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IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE)
e-ISSN: 2278-1676,p-ISSN: 2320-3331, Volume 8, Issue 6 (Nov. - Dec. 2013), PP 44-50
www.iosrjournals.org
www.iosrjournals.org 44 | Page
Implementation of UPFC for Improvement of Power Stability
Savinder Malik1
, Lalit Dalal2
,
Research Scholar1
, Research Scholar2
GITAM, Kablana, Jhajjar, Haryana, India-1241041, 2
Abstract:The focus of this research work is on a FACTS device known as Unified Power Flow Controller
(UPFC), which can provide simultaneous control of basic power system parameters like voltage, active power
flow, reactive power flow, impedance and phase angle. In this research work, simulation models for different
multi machine systems are carried out, e.g. a hybrid power system, a power system with two synchronized hydro
power stations etc., without UPFC & with UPFC located at the load end of the power system, has been
developed. Simulation models have been incorporated into MATLAB based Power System Toolbox (PST) for
their voltage stability analysis. These models were analyzed for voltage, active power flow, and reactive power
flow and phase angle, with and without UPFC. The results of the power system with UPFC and without UPFC
are compared and the conclusion is given at the end.
Keywords: UPFC, FACTS, PST
I. Introduction
In today’s high complex and interconnected power systems, there is a great need to improve power
utilization while still maintaining reliability and security. Reducing the effective reactance of lines by series
compensation is a direct approach to increase transmission capability. However, a power transfer capability of
long transmission line is limited by stability consideration [13].Oscillation of generator angle or line angle are
generally associated with the transmission system disturbances and can occur due to step changes in load,
sudden change of generator output, transmission line switching and short circuit [18]. Different modes of rotor
oscillation are local mode, intra-area mode and inter-area mode. The frequency of oscillations of rotor swings
varies from 0.2 to 4 Hz [2]. The lower end of frequency spectrum corresponds to inter-area modes, in which a
large number of generators participated and their damping is difficult. This low frequency is important to damp
as quickly as possible because they cause mechanical wear in power plants and cause power quality problem. If
the electromechanical oscillations are not properly controlled in the electric power system operation, it may lead
to a partial or total system outage [18]. Instability problems in power systems that can lead to partial or full
blackout can be broadly classified into three main categories, namely voltage, phase angle and frequency related
problems [3]. In early age this signal instability problem was solved by amortisseurs implemented in generator
rotors, later with the application of fast excitation system this was solved by development & utilization of Power
System Stabilizer (PSS) and however in modern power system due to the connection of power grids in vast area,
for inter area oscillation damping due to the ability of controlling line impedance, power flow and bus voltage,
Flexible AC transmission Systems (FACTS) devices implementation offers an alternative solution [19].
II. Case-With Two Hydro Generating Stations
1) Under 3-Phase to Ground Fault Condition without FACTS Devices
Implementation of UPFC for Improvement of Power Stability
www.iosrjournals.org 45 | Page
230 kV
500 kV
13.8kV 1200 MVA
13.8kV 1000 MVA
Phasors
powergui
A+
B+
C+
A-
B-
C-
a3
b3
c3
Zigzag
Phase-Shifting Transformer
Vphase
V P Q
