Feuillet, Senior Member, IEEE Abstract—This paper discusses various aspects of unified power flow controller UPFC control modes and settings and evaluates their impacts on the power syst
Trang 1UPFC for Enhancing Power System Reliability
A Rajabi-Ghahnavieh, Graduate Student Member, IEEE, M Fotuhi-Firuzabad, Senior Member, IEEE,
M Shahidehpour, Fellow, IEEE, and R Feuillet, Senior Member, IEEE
Abstract—This paper discusses various aspects of unified power
flow controller (UPFC) control modes and settings and evaluates
their impacts on the power system reliability UPFC is the most
versatile flexible ac transmission system device ever applied to
improve the power system operation and delivery It can control
various power system parameters, such as bus voltages and line
flows The impact of UPFC control modes and settings on the
power system reliability has not been addressed sufficiently yet.
A power injection model is used to represent UPFC and a
com-prehensive method is proposed to select the optimal UPFC control
mode and settings The proposed method applies the results of a
contingency screening study to estimate the remedial action cost
(RAC) associated with control modes and settings and finds the
optimal control for improving the system reliability by solving
a mixed-integer nonlinear optimization problem The proposed
method is applied to a test system in this paper and the UPFC
performance is analyzed in detail.
Index Terms—Composite system reliability, optimal control
mode and settings, unified power flow controller (UPFC).
NOMENCLUTURE
Power flow equation
cost
Active and reactive power injection
of parallel inverter
Magnitude and phase angle of parallel inverter voltage
Active and reactive power injection
of series inverter
Magnitude and phase angle of series inverter voltage
Manuscript received August 05, 2009; revised October 30, 2009 Date of
pub-lication August 12, 2010; date of current version September 22, 2010 Paper no.
TPWRD-00590-2009.
A Rajabi-Ghahnavieh is with the Department of Electrical Engineering,
Sharif University of Technology, Tehran 11365-8639, Iran and also with the
Laboratoire de Génie Electrique de Grenoble, INPG/ENSIEG, Saint Martin
d’Here 38402, France (e-mail: a_rajabi@ee.sharif.edu).
M Fotuhi-Firuzabad is with the Center of Excellence in Power System
Con-trol and Management, Department of Electrical Engineering, Sharif University
of Technology, Tehran, Iran (e-mail: fotuhi@sharif.edu).
M Shahidehpour is with the Electrical and Computer Engineering
Depart-ment, Illinois Institute of Technology, Chicago, IL 60616 USA (e-mail: ms@iit.
edu).
R Feuillet is with the Laboratoire d’Electrotechnique de Grenoble, Saint
Martin d’Here 38402, France (e-mail: Rene.Feuillet@g2elab.inpg.fr).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPWRD.2010.2051822
Magnitude and phase angle of PB
Difference between PB and SB voltages
Active and reactive power injection
of PS
Currents of PB and SB
Equivalent reactance of parallel transformer
Equivalent reactance of series transformer
contingency Duration of contingency (in hours)
Curtailed load cost (in U.S$) of contingency
Curtailed load at point for contingency (j) (in megawatts) Curtailment cost of load point for duration (in U.S.$/megwatt-h) Remedial action cost of contingency
Re-dispatch cost of generating unit (g) (in U.S.$/MW)
MW re-dispatch of unit in contingency
Active and reactive power of unit (g) Generation cost of unit
Max and Min active power generation for unit
Max and Min reactive power generation for unit Vectors of active and reactive power generation, respectively
Vectors of magnitude and phase angle of bus voltages
0885-8977/$26.00 © 2010 IEEE
Trang 2Max loading of line
respectively
Voltage and current of PB for contingency
Voltage of PB and SB for contingency when UPFC is disconnected
Self-impedance of SB for contingency
Mutual impedance of PB and SB for contingency
Max and Min voltage of inverters
Max current of inverters
modes
Estimated when the control modes and injections of PS and SS
