improved. The proposed method is tested with
simulated condition on 24 bus 400 kV Southern grid of India.
Keywords: Line Stability Index, Minimum Singular Value, Voltage
Change Index, Voltage Stability Margin Index
I. INTRODUCTION
P
OWER system security forms an integral part of modern
energy management systems, but its implementation is
still a challenging task to power system engineers. Steadystate security assessment enables the operating personnel to
know which system disturbances or contingencies may cause
limit violations and force the system to enter into emergency
state. The studies on assessing the static voltage stability
margin of a system have revealed that, the system reaches to
the proximity of voltage collapse due to an excessive loading
of a bus or due to a sudden line outage in the system. In both
the cases it is the excessive line flows through a particular line
which exceedthe static stability limit and results in pushing the
system to voltage collapse. Hence, under these conditions, if a
Unified Power Flow Controller (UPFC) comes into operation
with appropriate control parameters, it is possible to enhance
the line flow capacity of few such lines and thereby avoiding
the possible voltage collapse.With the increased loading of
existing power transmission system and the tendency towards
maximizing economic benefits has led power system utilities
to run close to the limits of stable operation.
1
Dr. Shobha Shankar is with Department of Electrical and Electronics Engg.,
Vidyavardhaka College of Engineering, Mysore, India. (phone: 94484 88697,
fax: 0821 2510677, e-mail: [email protected])
2
Dr. T. Ananthapadmanabha is with Department of Electrical and Electronics
Engg.,The National Institute of Engineering, Mysore, India. (e-mail:
[email protected])
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International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011
power flow model is completely general. The UPFC state
variables are incorporated inside the Jacobian and mismatch
equations, leading to very robust iterative solutions. It
controls active and reactive power simultaneously as well as
voltage magnitude. It can also be set to control one or more of
the parameters in any combination or to control none of them.
A set of analytical equations has been derived to provide good
UPFC initial conditions. The algorithm exhibits quadratic or
near quadratic convergence characteristics [13].
There are several methods in the literature for finding
locations of FACTS device in vertically integrated power
system. However, very little work has been reported in the
area of identifying suitable location of UPFC with static
considerations under various network contingencies.K.S.
Verma et al have developed sensitivity based approach for
suitable location of UPFC with static point of view, for
congestion management. The location of UPFC with high
sensitive factor is considered as the best location, as it
indicates more loss reduction in the system [14]. B.
Venkatesh and H.B. Gooi have proposed a model of UPFC
and its inclusion in polar form of fast decoupled power flow
algorithm. The optimal siting of UPFC devices leads to
reduction of operating costs [15]. Mehmet Tumay et al have
developed complete power injection model of UPFC including
both the series injection branch and shunt exciting branch in
rectangular form [16]. D. Thukaram et al have selected
suitable locations of UPFC using voltage stability index (Lindex) of load buses and minimum singular value [17]. Lucio
Ippolito et al have proposed a methodology based on genetic
algorithm to identify the optimal number and location of
UPFC devices by minimizing generation costs, line overload
and the costs of installation and maintenance of UPFC devices
[18].
Line stability is used for tasks (i) and (ii) and fuzzy
approach which combines voltage change index and voltage
stability margin index is used for task (iii). Minimum singular
value of load flow Jacobian matrix is computed for monitoring
the enhancement in voltage stability margin.
A. Line Stability Index
LS index = L ij = P r / P r(max) =
Real power transferred from node i to node j
Maximum real power that can be transferred (1)
LS index is capable of identifying critical line outages and
possible lines for installing UPFC.
B. Voltage Change Index
The Voltage Change Index quantifies the improvement in
the bus voltage profile after incorporating UPFC at the
selected location in the system. It is defined as:
𝑉𝑉𝑉𝑉𝑉𝑉 = ∑𝑛𝑛𝑖𝑖=1
�𝑉𝑉𝑖𝑖𝑤𝑤 −𝑉𝑉𝑖𝑖𝑜𝑜 �
𝑉𝑉𝑖𝑖𝑜𝑜
(2)
where, n is the number of buses,
𝑉𝑉𝑖𝑖𝑜𝑜 is bus voltage profile without UPFC and
𝑉𝑉𝑖𝑖𝑤𝑤 is bus voltage profile with UPFC.
C. Voltage Stability Margin Index
The voltage stability margin index quantifies the
improvement in the voltage stability margin indicated by the
Minimum Singular Value of modified Jacobian matrix (MSV)
after incorporating UPFC at the selected location in the
system. It is defined as
�𝑀𝑀𝑀𝑀𝑀𝑀 𝑊𝑊 −𝑀𝑀𝑀𝑀𝑀𝑀 𝑂𝑂 �
𝑉𝑉𝑉𝑉𝑉𝑉𝐼𝐼 =
𝑀𝑀𝑀𝑀𝑀𝑀 𝑜𝑜
(3)
where MSVo is the MSV without UPFC in the system
andMSVw is the MSV with UPFC incorporated in the system.