Measurements
V Lines
A
B
C
a
b
c
Tr4: 1200 MVA
13.8 kV/230 kV
A
B
C
a
b
c
Tr2: 800 MVA
230 kV/500 kV
A
B
C
a
b
c
Tr1: 1000 MVA
230kV/500kV
A
B
C
A
B
C
Three-Phase Fault1
m
Pref
Pm
Vf
Reg_M2
m
Pref
Pm
Vf
Reg_M1
Q Lines
0.5
0.833333
P Lines
Vf_
m
A
B
C
Pm
M2
L3_50km
L2_50km
L1_65km double circuit
A
B
C
Equivalent
500 kV
15 000 MVA
A
B
C
a
b
c
B5
A
B
C
a
b
c
B4
A
B
C
a
b
c
B3
A
B
C
a
b
c
B2
A
B
C
a
b
c
B1
96.55
585.2
583.4
897.3
1279
Active Powers(MW)
B1 B2 B3 B4 B5
A
B
C
200 MW
A
B
C
195 MW
Vf_
m
A
B
C
Pm
1000 MVA
Vpos. seq. B1 B2 B3 B4 B5
Q B1 B2 B3 B4 B5 (Mvar)
P B1 B2 B3 B4 B5 (MW)
Fig.1 Two Hydro Generating Stations Under 3-Phase to Ground Fault Condition
A three phase to ground fault is created at t=10 sec for 0.08 sec at bus 2 as shown in fig. 1. The active power,
reactive power, voltage and phase angle curves with respect to time at different buses (B1 B2 B3 B4 B5) are
shown in fig. 1.1.1-1.1.8
Fig 1.1 Active Power At Bus B2
Fig. 1.2 Reactive Power At Bus B2
Implementation of UPFC for Improvement of Power Stability
www.iosrjournals.org 46 | Page
Fig. 1.3 Voltage Bus B2
Fig.1.4 Phase Angle At Bus B2
Fig. 1.5 Active Power At Different Bus
Fig. 1.6 Reactive Power At Different Bus
Fig. 1.7 Voltage At Different Bus
Implementation of UPFC for Improvement of Power Stability
www.iosrjournals.org 47 | Page
Fig. 1.8 Phase Angle At Different Buses
2) Using UPFC under 3-Phase to Ground Fault Condition
230kV
500kV
Hydro plant
13.8kV 1000 MVA Hydro plant
13.8kV 1200 MVA
Shunt 500 kV, 100 MVA
Series100 MVA,10% injection
Phasors
powergui
Vphase
Vdqref
Vdqref
V P Q
Measurements
V Lines1
UPFC1
UPFCphase
UPFC
Measurements
Trip
Bypass
PQref
Vdqref
m
A1
B1
C1
A2
B2
C2
UPFC
UPFC
A
B
C
a
b
c
Tr4: 1200 MVA
13.8 kV/230 kV
A
B
C
a
b
c
Tr3: 1000 MVA
13.8 kV/230 kV
A
B
C
a
b
c
Tr2: 800 MVA
230 kV/500 kV
A
B
C
a
b
c
Tr1: 1000 MVA
230kV/500kV
A
B
C
A
B
C
Three-Phase Fault
m
Pref
Pm
Vf
Reg_M2
m
Pref
Pm
Vf
Reg_M1
-0.27
Qref (pu)
Q Lines1
0.5 0.833333
Pref (pu)
P Lines1
Vf_
m
A
B
C
Pm
M2
L3_50km
L2_50km
L1_65km double circuit
[PQref]
[Vdqref]
[Vdqref]
[PQref]
m
A
B
C
Equivalent
500 kV
15 000 MVA
Bypass
A
B
C
a
b
c
B_UPFC
A
B
C
a
b
c
B5
A
B
C
a
b
c
B4
A
B
C
a
b
c
B3
A
B
C
a
b
c
B2
A
B
C
a
b
c
B1
196.8
689.7
687
795.7
1276
Active Powers(MW)
B1 B2 B3 B4 B1
A
B
C
200 MW
Vf_
m
A
B
C
Pm
1000 MVA
Vconv_mag (pu)Vconv_mag (pu)
Vconv_phase (deg.)Vconv_phase (deg.)
Vpos. seq. B1 B2 B3 B4 B5
Q B1 B2 B3 B4 B5 (Mvar)
P B1 B2 B3 B4 B5 (MW)
Fig: 2 Two Hydro Generating Stations Using UPFC under 3-Phase to Ground Fault Condition
A three phase to ground fault is created at t=10 sec for 0.08 sec at bus 2 as shown in fig. 2. The ratings of the
various components used are given in appendix-B. The UPFC is made on at t=8sec and the power flow in the
system goes from 5.87pu to 6.87pu. The active power, reactive power, voltage and phase angle curves, voltage
at UPFC with respect to time at all five buses (B1 B2 B3 B4 B5) are shown in fig. 2.1-2.10.
Fig 2.1 Active Power at Bus B2
Implementation of UPFC for Improvement of Power Stability
www.iosrjournals.org 48 | Page
Fig. 2.2 Reactive Power at Bus B2
Fig. 2.3 Voltage at Bus B2
Fig. 2.4 Phase Angle at Bus B2
Fig. 2.5 Voltage at UPFC
Fig. 2.6 Active Power at Different Bus
Implementation of UPFC for Improvement of Power Stability
www.iosrjournals.org 49 | Page
Fig. 2.7 Reactive Power at Different Bus
Fig. 2.8 Voltage at Different Bus
Fig. 2.9 Phase Angle at Different Buses
Fig. 2.10 Phase Angle at UPFC
Active Power Flow (MW)
Buses Without UPFC With UPFC
Bus 1 95.2 194.9
Bus 2 588.8 689.85
Bus 3 586.8 687.16
Bus 4 899 799.11
Bus 5 1279.5 1279.87
It is observed that the time of clearing the fault is less when the system is provided with UPFC.