Post-contingency reactive injection
of PS for contingency for
Post-contingency active injection
of SS for contingency for
Post-contingency reactive injection
of SS for contingency for
Post-contingency active injection
of PS for contingency for
I INTRODUCTION
T HE UNIFIED power flow controller (UPFC) is one of the
most versatile flexible ac transmission systems (FACTS)
devices that has ever been used for the control and
optimiza-tion of power flows [1] Some practical applicaoptimiza-tions of UPFC
are reported in [2], [3] UPFC can also operate as STATCOM
or SSSC which would affect power flows and reliability indices
[3] UPFC consists of a series and a parallel inverter which
ex-changes active and reactive power to manipulate electric power
flows The inverters can operate in various control modes to
reg-ulate power system parameters, such as bus voltage magnitudes
and phase angles and transmission flows Active and reactive
In the past, little effort was devoted to quantitatively assess the impact of UPFC on the power system reliability In [4], the UPFC impact on system reliability is investigated in which a two-state up/down UPFC reliability model is considered and the UPFC is used to balance the power sharing between two par-allel non-identical transmission lines The UPFC operates in an automatic power flow control mode to adjust the flow on one line and the UPFC settings are selected to utilize the maximum transfer capacity of the lines The impact of UPFC application
on reliability indices is then analyzed However, the paper has neither discussed the impact of various UPFC control modes on reliability indices nor proposed a method for determining op-timal UPFC control modes and settings An extensive three-state UPFC reliability model is presented in [5] which incorporates failure and repair of various UPFC components A four-state model is presented in [6] to incorporate the operating states of UPFC in reliability assessments Such studies did not consider the impact of various UPFC control modes and settings in reli-ability analyses and did not address the impact of UPFC thor-oughly on the calculation of reliability indices Other studies found optimal UPFC parameters for maximizing transfer capa-bilities [7], minimizing active power losses [8], and improving transient responses of power systems [9]
This paper is aimed at finding the optimal UPFC control mode and settings to improve the composite reliability of power sys-tems when all UPFC components are available The proposed approach will minimize ESRAC for improving the system re-liability A selected set of contingencies are analyzed and the optimal power flow (OPF) is used to minimize RAC and cal-culate the optimal UPFC injections and the sensitivity of RAC
to UPFC injections The results of contingency analyses are used to calculate post-contingency injections of UPFC and to estimate the ESRAC associated with control modes and set-tings The optimal UPFC control mode and settings are obtained
by solving the proposed mixed-integer nonlinear optimization problem
The paper is arranged as follows: Section II discusses the structure and operation principles of a typical UPFC and describes the two-source power injection model for UPFC The proposed method is described in Section III The impact
of UPFC control modes and settings on reliability indices are discussed in Section IV and then the proposed method is applied to a test system to find the optimal control mode and setting of UPFC and to discuss various aspects of the method performance The proposed method is extended in Section V
to find optimal control mode and settings of two UPFC units Concluding remarks are finally summarized in Section VI
II UPFC: STRUCTURE, OPERATION,ANDCONTROL
A UPFC consists of two identical inverters which are con-nected in parallel and series to power systems through corre-sponding power transformers Fig 1 shows the single line dia-gram of a UPFC installed in a power system in which the UPFC
is represented by a voltage source models [1]
Trang 3Fig 1 Single line diagram of UPFC.
