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IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 5, NO. 2, SUMMER-FALL 2006
Installation of Unified Power Flow Controller for Voltage Stability Margin Enhancement Under Line Outage Contingencies P. S. Venkataramu and T. Ananthapadmanabha
Index Terms—Contingency, voltage stability margin, VCI, VSI, UPFC.
NOMENCLATURE
D
ECENT power systems are being subjected to stressed operating conditions due to ever increasing load demand and the environmental constraints on expansion of transmission networks. Hence, the power systems are more vulnerable to stability and security problems. Voltage instability leading to voltage collapse is one of the major threat for secured operation of grid connected power systems [1]-[3]. The problem of voltage collapse may simply be explained as the inability of the power system to supply the reactive power or by an excessive absorption of reactive power by the system itself [4]. Voltage instability problem is being addressed in two different ways. The first approach is to mitigate the problem and the second approach is to enhance the VSM of the system for the selected operating condition (Includes the contingencies). Tiranuchit and Thomas [5] presented a control strategy against voltage instabilities utilizing minimum singular value of the load flow Jacobian as voltage security index. Overbye and Demarco [6] developed energy based controller sensitivities for voltage security enhancement. Sensitivity analysis has been used by Begovic and Phadke [7] for static voltage stability control. Mansour et al. [8] used modal analysis as a tool for SVC placement to prevent voltage instability. Bansilal et al. [9] presented a reactive power dispatch for voltage stability margin improvement using ‘L’ index and nonlinear least squares optimization algorithm. Recently, flexible AC transmission system (FACTS) devices are being increasingly utilized in many electric power systems to enhance voltage control and system dynamic performance. The most comprehensive device that emanated from the FACTS technology is the UPFC [10], [11]. For the last few years, the focus of research in the FACTS area is mainly on UPFC. This has resulted in many useful contributions in the areas of modeling of UPFC [12]-[14], effective control strategy for UPFC [15], [16] and the system transient stability enhancement using UPFC [17], [18]. Efforts are also made by a few researches to investigate the possibility of enhancement of static voltage stability margin of the system through application of UPFC. However, the decision on embedding a UPFC into the system is mainly decided by other unique functionalities like controlling real and reactive power flows in line. But the quantitative information with regards to capability of UPFC in enhancing the voltage stability margin will definitely influence power engineers in effective utilization
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bS = Equivalent susceptance H , J , L , N = Sub-matrices of load flow Jacobian Pr ,Qr = Real & reactive powers at the receiving end bus, respectively Psi ,Qsi = Injected real & reactive powers at bus i , respectively Psj ,Qsj = Injected real & reactive powers at bus j , respectively r = Non zero scalar number Viu = Voltage magnitude of i -th bus for a specific contingency with UPFC in the system Vio = Voltage magnitude of i -th bus for a specific contingency without UPFC in the system VR = Receiving end voltage VS = Source voltage/sending end voltage YL ∠θ = Line admittance YR ∠φ = Load admittance Z L ∠φ = Load impedance Z S ∠θ = Internal impedance β ij = Bus voltage angle difference γ = Angle at which the voltage is injected ∆P = Incremental change in active power ∆Q = Incremental change in reactive power ∆v = Incremental change in bus voltage ∆δ = Incremental change in bus voltage angle
R
I. INTRODUCTION
SI
Abstract—Voltage stability margin (VSM) enhancement of a system under line outage contingencies is an important task for secured operation of large interconnected power system. This paper proposes a novel placement strategy for a unified power flow controller (UPFC), which enhances the VSM of the system. The location for the installation of UPFC is identified using voltage stability index (VSI) and the voltage change index (VCI). The proposed method has been tested under simulated conditions on a few power systems and the results of a 22-node real-life equivalent power network are presented for illustration.