Here as can be seen from the table that the UPFC don’t have much impact on the active power flow of the
system but in case of fault, the oscillations produced in the system are much less in magnitude and also the time
of clearing the fault is less when the system is provided with UPFC.
Implementation of UPFC for Improvement of Power Stability
www.iosrjournals.org 50 | Page
References
[1]. N. G. Hingorani, L. Gyugyi, “Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems”, New
York: IEEE Press, 2000.
[2]. K. R. Padiyar, “FACTS Controllers in Power Transmission and Distribution”
New Age International Publishers.
[3]. R. Mohan Mathur, Rajiv K. Verma,” Thyristor Based FACTS Controller for Electrical Transmission System” Wiley-IEEE Press,
2002.
[4]. H. Saadat, “Power Stability Analysis”, TMH Publication Edition, 2002, pp. 460-526.
[5]. L. Gyugyi, T. R. Rietman, A. Edris, “The Unified Power flow Controller: A New Approach to Power Transmission Control” IEEE
Transactions on Power Delivery, Vol. 10, No. 2, April 1995, pp. 1085-1097.
[6]. Vibhor Gupta, “Study and Effects of UPFC and its Control System for Power Flow Control and Voltage Injection in a Power
System” International Journal of Engineering Science and Technology, Vol. 2(7), 2010, 2558-2566
[7]. Ejebe G., Irisari G., Mokhtari S., Obadina O., Ristanovic P., and Tong J., "Methods for Contingency Screening and Ranking for
Voltage Stability Analysis of Power Systems," IEEE Trans. Power Systems, Vol. 11, no. 1 , February 1 996, pp. 350-356
[8]. Gao B, Morison G., Kundur P., "Towards the Development of a Systematic Approach for Voltage Stability Assessment of Large-
Scale Power Systems," IEEE Trans. Power Systems, Vol. 11, no. 3, August. 1996, pp. 1314-1324.
[9]. M. R. Aghaebrahimi, M. Amiri, and M. Kamali Moghaddam, “A Short Circuit Study of an Induction Generator Wind Farm
Considering Wind Speed Changes”.
[10]. T. R. Mtshali, G. Coppez, S.Chowdhury, and S.P. Chowdhury, Member, “Simulation and Modeling of PV-Wind-Battery Hybrid
Power System” IEEE 2011, pp.1-7.
[11]. S. M. Muyeen, M. H. Ali, R. Takahashi, T. Murata, and J. Tamura, “Stabilization of Wind Farms Connected with Multi Machine
Power System by Using STATCOM” IEEE 2007, Paper ID 152, pp. 299-304
[12]. Ognedal R., Carlsen T., "Voltage Stability Condition in a Power Transmission System Calculated by Sensitivity Methods," IEEE
Trans. Power Systems, Vol.5, no. 4, November 1990, pp. 1286-1293.
[13]. P. Kannan, S. Chenthur Pandian, C. Ramesh, M. Rajaram, “Voltage Sag Compensation of Thirty Bus System using Unified Power
Flow Controller” European Journal of Scientific Research, ISSN 1450-216X Vol.51 No.3 (2011), pp.372-382
[14]. Padiyar K., Kulkarni A., "Control Design and Simulation of Unified Power Flow Controller," IEEE Trans. Power Delivery, Vol. 13,
no. 4, October 1998, pp. 1348-1354
[15]. Papic I., Zunko P., Povh D., Weinhold M., "Basic Control of Unified Power Flow Controller," IEEE Trans. Power Systems, Vol.
12, no. 4, November 1997, pp. 1734-1739
[16]. Popovic D., Hiskens I., Hill D., "Stability Analysis of Induction Motor Networks," Electrical Power & Energy Systems, Vol. 20, no.
7, 1998, pp. 475-487
[17]. Rahman M., Ahmed M., Gutman R., O'Keefe R., Nelson R., Bian J., "UPFC Application on the AEP System: Planning
considerations," IEEE Trans. Power Systems, Vol. 12, no. 4, November 1997, pp. 1695-1701
[18]. Schauder C., Gyugyi L., Lund M., Hamai D., Rietman T., Torgerson D., Edris A., "Operation of the Unified Power Flow Controller
(UPFC) Under Practical Constraints," IEEE Trans. Power Delivery, vol. 1 3, no. 2, April 1998, pp. 630-639
[19]. Vournas C., "Voltage Stability and Controllability Indices for Multi Machine Power Systems," IEEE Trans. Power Systems, Vol.