In Fig 1, the UPFC is installed between buses PB and SB
The net active power exchange of inverters is zero if we neglect
power losses in inverters
(1) Each inverter is equipped with a control unit for firing
com-mands according to measured signals and control modes of the
inverter The designated power system parameters are regulated
at the associated settings Control modes are given as follows
A Parallel Inverter
The parallel inverter can operate either as a constant reactive
power source or a voltage controller as follows [1]:
1) Reactive Control Mode (RCM): a constant positive or
negative reactive power is injected at PB
2) Voltage Control Mode (VCM): is automatically
reg-ulated in Fig 1 to maintain at associated settings
B Series Inverter
The control modes of the series inverter are as follows [1]
1) Power Flow control Mode (PFM): Fig 1 shows that
UPFC regulates and independently at associated
settings This control mode distinguishes UPFC from
STATCOM and SSSC
2) Voltage Control Mode (VCM): and are
deter-mined for regulating at associated settings
3) Voltage Injection Mode (VIM): and are
deter-mined to maintain at associated settings
A survey of various models is conducted in [10] for
incor-porating the UPFC in OPF studies Two models are proposed
by [11], [12] to incorporate the UPFC in OPF studies In this
paper, the two-source power injection model shown in Fig 2 is
used to represent the UPFC in optimal power flow studies In
this model, parallel source (PS) and series source (SS) are
con-nected to PB and SB, respectively, so that the total real power
injection of PS and SS is zero
(2)
In Fig 2, once the three independent injections of PS and SS
(i.e., and ) are known, the voltage and current of
series and parallel inverters in Fig 1 are calculated as follows:
(3)
Fig 2 Two-source power injection model for UPFC.
(4) (5) (6) Control modes associated with series and parallel inverters are also considered for PS and SS, respectively, as
(7)
(8) UPFC has other operating states for operating as STATCOM or SSSC when exploiting only one of parallel or series inverters, respectively In these states, the device manipulates power flows for the operation and control of power systems [1] The impact
of these two operating states on the system reliability are much smaller than the case when the UPFC operates in the up state (i.e., components are operational [2])
In this paper, the two-state up/down model is used for re-liability studies The proposed method finds the optimal con-trol mode and settings when the UPFC is in the up state The method can further be extended to include other operating states
of UPFCs The composite system reliability analysis considers various power system contingencies and performs post-contgency remedial actions [13] The system reliability indices in-cluding expected unserved energy cost (EUEC) and expected load curtailment (ELC), are given as
(9)
(10)
(11)
For each contingency, and are obtained by mini-mizing RAC as
(12) (13)
Trang 4Fig 3 Flowchart of the proposed method.
The optimization is subject to
(14) (15) (16) (17) (18)
in which (18) represents power flow for contingency
III DESCRIPTION OFMETHOD
The proposed method consists of the following four steps:
Step 1) selection of base case;
Step 2) contingency selection;
Step 3) contingency analysis;
Step 4) optimization of UPFC control modes and settings
Fig 3 describes the procedure for calculating the optimal UPFC
control mode and settings
A Selection of Base Case
The power system base case, without UPFC, minimizes the
total dispatch cost of committed generating units by applying
the optimal power flow as
(19)
Fig 4 Two-port model of the power system base case for contingency (j).
(20)
Using the base case solution, the UPFC is installed at designated
PB and SB buses
B Contingency Selection
Reliability assessment includes the analyses of selected con-tingencies The post-contingency condition of certain contin-gencies, including those which disconnect PB or SB, will not be affected by UPFC injections These contingencies are excluded from the optimal calculation of UPFC control mode and set-tings A NC set of contingencies is selected accordingly
C Contingency Analysis