The criteria for selection of best location for installation of
UPFC are enhancement in voltage stability margin and
improvement in the voltage profile. The Line Stability Index is
used to screen down the possible locations for installing
UPFC. Further fuzzy approach is used to combine the effect of
voltage stability margin indicated by Minimum Singular Value
of load flow Jacobian matrix (MSV) and voltage change to
select the optimal location. The proposed method is tested
with simulated condition on 24 bus 400 kV Southern grid of
India. The validity of the proposed method is verified with the
results of [14].
P
III.FUZZY BASED OPTIMAL LOCATION OF UPFC
The fuzzy approach computes fuzzy rank coefficient with
Voltage Change Index rank (VCIrank) and Voltage Stability
Margin Index rank (VSMI rank) as inputs to the Fuzzy
Inference System (FIS). The VCI and VSMIrank are
expressed in fuzzy set notation. The fuzzy rank coefficient is
also divided into different categories. The fuzzy rules are used
to evaluate the fuzzy rank coefficient for each UPFC location.
Based on fuzzy rank coefficient, synergized rank is obtained.
Lower the fuzzy rank coefficient; lower the synergized rank
and the best location of UPFC. The Fuzzy Inference Structure
is tested in MATLAB 7 Fuzzy Toolbox.
II.METHODOLOGY FOR OPTIMAL LOCATION OF
UPFC
The methodology involves
i)
Short listing of line outage contingencies
ii)
Possible lines for incorporating UPFC
iii)
Optimal location of UPFC with enhancement of
voltage stability margin and improvement in bus voltage
profiles.
A. VCI Rank
The VCIrank is divided into three categories using fuzzy set
notation: low (1-3), medium (3-5) and high (5-7). The
membership functions for all the linguistic terms are taken as
trapezoidal function.
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International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011
Defuzzification: ‘centroid’
Fig. 1 Membership function for 3 linguistic variables of VCI rank
B.VSMI Rank
The VSMI SUM rank is divided into three categories using
fuzzy set notation: low (1-3), medium (3-5) and high (5-7).
The membership functions for all the linguistic terms are taken
as trapezoidal function.
Fig. 4 Fuzzy surface for the proposed model
The fuzzy rules for evaluation of fuzzy rank coefficient are
given in the Table I
Rule No.
1
2
3
4
5
6
7
8
9
TABLE I FUZZY IF-THEN RULES
VCI rank
VSMI rank
Fuzzy Rank Coefficient
Low
Low
Low
Low
Medium
Low
Low
High
Medium
Medium
Low
Low
Medium
Medium
Medium
Medium
High
High
High
Low
Medium
High
Medium
High
High
High
High
Based on fuzzy rank coefficient synergized rank list is
prepared. The location of UPFC with lowest synergized rank
is the best location. The proposed fuzzy approach not only
takes into account the improvement in the voltage profiles but
also enhancement in the voltage stability margin.
Fig. 2 Membership function for 3 linguistic variables of VSMI rank
C. Fuzzy Rank Coefficient
The Fuzzy Rank coefficient is divided into three categories
using fuzzy set notation: low (1-3), medium (3-5) and high (57). The membership functions for all the linguistic terms are
taken as trapezoidal function.
VCI rank
Fuzzy
Inference
System
Fuzzy
rank
coefficient
VSMI rank
Fig. 5 Fuzzy Inference System for
optimal location of UPFC
E.Procedure
For a given system, critical line outage contingencies are
identified.
a) Load flow analysis is carried out for a precontingency system to obtain bus voltage profiles.
b) Minimum Singular Value of the load flow Jacobian
matrix is computed.
c) For each critical contingency, the LS index value is
calculated for each of the lines.
d) Lines having high values of LS index are selected as
possible locations of UPFC.
e) UPFC is installed in each one of the selected line and
Fig. 3 Membership function for 3 linguistic variables of Fuzzy Rank
coefficient
D. Fuzzy Inference System
Type: ‘Mamdani’
And method: ‘min’
Or method: ‘max’
Implication method: ‘min’
Aggregation method: ‘max’
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International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011
Voltage Change Index and Voltage Stability Margin
Index are computed for all the critical contingencies.
f) VCI obtained for all the contingencies for a specific
location of UPFC are added to get VCI SUM .
g) Voltage Stability Margin Index computed for all the
contingencies for a specific location of UPFC are
added to get VSMI SUM .
h) The UPFC locations are ranked separately based on
VCI SUM and VSMI SUM .
i) Using Fuzzy-If-Then rules, fuzzy rank coefficient is
obtained and further synergized rank is obtained and
the location with lowest synergized rank is the best
location of the UPFC.