10, no. 3, August 1995, pp. 1183-1194

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Implementation of UPFC to Improve Power System Stability

  • 1. IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) e-ISSN: 2278-1676,p-ISSN: 2320-3331, Volume 8, Issue 6 (Nov. - Dec. 2013), PP 44-50 www.iosrjournals.org www.iosrjournals.org 44 | Page Implementation of UPFC for Improvement of Power Stability Savinder Malik1 , Lalit Dalal2 , Research Scholar1 , Research Scholar2 GITAM, Kablana, Jhajjar, Haryana, India-1241041, 2 Abstract:The focus of this research work is on a FACTS device known as Unified Power Flow Controller (UPFC), which can provide simultaneous control of basic power system parameters like voltage, active power flow, reactive power flow, impedance and phase angle. In this research work, simulation models for different multi machine systems are carried out, e.g. a hybrid power system, a power system with two synchronized hydro power stations etc., without UPFC & with UPFC located at the load end of the power system, has been developed. Simulation models have been incorporated into MATLAB based Power System Toolbox (PST) for their voltage stability analysis. These models were analyzed for voltage, active power flow, and reactive power flow and phase angle, with and without UPFC. The results of the power system with UPFC and without UPFC are compared and the conclusion is given at the end. Keywords: UPFC, FACTS, PST I. Introduction In today’s high complex and interconnected power systems, there is a great need to improve power utilization while still maintaining reliability and security. Reducing the effective reactance of lines by series compensation is a direct approach to increase transmission capability. However, a power transfer capability of long transmission line is limited by stability consideration [13].Oscillation of generator angle or line angle are generally associated with the transmission system disturbances and can occur due to step changes in load, sudden change of generator output, transmission line switching and short circuit [18]. Different modes of rotor oscillation are local mode, intra-area mode and inter-area mode. The frequency of oscillations of rotor swings varies from 0.2 to 4 Hz [2]. The lower end of frequency spectrum corresponds to inter-area modes, in which a large number of generators participated and their damping is difficult. This low frequency is important to damp as quickly as possible because they cause mechanical wear in power plants and cause power quality problem. If the electromechanical oscillations are not properly controlled in the electric power system operation, it may lead to a partial or total system outage [18]. Instability problems in power systems that can lead to partial or full blackout can be broadly classified into three main categories, namely voltage, phase angle and frequency related problems [3]. In early age this signal instability problem was solved by amortisseurs implemented in generator rotors, later with the application of fast excitation system this was solved by development & utilization of Power System Stabilizer (PSS) and however in modern power system due to the connection of power grids in vast area, for inter area oscillation damping due to the ability of controlling line impedance, power flow and bus voltage, Flexible AC transmission Systems (FACTS) devices implementation offers an alternative solution [19]. II. Case-With Two Hydro Generating Stations 1) Under 3-Phase to Ground Fault Condition without FACTS Devices