Fig 4 shows the two-port equivalent model of the base power system from PB and SB points for each contingency where
(21)
In Fig 1, UPFC is disconnected by opening the breakers CB1
and A power flow analysis is performed for
in the Appendix to represent post-contingency power systems Then CB1 and CB2 are closed and the contingency is analyzed
to minimize RAC in which active and reactive dispatch of gen-erating units, PS and SS injections, and load curtailments are considered as remedial actions For NC contingencies, the set
of (11)–(17) and (22) are solved to incorporate PS and SS injec-tions
(22)
in which (22) represents the power flow equations for contin-gency when incorporating UPFC Here, (2)–(6) associated
Trang 5with the UPFC as well as limits on voltage, current, and apparent
power of the inverters are represented as
(23) (24) (25) (26)
We obtain the following items by solving (11)–(17), (22) and
considering (23)–(26) for each contingency :
• optimal UPFC injections for PS and SS (i.e.,
• sensitivity coefficients of RAC for the contingency
to injections of PS and SS, i.e.,
(27)
(28) (29)
These items as well as the parameters of two-port equivalent
model are used in the next step to find the optimal control mode
and settings
D Optimization of Control Mode and Settings
This part uses the parameters and coefficients obtained in step
C to calculate the optimal UPFC control mode and settings The
binary variables and represent the selection of
con-trol modes for PS and SS, respectively, as
selected
selected
The system ESRAC is defined as
(32)
The objective is to minimize the ESRAC associated with control
modes and settings of PS and SS (i.e.,
and , respectively)
(33) where ESRAC is calculated as the estimated value of RAC for
contingencies
(34)
the estimated post-contingency injections of PS and SS and sensitivity coefficients of (27)–(29) as
(35)
calculate the estimated post-contingency injections of
PS and SS, which are obtained as
(36) Equations (22)–(25) are considered for incorporating limits on inverter voltages and currents Since only one control mode is selected for series and parallel inverters
(37)
(38)
Equations (33)–(38) would form a mixed-integer nonlinear problem for calculating the optimal control mode and injec-tions of PS and SS The branch and bound technique is used here Once the optimal PS and SS injections are found, UPFC settings are determined by applying (3)–(6)
IV NUMERICALRESULTS
In order to demonstrate the impact of UPFC control modes and settings on reliability, the WSCC nine-bus test system [14]
is used in Fig 5 The system is modified by adding a 230 kV transmission line from B4 to B8 Since the WSCC reliability data are unavailable, those of the IEEE reliability test system (IEEE-RTS) [15] are used
A composite reliability evaluation has identified that the loading of L48 is the main source of system unreliability So,
in order to improve the system reliability, a UPFC is installed
on L48 at B4 to reduce L48 loading Fig 5 shows that PB is directly connected to B4 and L48 is connected between BS and B8 The UPFC is assumed to have two identical 160 MVA inverters interconnected by a DC link [2] The specification of the inverters and transformers are presented in Table I
The purpose of UPFC is to reduce the power extraction of L48
the loading of L48 by 18% Six cases are studied in which six possible combinations of control modes for parallel and series inverters are used For each case, the settings are determined such that the power extraction of L48 from B8 would be MVA The pre-contingency condition is the same for all cases
Trang 6Fig 5 UPFC application to the modified WSCC test system.
TABLE I UPFC SPECIFICATIONS
TABLE II RELIABILITY INDICES WITHOUT AND WITH UPFC
Table II shows the study results for the base case (without
UPFC, case 1) and the six cases with UPFC (cases 2 to 7)
In order to show how UPFC control modes and settings affect
the post-contingency following the outage of L57, the injection
of line L89 at bus B8 as well as the settings associated with
indi-vidual cases are shown in Table III In cases 2 to 5, the injection
of L89 is reduced from its original level in case 1, while it is
in-creased from its original level in cases 6 and 7 This shows that