6
DLO
7
DLO
8
DLO
9
DLO
10
DLO
9
8
8
14
5
8
21
15
12
14
10
9
11
23
8
14
9
8
8
17
Simulations are carried out to compute LS index values for
all the lines under these contingencies. The lines having
maximum LS index are (12-17), (17-19), (5-6) and (5-8). They
are the possible locations for installing UPFC in the system.
UPFC is installed at each of these selected lines and VCI and
VSMI are computed. Further VCI rank and VSMI rank list is
prepared which are given as inputs to the Fuzzy Inference
System. Table III and IV shows the VCI rank and VSMI rank
for possible locations of UPFC under selected contingencies.
F. UPFC equivalent circuit
The UPFC equivalent circuit for steady state model as
shown in fig 6. is used in the evaluation of system
performance under network contingency.
TABLE III VCI RANK FOR ALL POSSIBLE LOCATIONS OF UPFC: 24
BUS EHV SYSTEM
Contingencies
5-8
12-15
21-19
12-14,10-11
9-8,8-14
12-14,10-9
9-8,8-17
11-23,8-14
VCI SUM
VCI Rank
Fig. 6 UPFC equivalent circuit
The equivalent circuit consists of two ideal voltage
sources,
V CR = V CR (cosθ CR +j sinθ CR )
V VR = V VR (cosθ VR +jsinθ VR )
where V VR and θ VR are the controllable magnitude (V VRmin
≤V VR ≤ V VRmax ) and angle (0 ≤ θ VR ≤ 2Л) of the parallelvoltage source. The magnitude V CR and angle of the series
voltage source are controlled between limits (V cRmin ≤V cR ≤
V cRmax ) and angle (0 ≤ θ cR ≤ 2Л), respectively[13].
For the placement strategy line outage contingencies
considered are shown in Table II.
TABLE II LIST OF LINE OUTAGE CONTINGENCIES: 24
BUS EHV SYSTEM
Type of
no.
contingency
From bus
To bus
1
SLO
5
8
2
SLO
12
15
3
SLO
21
15
4
SLO
21
19
6
DLO
12
14
10
11
VCI
UPFC in
(17-19)
0.0769
………..
………….
1.5081
0.8373
2.1314
-0.7874
-0.1564
3.6099
4
values
UPFC in
(5-6)
………….
0.1420
1.0674
2.1519
1.1258
2.5977
-0.8372
-0.2570
5.9906
2
UPFC in
(5-8)
…………..
0.1225
1.1300
2.3540
1.1742
2.6402
-0.6557
0.4654
7.2306
1
TABLE IV VSMI RANK FOR ALL POSSIBLE LOCATIONS OF UPFC :
24 BUS EHV SYSTEM
VSMI values
ContinUPFC in
UPFC in
UPFC in
UPFC in
gencies
(12-17)
(17-19)
(5-6)
(5-8)
5-8
0.0329
-0.2341
…………..
………….
12-15
0.1644
…………..
0.1492
-0.4837
21-19
0.0619
……….
0.1422
-0.4356
12-14,10-11
-0.5761
-0.2403
0.4378
-0.2010
9-8,8-14
0.2014
-0.3917
-0.0880
-0.6404
12-14,10-9
-0.4943
0.2485
0.7166
-1.0751
9-8,8-17
0.4269
-0.3826
-0.2800
-0.5848
11-23,8-14
-0.4377
-0.1511
-0.2540
-0.6010
VSMI SUM
-0.6203
-1.1515
0.8218
-4.0219
VSMI Rank
2
3
1
4
IV. TEST RESULTS
Contingency
UPFC in
(12-17)
0.1083
-0.0530
0.8599
1.5343
0.4753
1.7467
-1.4145
0.8550
4.1120
3
Based on fuzzy If-Then rules fuzzy rank coefficient and
synergized rank is obtained. Table V shows fuzzy rank
coefficient and synergized rank. The location of UPFC with
highest rank is the best location which provides improvement
in bus voltage profiles and enhancement in voltage stability
margin.
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International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011
TABLE V SYNERGIZED RANK FOR ALL POSSIBLE LOCATIONS
OF UPFC: 24 BUS EHV SYSTEM
UPFC
Locations
VCI
Rank
VSMI
Rank
Fuzzy Rank
Coefficient
Synergized
Rank
12-17
17-19
5-6
5-8
3
4
2
1
2
3
1
4
2.72
3.40
1.60
2.50
3
4
1
2
Rank-3 contingency (12-14, 10-9)
At base load condition without UPFC the power loss is
84.59 MW. At bus number 24, the minimum voltage is 0.835
p.u. and MSV of the system is 0.1276. After installing UPFC
at (5-6) the voltage stability margin has increased to 0.4738
and the voltage at bus number 24 has increased to 1.06 p.u.