  • 2. Implementation of UPFC for Improvement of Power Stability www.iosrjournals.org 45 | Page 230 kV 500 kV 13.8kV 1200 MVA 13.8kV 1000 MVA Phasors powergui A+ B+ C+ A- B- C- a3 b3 c3 Zigzag Phase-Shifting Transformer Vphase V P Q Measurements V Lines A B C a b c Tr4: 1200 MVA 13.8 kV/230 kV A B C a b c Tr2: 800 MVA 230 kV/500 kV A B C a b c Tr1: 1000 MVA 230kV/500kV A B C A B C Three-Phase Fault1 m Pref Pm Vf Reg_M2 m Pref Pm Vf Reg_M1 Q Lines 0.5 0.833333 P Lines Vf_ m A B C Pm M2 L3_50km L2_50km L1_65km double circuit A B C Equivalent 500 kV 15 000 MVA A B C a b c B5 A B C a b c B4 A B C a b c B3 A B C a b c B2 A B C a b c B1 96.55 585.2 583.4 897.3 1279 Active Powers(MW) B1 B2 B3 B4 B5 A B C 200 MW A B C 195 MW Vf_ m A B C Pm 1000 MVA Vpos. seq. B1 B2 B3 B4 B5 Q B1 B2 B3 B4 B5 (Mvar) P B1 B2 B3 B4 B5 (MW) Fig.1 Two Hydro Generating Stations Under 3-Phase to Ground Fault Condition A three phase to ground fault is created at t=10 sec for 0.08 sec at bus 2 as shown in fig. 1. The active power, reactive power, voltage and phase angle curves with respect to time at different buses (B1 B2 B3 B4 B5) are shown in fig. 1.1.1-1.1.8 Fig 1.1 Active Power At Bus B2 Fig. 1.2 Reactive Power At Bus B2
  • 3. Implementation of UPFC for Improvement of Power Stability www.iosrjournals.org 46 | Page Fig. 1.3 Voltage Bus B2 Fig.1.4 Phase Angle At Bus B2 Fig. 1.5 Active Power At Different Bus Fig. 1.6 Reactive Power At Different Bus Fig. 1.7 Voltage At Different Bus
  • 4. Implementation of UPFC for Improvement of Power Stability www.iosrjournals.org 47 | Page Fig. 1.8 Phase Angle At Different Buses 2) Using UPFC under 3-Phase to Ground Fault Condition 230kV 500kV Hydro plant 13.8kV 1000 MVA Hydro plant 13.8kV 1200 MVA Shunt 500 kV, 100 MVA Series100 MVA,10% injection Phasors powergui Vphase Vdqref Vdqref V P Q Measurements V Lines1 UPFC1 UPFCphase UPFC Measurements Trip Bypass PQref Vdqref m A1 B1 C1 A2 B2 C2 UPFC UPFC A B C a b c Tr4: 1200 MVA 13.8 kV/230 kV A B C a b c Tr3: 1000 MVA 13.8 kV/230 kV A B C a b c Tr2: 800 MVA 230 kV/500 kV A B C a b c Tr1: 1000 MVA 230kV/500kV A B C A B C Three-Phase Fault m Pref Pm Vf Reg_M2 m Pref Pm Vf Reg_M1 -0.27 Qref (pu) Q Lines1 0.5 0.833333 Pref (pu) P Lines1 Vf_ m A B C Pm M2 L3_50km L2_50km L1_65km double circuit [PQref] [Vdqref] [Vdqref] [PQref] m A B C Equivalent 500 kV 15 000 MVA Bypass A B C a b c B_UPFC A B C a b c B5 A B C a b c B4 A B C a b c B3 A B C a b c B2 A B C a b c B1 196.8 689.7 687 795.7 1276 Active Powers(MW) B1 B2 B3 B4 B1 A B C 200 MW Vf_ m A B C Pm 1000 MVA Vconv_mag (pu)Vconv_mag (pu) Vconv_phase (deg.)Vconv_phase (deg.) Vpos. seq. B1 B2 B3 B4 B5 Q B1 B2 B3 B4 B5 (Mvar) P B1 B2 B3 B4 B5 (MW) Fig: 2 Two Hydro Generating Stations Using UPFC under 3-Phase to Ground Fault Condition A three phase to ground fault is created at t=10 sec for 0.08 sec at bus 2 as shown in fig. 2. The ratings of the various components used are given in appendix-B. The UPFC is made on at t=8sec and the power flow in the system goes from 5.87pu to 6.87pu. The active power, reactive power, voltage and phase angle curves, voltage at UPFC with respect to time at all five buses (B1 B2 B3 B4 B5) are shown in fig. 2.1-2.10. Fig 2.1 Active Power at Bus B2
  • 5. Implementation of UPFC for Improvement of Power Stability www.iosrjournals.org 48 | Page Fig. 2.2 Reactive Power at Bus B2 Fig. 2.3 Voltage at Bus B2 Fig. 2.4 Phase Angle at Bus B2 Fig. 2.5 Voltage at UPFC Fig. 2.6 Active Power at Different Bus
  • 6. Implementation of UPFC for Improvement of Power Stability www.iosrjournals.org 49 | Page Fig. 2.7 Reactive Power at Different Bus Fig. 2.8 Voltage at Different Bus Fig. 2.9 Phase Angle at Different Buses Fig. 2.10 Phase Angle at UPFC Active Power Flow (MW) Buses Without UPFC With UPFC Bus 1 95.2 194.9 Bus 2 588.8 689.85 Bus 3 586.8 687.16 Bus 4 899 799.11 Bus 5 1279.5 1279.87 It is observed that the time of clearing the fault is less when the system is provided with UPFC. Here as can be seen from the table that the UPFC don’t have much impact on the active power flow of the system but in case of fault, the oscillations produced in the system are much less in magnitude and also the time of clearing the fault is less when the system is provided with UPFC.