the post-contingency condition depends on the UPFC control
mode Post-contingency overloads of L89 in cases 4, 6, and 7 in
Table III are mitigated by changing the settings associated with
the control modes of these cases Table IV shows the updated
settings and corresponding L89 injections following the outage
of L57 in cases 4, 6 and 7
By comparing the results in Tables III and IV, we learn that
the post-contingency condition is substantially improved based
on updated settings So proper selections of the UPFC control
modes and settings can lead to a considerable enhancement of
system reliability Table II shows that:
TABLE IV POST-CONTINGENCY L89 INJECTION FOR UPDATED SETTINGS OF UPFC
TABLE V OPTIMAL UPFC CONTROL MODE AND SETTINGS
1) although the pre-contingency power system parameters in cases 2 to 7 are the same, the reliability indices associated with those cases are different;
2) for cases 2 to 5, the UPFC application has led to improve-ments in reliability indices from 10% in case 2 to 2% in case 5;
3) UPFC applications in cases 6 and 7 would deteriorate reli-ability indices
The best reliability enhancement is achieved when the parallel inverter operates in the RCM mode and the series inverter op-erates in the VIM mode Now a set of 133 contingencies, in-cluding the power system base case and all single and double contingencies are selected except for those including the outage
of L48 which disconnects SB from the rest of the power system The optimal PS and SS control modes and injections are calcu-lated and presented in Table V
According to the inverter output voltage and series trans-former voltage ratings, the maximum series injected voltage is
30 kV which is about 13% of the nominal bus voltage Table V,
on the other hand, shows that the optimal series injected voltage
is about 0.042 per unit which is well below the maximum series injected voltage (i.e., 0.13 per unit) The optimal series injected voltage is determined to minimize the objective function in (33) and the limitation on the magnitude of series injected voltage has not influenced the optimal value of series voltage
So, the same solution would be obtained if the maximum series injected voltage was greater than 0.13 per units However, there could be some cases where the limitation on the maximum series injected voltage would restrict the optimal solution In these cases, both the magnitude and the angle of the optimal solution would change by increasing the maximum series
Trang 7TABLE VI RELIABILITY INDICES WITHOUT AND WITH UPFC APPLICATIONS
Fig 6 Rotor angle oscillation following short-circuit without uPFC.
injected voltage The reliability indices along with the value
of objective function associated with base case system and
optimal settings of Table V are shown in Table VI
The comparison of EUEC, ELC, and ESRAC, with/without
UPFCs shows that the optimal UPFC application would lead
to a considerable improvement in reliability In this context,
EUEC and ELC are decreased by 29% and 23%, respectively
Comparing EUEC, ELC obtained with the optimal UPFC
ap-plication shown in Table VI with those of cases 2 to 7 shown
in Table II, we learn that the indices are enhanced by 12% to
40% when the optimal control mode and settings are used This
shows that the optimal setting can considerably enhance the
im-pact of UPFC on reliability indices There is about 5%
differ-ence between ESRAC and for the optimal UPFC application
in Table VI The value of Z in (34) is an ESRAC estimate which
indicates the error in the ESRAC estimation is less than 5%
The impact of optimal UPFC on the dynamic performance of
the power system is evaluated A short-circuit fault is applied
to bus B6 at 1 s and is cleared after 5 cycles The resulting
rotor angle oscillations are shown in Figs 6 and 7 for the base
case system and the system with UPFC, respectively
The UPFC controller is included in Fig 7 which has damped
the rotor angle oscillations However, the maximum G3 angle
deviation is slightly increased from 0.3 radian in Fig 6 to 0.4
radians in Fig 7
Now we eliminate the optimal control mode selection from
the proposed method In essence, we obtain (39) by eliminating
the binary variables and from (33)
(39)
Fig 7 Rotor angle oscillations with UPFC application.