The system losses have reduced to 83.63 MW.
From Table V, it can be observed that locations (5-8), (5-6),
and (12-17) have been ranked as 1, 2 and 3 respectively
according to VCI rank. Similarly, (5-6), (12-17) and (17-19)
are ranked as 1, 2 and 3 respectively based on VSMI rank.
Based on fuzzy rank coefficient, synergized rank list is
prepared and accordingly (5-6) is ranked as the first best
location and (5-8) as next best location. UPFC is installed at
(5-6) and voltage profiles are computed for selected critical
contingencies namely (5-8), (12-15), (21-19), (12-14, 10-11),
(9-8, 8-14), (12-14, 10-9), (9-8, 8-17) and (11-23, 8-14). Fig. 7
to 10 shows the bus voltage profile for selected contingencies
with UPFC located at (5-6).
Voltage Profile for (12-14, 10-9) Contingency
Voltage Magnitude in p.u.
1.1
1.05
1
without UPFC
0.95
with UPFC in 5-6
0.9
0.85
0.8
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Bus Number
Fig. 9 Voltage Profile for Rank-3 Contingency
Less Critical contingency (12-15)
At base load condition without UPFC the power loss is
50.857MW. At bus number 7, the minimum voltage is 0.991
p.u. and MSV of the system is 0.53. After installing UPFC at
(5-6) the voltage stability margin has increased to 0.6091 and
the voltage at bus number 7 has increased to 1.0258 p.u. The
system losses have reduced to 50.609 MW.
Rank-1 Contingency (9-8, 8-17)
Without UPFC at base load condition the power loss is
130.579 MW. At bus number 7, the minimum voltage is 0.925
p.u. and MSV of the system is 0.271. After installing UPFC at
(5-6) the voltage stability margin has increased to 0.347 and
the voltage at bus number 7 has increased to 0.9488 p.u. The
system losses have reduced to 84.84MW.
Voltage Profile for (9-8,8-17) Contingency
Voltage Profile for 12-15 Contingency
1.08
1.08
1.04
1.02
1
Voltage Magnitude in p.u.
Voltage Msgnitude in p.u.
1.06
without UPFC
0.98
with UPFC in 5-6
0.96
0.94
0.92
0.9
0.88
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1.06
1.04
1.02
without UPFC
with UPFC in 5-6
1
0.98
0.96
Bus Number
0.94
1
Fig. 7 Voltage Profile for Rank-1 Contingency
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Bus number
Rank-2 Contingency (11-23, 8-14)
At base load condition without UPFC the power loss is
88.27 MW. At bus number 23, the minimum voltage is 0.849
p.u. and MSV of the system is 0.358. After installing UPFC at
(5-6) the voltage stability margin has increased to 0.4492 and
the voltage at bus number 26 is increased to 0.8626 p.u. The
system losses have reduced to 11.1647 MW.
Fig. 10 Voltage Profile for Rank-7 Contingency
TABLE VI COMPARISON OF RESULTS: 24 BUS EHV SYSTEM
Voltage Profile for (11-23, 8-14) Contingency
1.1
Voltage magnitude in p.u.
2
1.05
Line
section
Fuzzy rank
coefficient
Synergized
rank
Sensitivity
factor (b i k)
5-6
5-8
12-17
1.6000
2.5000
2.7200
1
2
3
-0.9318
-0.6823
-0.5134
Best
UPFC
location
1
2
3
1
The location of UPFC obtained from the proposed method
is verified by finding total loss sensitivity factor (b i k) with
respect to voltage as proposed in [14]. It is found from Table
VI that concurrent results are obtained from fuzzy approach
and sensitivity factor method.
without UPFC
0.95
with UPFC in 5-6
0.9
0.85
0.8
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Bus Number
Fig. 8 Voltage Profile for Rank-2 Contingency
126
International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011
[7]
V. CONCLUSIONS
The Unified Power Flow Controller (UPFC) is very
expensive device, therefore it is important to ascertain the
location for placement of UPFC which is suitable for various
contingencies. In this paper, an effective but simple placement
strategy for UPFC is proposed. The method uses Line Stability
index which is sensitive to line flow to screen down the
possible locations for UPFC. Further Voltage Change Index
and Voltage Stability Margin Index are combined using fuzzy
approach to determine optimal location of UPFC. The method
guarantees improvement in voltage profile and enhancement
in voltage stability margin.
[8]
[9]
[10]
[11]
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