  • 7. Implementation of UPFC for Improvement of Power Stability www.iosrjournals.org 50 | Page References [1]. N. G. Hingorani, L. Gyugyi, “Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems”, New York: IEEE Press, 2000. [2]. K. R. Padiyar, “FACTS Controllers in Power Transmission and Distribution” New Age International Publishers. [3]. R. Mohan Mathur, Rajiv K. Verma,” Thyristor Based FACTS Controller for Electrical Transmission System” Wiley-IEEE Press, 2002. [4]. H. Saadat, “Power Stability Analysis”, TMH Publication Edition, 2002, pp. 460-526. [5]. L. Gyugyi, T. R. Rietman, A. Edris, “The Unified Power flow Controller: A New Approach to Power Transmission Control” IEEE Transactions on Power Delivery, Vol. 10, No. 2, April 1995, pp. 1085-1097. [6]. Vibhor Gupta, “Study and Effects of UPFC and its Control System for Power Flow Control and Voltage Injection in a Power System” International Journal of Engineering Science and Technology, Vol. 2(7), 2010, 2558-2566 [7]. Ejebe G., Irisari G., Mokhtari S., Obadina O., Ristanovic P., and Tong J., "Methods for Contingency Screening and Ranking for Voltage Stability Analysis of Power Systems," IEEE Trans. Power Systems, Vol. 11, no. 1 , February 1 996, pp. 350-356 [8]. Gao B, Morison G., Kundur P., "Towards the Development of a Systematic Approach for Voltage Stability Assessment of Large- Scale Power Systems," IEEE Trans. Power Systems, Vol. 11, no. 3, August. 1996, pp. 1314-1324. [9]. M. R. Aghaebrahimi, M. Amiri, and M. Kamali Moghaddam, “A Short Circuit Study of an Induction Generator Wind Farm Considering Wind Speed Changes”. [10]. T. R. Mtshali, G. Coppez, S.Chowdhury, and S.P. Chowdhury, Member, “Simulation and Modeling of PV-Wind-Battery Hybrid Power System” IEEE 2011, pp.1-7. [11]. S. M. Muyeen, M. H. Ali, R. Takahashi, T. Murata, and J. Tamura, “Stabilization of Wind Farms Connected with Multi Machine Power System by Using STATCOM” IEEE 2007, Paper ID 152, pp. 299-304 [12]. Ognedal R., Carlsen T., "Voltage Stability Condition in a Power Transmission System Calculated by Sensitivity Methods," IEEE Trans. Power Systems, Vol.5, no. 4, November 1990, pp. 1286-1293. [13]. P. Kannan, S. Chenthur Pandian, C. Ramesh, M. Rajaram, “Voltage Sag Compensation of Thirty Bus System using Unified Power Flow Controller” European Journal of Scientific Research, ISSN 1450-216X Vol.51 No.3 (2011), pp.372-382 [14]. Padiyar K., Kulkarni A., "Control Design and Simulation of Unified Power Flow Controller," IEEE Trans. Power Delivery, Vol. 13, no. 4, October 1998, pp. 1348-1354 [15]. Papic I., Zunko P., Povh D., Weinhold M., "Basic Control of Unified Power Flow Controller," IEEE Trans. Power Systems, Vol. 12, no. 4, November 1997, pp. 1734-1739 [16]. Popovic D., Hiskens I., Hill D., "Stability Analysis of Induction Motor Networks," Electrical Power & Energy Systems, Vol. 20, no. 7, 1998, pp. 475-487 [17]. Rahman M., Ahmed M., Gutman R., O'Keefe R., Nelson R., Bian J., "UPFC Application on the AEP System: Planning considerations," IEEE Trans. Power Systems, Vol. 12, no. 4, November 1997, pp. 1695-1701 [18]. Schauder C., Gyugyi L., Lund M., Hamai D., Rietman T., Torgerson D., Edris A., "Operation of the Unified Power Flow Controller (UPFC) Under Practical Constraints," IEEE Trans. Power Delivery, vol. 1 3, no. 2, April 1998, pp. 630-639 [19]. Vournas C., "Voltage Stability and Controllability Indices for Multi Machine Power Systems," IEEE Trans. Power Systems, Vol. 10, no. 3, August 1995, pp. 1183-1194