Manuscript received November 16, 2005; revised Mach 15, 2006. P. S. Venkataramu, is with the Department of Electrical and Electronics Engineering, Vellore Institute of Technology, Deemed University, Vellore 632 014, India (e-mail:
[email protected]). T. Anathapadmanabha is with the Electrical Engineering Department, The National Institute of Engineering, Mysore, India. Publisher Item Identifier S 1682-0053(06)0440
1682-0053/06$10 © 2006 JD
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VENKATARAMU AND ANANTHAPADMANABHA: INSTALLATION OF UNIFIED POWER FLOW CONTROLLER … YL∠θ Y∠θ
VS, PS+JQS
91
I
VR, Pr+JQR
Load Pr+JQr
Total load at the node
Fig. 1. Typical transmission line of a power system network.
VR
Vs
YR∠φ
Zs∠θ Fig. 3. Transmission line modeled with admittance.
Load
Vs Source
ZL∠θ
II. DEVELOPMENT OF VSI
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D
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of UPFC. Messina et al. [19] have demonstrated through analytical studies that, placement of UPFC at a weak transmission line enhances the voltage stability margin in the system. K. Visakha et al. [20] have shown that application of UPFC enhances the system security as measured by the improvement in the static voltage stability margins under normal and network contingencies. But the authors of the paper have not suggested any criterion on which a particular line is selected for UPFC placement. However, to achieve the good performance of UPFC, proper placement of UPFC is an important task. There are several methods for finding the locations of UPFC in vertically integrated systems but little attention has been devoted to interconnected power system under contingency [21]. In this paper, an attempt has been made to enhance the VSM of the system under various line outage contingencies by installing a UPFC at an appropriate location. The location is identified using a novel placement strategy. Generally, the VSM of the system is assessed using static voltage collapse proximity indicators (SVCPI). There are many SVCPI reported in the literature. A comparative study of some of the SVCPI reveals that most of these indices are developed based on the sensitivity to the variations in the bus quantities [22]. However, to rank the line outage contingencies and for suggesting a suitable line section for installation of UPFC, an indicator which is sensitive to the line flow will be of more relevant and accurate. Hence, in this paper a new voltage stability index (VSI) is developed using the line flow information and the maximum power transfer theorem. This index is used to select contingencies, identify possible locations for installation of UPFC. Final location of the UPFC is selected using Voltage Change Index (VCI). The proposed method has been tested under simulated conditions on few power systems. The installation of UPFC in the selected location has enhanced the VSM of the system. The enhancement in VSM is evident from the increase in the minimum singular values of the load flow Jacobian . [23]. Section II briefly explains the development of indicators used in this method and the static model of UPFC. Section III presents the placement strategy and the stepwise procedure. In Section IV results are presented. Finally, Section V concludes the paper.
Consider a typical transmission line of an interconnected power system shown in Fig. 1. Fig. 2 represents the Thevenin’s equivalent of the above network. A load impedance Z L ∠φ fed by a constant voltage source Vs with an internal impedance Z S ∠θ . Application of maximum power transfer theorem to the equivalent circuit shown in Fig. 2, results in the ratio Z L / Z S = 1 for maximum power to be flown to the load from the source. Z L / Z S is used as the voltage stability indicator. Till this ratio is less than 1 the system is considered to be voltage stable and if it is greater than 1, voltage collapse occurs in the system [24]. In development of a new indicator, the single line model given in [24] is used, but the system is represented using an admittance model. The load of the line will be treated as the power that is transferred at the receiving end through that particular line only, instead of the total load at the node. Equivalent admittance model is shown in Fig. 3 where YL ∠θ is the line admittance, YR ∠φ is the load admittance and φ = tan -1 (Qr / Pr ) . The index is developed considering the case which is more often encountered, where only the modulus of the load admittance is varied while φ remains constant. This assumption does not significantly reduce the accuracy but will simplify the problem at hand. In practice, efforts are taken to maintain constant power factor load in the system. Increase in load results in increase in admittance and there by increase in current and the line drop and hence decrease in the voltage at the receiving end. In the circuit shown in Fig. 3,
SI
Fig. 2. Thevenin’s equivalent of a network.
I = VS Yeq ,
(1)
⎡ ⎤ YLYR Yeq = ⎢ 2 ⎥ , 2 0 .5 ⎣⎢ [Y L + YR + 2Y L Y R Cos( θ − φ )] ⎦⎥ V R = I / YR
(2)
⎡ ⎤ YL YR VS ⎢ 2 2 0 .5 ⎥ ⎢⎣ [YL + YR + 2YL YR Cos( θ − φ )] ⎥⎦ = . YR
Now the active power at the receiving end is given by Pr = V R I Cos(Φ ) ⎤ ⎡ V S 2 YL 2Y R Cos(φ ) =⎢ 2 ⎥ . 2 ⎣⎢ [YL + Y R + 2YL Y R Cos(θ − φ )] ⎦⎥
(3)
The maximum real power transfer to the bus is obtained by applying the condition, ∂PR / ∂YR = 0 which leads to a criterion of | YL |=| YR | .
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IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 5, NO. 2, SUMMER-FALL 2006
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Substituting | YL |=| YR | in (3) VS 2YL Cos(φ ) . 2[1 + Cos(θ − φ )]
Prmax
(4)
Equation (4) gives the maximum real power that can be transferred through a given line safely without any voltage instability threat. Now the actual line flow for a given operating condition is compared with the maximum power transfer and the stability margin for that line is defined as, VSI = Pr / Pr max .
V VSI Prmax
Prmax =
VSI
(5)
Pr values can be obtained from the load flow solution or as the output of the state estimator. Similar indicator can be developed using the reactive power flow, which is given by, Fig. 4. Variation of Prmax and VSI.
(6)
2
Qrmax =
VS YL Sin(φ ) . 2[1 + Cos(θ − φ )]
of
The simulation results have shown that both indicators convey the same information and hence in this paper the real power flow based indicator is considered. It is established that the main cause for the problem of voltage instability leading to voltage collapse is the stressed power system characterized by excessive line loadings. As the maximum power transfer theory restricts the amount of load that can be transferred through a line, the indicator shown in (5) precisely indicates the voltage stability margin of a system for a selected line loading condition.
indicator is computed for all the lines under a specific contingency and the most critical line based on its VSI value is selected. The severity of a contingency is assessed based on the maximum value of the VSI that a line attains due to the contingency. As the outages are ranked based on the VSI, the severity of any line outage is accurately assessed with respect to its effect of forcing the system to voltage collapse condition. The rankings can be obtained for different loading conditions and the simulation required is only for the load flow results and the computation of VSI for all the lines. Stepwise procedure for contingency ranking using the VSI is given below: Step 1: Load flow results are obtained for a selected operating condition (or obtain the state estimator output) and the VSI for all the lines using (4) and (5) are computed. Step 2: Line outage contingency is imposed one at a time and the VSI values are computed for all the lines. Step 3: The maximum value of VSI among all the lines for each of the contingency is selected and the contingency is ranked in the descending order of VSI (i.e., higher the VSI severe is the contingency). Possibilities of ranking contingency based on the maximum number of lines reaching to higher values of VSI was investigated, though the approach appears to be logical, but simulation results have shown that VSI of single line approaching to unity is more severe than the few lines having VSI in the range of 0.7 to 0.9. The effectiveness of the proposed indicator in ranking line outage contingencies is compared with the contingency ranking obtained using ‘L’ index [4]. A sample contingency ranking result is shown in Table I. From the result it is very clear that the proposed index has equal accuracy as that of ‘L’ index in ranking line outages.
D
Qr , Qr max
SI
VSI =
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A. Behavior of Proposed VSI In (4) and (5), Pr is the real power transferred through the line to the receiving end, which is a function of bus voltages, line parameter and the system configuration. But the Pr max is a function of sending end voltage and the load power factor as the line admittance remains constant. Normally, the variations in the sending end voltage is small and if the power factor angle of the load is assumed constant, then the Pr max remains constant for variations in the bus power and hence the VSI proposed will have almost linear relation with the increase in bus power. Fig. 4 shows variation in bus power at constant power factor and for the corresponding computed values of Pr max and VSI. It is seen from Fig. 4 that the curve Pr max almost remains constant at 0.6 pu for all the values of bus power and the VSI show a linear relation to bus power till it is nearer to the collapse point. At collapse point VSI reaches one. B. Contingency Ranking Using VSI The indicator proposed in Sub-Section II.A conveys the information about the criticality of a line with respect to voltage instability for a given loading condition. Line outage contingencies alter the system configuration and hence the line flows are changed considerably. Line flow increase in some of the lines correspondingly reduces the VSM of the system. The reduction of VSM is a good indicator to measure the severity of the line outage and hence can be used for ranking line outages. The proposed
C. Voltage Change Index This index is defined to quantify the overall improvement in the bus voltage profile after embedding a UPFC in the selected location. It is defined as n
Vi u − Vi o
i =1
Vi o
VCI = ∑
, i =1,2,..., n , n = No. of Buses . (7)
The VCI value is a number, which accounts for the improvement in the bus voltage magnitudes. Higher value of VCI indicates that the voltage improvement is more and
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VENKATARAMU AND ANANTHAPADMANABHA: INSTALLATION OF UNIFIED POWER FLOW CONTROLLER …
93
2
Psj, Qsj
Psi, Qsi Fig. 5. UPFC model.
TABLE I COMPARISON OF CONTINGENCY RANKING Base load rank based on ‘L’ Index VSI 6 6 11 10 7 7 8 8 3 2 12 11 5 5 9 9 1 1 4 3 10 12 2 4
10 6
16
13
11
17
7
14
20
18 19
21
Fig. 6. 22 Bus 400 kV, southern regional grid (May 2002, operating condition).
H(i,i)=Ho(i,i)-Qsj H(i,j)=Ho(i,j)+Qsj H(j,i)=Ho(j,i)+Qsj H(j,j)=Ho(j,j)-Qsj
N(i,i)=No(i,i)-Psj N(i,j)=No(i,j)-Psj N(j,i)=No(j,i)+Psj N(j,j)=No(j,j)+Psj
hence the system is operating at a better security level. As the overall index computed is a summation, any possibility of reduction in the bus voltage due to UPFC contributes to the negative value and hence the overall index value reduces. The effectiveness of the proposed index in accurately conveying the information about the overall improvement in the voltage profile due to installation of UPFC was compared with the index proposed in [25] for contingency ranking using bus voltages and found to be good. This index is used in this paper to select the final location of the UPFC after initial screening based on VSI.
SI
15-10 11-17 11-19 17-20 2-3 5-6 16-17 19-21 1-2 & 20-21 5-6 & 3-9 5-4 & 11-17 2-3 & 17-20
5
12 22
9
D
Contingency
15
4
90% of base load rank based on ‘L’ Index VSI 6 7 11 10 7 6 8 8 3 3 12 12 5 5 9 9 1 2 4 4 10 11 2 1
8
3
D. Static Model of UPFC The static UPFC model proposed in [12] is incorporated in this paper. This UPFC injection model can easily be incorporated in to the steady state power flow model. The UPFC injection model is shown in Fig. 5. The active and reactive powers at the buses are given as
The basic objective of the proposed method is to enhance the VSM of the system under various line outage contingencies by installing a UPFC at an appropriate location. The major tasks involved are: • Selection of line outage contingencies for study. • Short-listing of possible lines for installation of UPFC. • Identification of one or two locations among the short listed locations. • Investigating the enhancement in Voltage Stability Margin (VSM) and improvement in bus voltage profiles. VSI proposed in Section II is used for tasks I and II and VCI is used for task III, task IV is accomplished by monitoring the minimum singular value (MSV) of the load flow Jacobian. Stepwise computational procedure is given below.
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J(i,i)=Jo(i,i) L(i,i)=Lo(v)+2Qsi o J(i,j)= J (i,j) L(i,j)= Lo(i,j) o J(j,i)= J (j,i)-Psj L(j,i)= Lo(j,i)+Qsj o J(j,j)= J (j,j)+Psj L(j,j)= Lo(j,j)+Qsj Modified Jacobian Matrix
(8)
Psj = - rbsViV j Sin( β ij + γ ) ,
(9)
Ar
Psi = rbsViV j Sin( β ij + γ ) ,
Qsi = rbsVi 2 Cos(γ ) ,
(10)
Qsj = - rbsViV j Cos(θ ij + γ ) ,
(11)
The UPFC is located between node i and j in the system. Adding a reactance equivalent to X S between node i and j modifies the admittance matrix. The Jacobian matrix is modified by addition of appropriate injection powers. The Jacobian matrix of the linearized load flow model shown in (12) is modified as given below, (where the superscript ‘o’ denotes the Jacobian elements without UPFC) ⎡∆P ⎤ ⎡ H ⎢∆Q ⎥ = ⎢ J ⎣ ⎦ ⎣
N⎤ L ⎥⎦
⎡∆δ ⎤ ⎢∆V ⎥ ⎢⎣ V ⎥⎦
(12)
III. PROPOSED PLACEMENT STRATEGY
A. Computational Procedure Step 1: For a given system, possible line outage contingencies are listed (in case of a real system, past data of line outages are used to arrive at the list). Step 2: Load flow study is carried out for a precontingency system and the VSI values are computed using (4) and (5) for each of the line and the MSV of the load flow Jacobian is computed. Step 3: The maximum value of VSI for each contingency is found and the contingencies are ranked in the decreasing order of maximum VSI. Few severe contingencies are
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IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 5, NO. 2, SUMMER-FALL 2006
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TABLE II VCIS FOR ALL POSSIBLE LOCATIONS OF UPFC Contingency
UPFC in (3-15)
UPFC in (16-15)
UPFC in (3-9)
UPFC in (9-10)
UPFC in (15-10)
UPFC in (13-14)
(2-3,17-20)
0.13096
(2-3)
0.11147
-0.07767
0.11585
0.13208
0.11311
0.024292
-0.13225
0.097264
0.11173
0.09602
(5-4,11-17)
0.087666
0.024292
-0.08697
0.070379
0.093417
0.081105
0.028085
(8-22)
0.03562
-0.06391
0.029878
0.035581
0.031878
0.04313
(5-4)
0.079719
-0.03815
0.07271
0.078573
0.073168
0.02604
(4-6)
0.082394
-0.03987
0.040807
0.081162
0.041149
0.026205
(2-8)
0.033916
-0.06288
0.028344
0.034347
0.030912
0.047379
(11-17)
0.059844
-0.05638
0.04756
0.063923
0.056502
0.026397
(5-6)
0.049669
-0.07453
0.042245
0.047523
0.041469
0.02626
(12-13)
0.036354
-0.03112
0.030611
0.035742
0.031959
0.035947
SUM
0.707612
-0.66371
0.575648
0.714078
0.597272
0.308027
Case
MSV (NO UPFC)
1
Base
0.85855
2
(2-3,17-20)
0.16234
3
(2-3)
0.19502
4
(5-4,11-17)
0.46281
5
(8-22)
0.81985
6
(5-4)
7
(4-6)
8
(2-8) (5-6)
11
(12-13)
3.476792
0.24751
52.46396
0.26826
37.55512
0.52889
14.278
0.85046
3.73361
0.76852
of
(11-17)
0.8884
% Improvement in MSV
5.348869
0.72089
0.76107
5.573666
0.81447
0.84549
3.808612
0.65891
0.70562
7.08898
0.75054
0.78569
4.683295
0.85444
0.88424
3.487664
ive
9 10
0.7295
MSV UPFC-(9-10)
SI
S No.
D
TABLE III IMPROVEMENT IN VOLTAGE STABILITY MARGIN FOR DIFFERENT CASES
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selected for study based on their severity. Step 4: Lines, which have high value of VSI for most of the contingencies are identified and listed. Step 5: UPFC is installed in one of the line selected at Step 4 and the VCI values are computed using (7) for all the selected contingencies. Step 6: VCIs obtained for all contingencies for a specific location of UPFC are added to get VCISUM and this process is repeated for all locations of UPFC. Step 7: The location, which yields higher value of VCISUM is selected as the best location for installation of UPFC. Step 8: UPFC is installed at the selected location and the MSV of the load flow Jacobian is computed. Step 9: The MSV compared in Step 8 is compared with the MSV computed at Step 2, if the VSM is found enhanced as indicated by percentage increase in MSV, this location is selected as the best location or else the next best location from the results in Step 7 is considered. IV. RESULTS The proposed method is applied on a real life system of 22-bus equivalent EHV power system network shown in Fig. 6. The system total peak load is about 3575 MW, 2273 MVAR and the system losses at base case (pre contingency case) are 141.52 MW (3.9%), and the MSV is 0.85855 least bus voltage is at bus no. 14 (0.805). Ten line outages are selected for simulation, out of which four line outages
are very critical and the remaining are less critical. The VSI values of all the lines are computed. Based on the VSI values of various lines, six lines are selected as possible locations for installation of UPFC, as these lines have maximum value of VSI for most of the contingencies. UPFC is connected in each of these lines one at a time and the VCI values are computed for different contingencies and the sum of VCI is obtained. It is seen from the Table II that, VCI is maximum if the UPFC is located in the line connecting bus no. 9 and bus no. 10. This indicates that, the effect of embedding a UPFC at this location has improved the overall voltage profile of the system for all the considered contingency conditions. It is also noted that if a UPFC is connected between bus no. 16 and bus no. 15 the VSI values are negative for all the contingencies, which indicates that, the voltage profiles are reduced due to UPFC. This is a vital observation, which highlights the importance of identifying an appropriate location for UPFC instillation. Some of the important observations about the VSM enhancement due to installation of a UPFC between bus no. 9 and bus no. 10 for two most critical contingencies are given below. A. Rank - I Contingency For this contingency (line outage 2-3, 17-20) at a peak load conditions the overall total real power loss is 175.17MW (4.9%). The minimum voltage is 0.76 pu at bus no. 12 and the MSV of the system is 0.1623.
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VENKATARAMU AND ANANTHAPADMANABHA: INSTALLATION OF UNIFIED POWER FLOW CONTROLLER …
1
1.2 1 0.8 0.6 0.4 0.2 0
Voltage Magnitude
Voltage Magnitude
1.05 0.95 0.9 0.85 0.8 0.75 1
3
5
7
9
11
13
15
17
19
1
21
3
5
7
9
7
9
Voltage Magnitude
1.2 1 0.8 0.6 0.4 0.2 0 5
11 13 15 17 19 21
1.2 1 0.8 0.6 0.4 0.2 0 1
3
5
7
9
(d)
7
9
11
13
15
17
19
21
Bus No.
(e) NO UPFC
SI
5
1.05 1 0.95 0.9 0.85 0.8 0.75
D
1.2 1 0.8 0.6 0.4 0.2 0
Voltage Magnitude
Voltage Magnitude
(c)
3
11 13 15 17 19 21 Bus No.
Bus No.
1
13 15 17 19 21
(b)
Voltage Magnitude
(a)
3
11 Bus No.
Bus No.
1
95
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Bus No.
(f)
of
UPFC(9 -10)
Fig. 7. Voltage profile with contingency, (a) 9-10, (b) 2-3, 17-20, (c) 2-3, (d) 5-4,11-17, (e) 8-22, and (f) 5-4.
ive
Installation of UPFC at the selected location (between bus no. 9 and bus no. 10) has enhanced the VSM to 0.2475 that is an enhancement of about 54% and the minimum bus voltage is found to be 0.821pu at bus no. 16.
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B. Rank - II Contingency In this contingency (line outage 2-3) for a peak load condition, the overall total real power loss is 164.45 MW (4.6 %). The minimum voltage is 0.77 pu at bus no. 12 and the MSV of the system is 0.19502. Installation of UPFC in the line between bus no. 9 and bus no. 10 has enhanced the MSV to 0.2682 that is an enhancement of about 37 % and the minimum bus voltage is found to be 0.832 pu at bus no. 14. Similar enhancement in the VSM is found for all the other contingencies. Table III illustrates the enhancement in the VSM for different contingencies. The initial and final bus voltages are given in Fig. 7.
measured by increase in the MSV of the load flow Jacobian. The proposed technique has been tested on a real-life power system. The results indicate that the proposed technique has a great potential in identifying a suitable location for UPFC installation. ACKNOWLEDGEMENT
The authors are grateful to the Management of Vellore Institute of Technology, Vellore and National Institute of Engineering, Mysore for their support and encouragement. REFERENCES [1]
[2] [3]
V. CONCLUSIONS The unified power flow controller has a unique capability of changing real and reactive power flows in a given line section. This capability can be explored for enhancing the system security levels during network contingencies. As the cost of installation of a UPFC in the system is very high, the location for placement of UPFC device is to be identified considering many criteria. In this paper the enhancement of voltage stability margin of the system is achieved through placement of a UPFC in a particular line section for all the selected line outage contingencies. The location is identified using two newly proposed indicators. The enhancement of the VSM is
[4] [5] [6] [7] [8]
IEEE Publication 90TH 0358-2 PWR, Voltage Stability Analysis of Power Systems: Concepts, Analytical Tools, and Industry Experience, Report prepared by IEEE Working Group on Voltage Stability, 1990. Cigre Task Force 38-02-10, Modeling of Voltage Collapse Including Dynamic Phenomena, CIGRE Brochure, No. 75:1993. IEEE PES Publication 93TH0620-5 PWR, Suggested Techniques for Voltage Stability Analysis, IEEE publication 96TP116-0, FACTS Application, Power Engineering Society, 1996. P. Kessel and H. Glavitch, "Estimating the voltage stability of a power system," IEEE Trans. on Power Delivery, vol. 1, no. 3, pp. 346-354, Jul. 1986. A. Tiranuchit and R. J. Thommas, "A posturing strategy against voltage instabilities in electric power systems," IEEE Trans. on Power System, vol. 3, no. 1, pp. 87-93, Feb. 1988. T. J. Overbye and C. L. DeMarco, "Voltage security enhancement using energy based sensitivity analysis," IEEE Trans. on Power System, vol. 6, no. 3, pp. 1196-1202, Aug. 1999. M. M. Begovic and A. G. Phadke, "Control of voltage stability using sensitivity analysis," IEEE Trans. on Power System, vol. 7, no. 1, pp. 114-133, Feb. 1992. Y. Mansour, W. Xu, F. Alvarado, and C. Rinzin, "SVC placement and transmission line reinforcement using critical modes," IEEE Trans. Power System, vol. 9, no. 2, pp. 757-63, May 1994.
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[14]
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[17]
[18]
[19]
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P. S. Venkataramu was born in India on June 20, 1961. He received his Graduation in Electrical Engineering from the Institution of Engineers (India) and his M.Tech. degree in Power Systems from Mysore University, India. He was employed as an Electrical Engineer in the Goa state Electricity Department and worked for 15 years in various capacities. He was primarily involved in carrying power system operational and planning studies for the regional grid system. He was also a visiting faculty in the Goa college of Engineering. In 1997, he joined as Assistant professor to the Vellore Engineering College, Vellore, India. At present he is Professor at the School of Electrical Sciences, Vellore Institute of Technology, Vellore, India. P. S. Venkataramu is a member of The institution of engineers (India), Indian society for technical education, and System society of India. His research interest includes AI applications to power system and distribution system automation.
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T. Ananthapadmanabha was born in India on May 15, 1958. He received his B.E. in Electrical Engineering in the year 1980, and M.E. in Power Systems in 1984 and the Ph.D. in 1997 from Mysore University, India. He has been working as a faculty in the Electrical Engineering Department at National Institute of Engineering, Mysore University since 1980. At present he is a Professor and Head of Electrical Engineering Department at National Institute of Engineering. He has several national and international journal publications. He is in the editorial boards of The Journal of Institution of Engineers (India) and The Journal of Current Sciences. He is a member of the institution of engineers (India), Indian society for technical education, and System society of India. Dr. Ananthapadmanabha is a member in the board of studies of few universities in India. His research interests includes AI applications to power system and distribution automation.
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