TABLE VII ESRAC WITH OPTIMAL SETTINGS
The set of equations resulting from (35)–(38) and (39) is solved for the cases shown in Table II The optimal UPFC control mode and setting are found and the corresponding cases are represented in Table VII The ESRAC of case 2 is the smallest while that of case 6 has the largest value This result explains the reason why the proposed method has chosen the control mode combination of case 2 as the best combination in Table V Table VII shows that ESRAC and are not the same However, the difference is small as they are both affected by the UPFC control modes and settings So would be used
to compare the impact of UPFC control modes and settings on ESRAC
V MULTIPLEUPFC APPLICATION
The proposed method is formulated and presented to select the optimal control mode and setting of one UPFC However, the method can be extended to calculate simultaneously the op-timal control mode and settings of multiple UPFC units The extension can be made without changing the basic techniques for calculating the optimal RAC, optimal UPFC injections, and the sensitivity coefficients in (27)–(29) The two-source model
of Fig 2 is used for all UPFCs and UPFC injections are con-sidered as a remedial action in (22) The optimal injections and sensitivity coefficients are then obtained for all UPFCs The two-port equivalent power system model of Fig 4 is re-placed by a port equivalent model in which is the number of UPFCs Equation (21) is extended by using self and mutual impedances of ports to represent the voltage and the cur-rent associated with each port Equation (35) is also extended
Trang 8TABLE IX RELIABILITY INDICES WITH OPTIMAL APPLICATION OF TWO UPFC%
to incorporate the impact of post-contingency injections of all
UPFCs in the estimation of
The proposed method is further extended to find
simultane-ously the control mode and settings of two UPFC units Here,
UPFC1 is installed on L48, bus B4 and UPFC2 is applied on
L57, bus B5 Table VIII shows that for both UPFCs, the
op-timal control mode for parallel and series inverters are chosen
as RCM and VIM, respectively The comparison of Tables VIII
and V shows that the application of UPFC2 has changed the
set-tings of UPFC1 Here, the injected series voltage is reduced and
the injected shunt reactive power is increased Table IX shows
the reliability indices for the optimal solution of the two UPFCs
The comparison of Tables IX and VI shows that the application
of second UPFC has slightly enhanced the reliability indices
Further enhancement is limited here by the small size of the
WSCC test system
VI CONCLUSION
This paper presented the optimal control mode and settings
of UPFCs A two-source power injection model was used for
UPFC and the impact of UPFC control modes and settings on
reliability indices were investigated It was shown that the UPFC
control mode has a considerable impact on post-contingency
conditions and reliability indices An approach was then
pro-posed to determine the optimal UPFC control mode and
set-tings The approach estimated the RAC associated with UPFC
power injections using the results of a contingency screening
study The estimated costs were then used in a mixed-integer
nonlinear optimization problem to find the optimal UPFC
con-trol mode and settings The approach was applied to a UPFC
installed in the modified WSCC test system The UPFC
appli-cation enhanced the reliability indices by 29% in the given
ex-ample The error in the estimation of RAC was about 5% The
impact of optimal UPFC settings on the dynamic performance
of the power system was evaluated It was observed that the
UPFC application would enhance the dynamic response of the
power system by damping the rotor angle oscillations The
pro-posed method was extended to find the optimal control mode
and settings of two UPFCs The application of the second UPFC
did not have a considerable impact on the reliability indices of
the given power system
the RCM mode and SS operate in the PFM mode (i.e., and ), the post-contingency injections are the same as pre-contingency injections
(40) (41) (42) For five other combinations of control modes of PS and SS, the calculation of post-contingency injections require pre-con-tingency injections and control modes of PS and SS as well as the post-contingency power system configuration The two-port equivalent model of Fig 5 obtained in the part C of Section 5
is used here to represent the post-contingency power system of selected contingencies in which
(43) and
(44) Once the UPFC model of Fig 2 is merged with the two-port equivalent model, the post-contingency apparent power of PS and SS (i.e., and , respectively, for contingency ), are obtained as follows:
(45) (46)
in which
(47) (48) Based on (43)–(48), and are obtained as
(49) (50) where (50) shows that the net real power injection of PS and
SS is zero For each of five remaining combinations of control modes, associated constraints are added to (49) and (50) to solve the resulting power flow problem and obtain the post-contin-gency injection as follows
Trang 9, are the same as pre-contingency injec-tions in (41)–(42) Since PS operates in the VCM mode, it
maintains the magnitude of PB voltage at its
pre-con-tingency level So
(51) The set of (49)–(51) is solved to obtain
2)
For PS, the post-contingency reactive injection
is obtained similar to (40) Since SS operates in the VCM mode, it maintains the voltage and
the phase angle of SB at the pre-contingency level So
(52) The set of (40) and (49)–(50) is solved to obtain
3)
solving (49)–(52)
4)
For PS, the post-contingency reactive injection
is the same as pre-contingency injections, which is similar to (40) SS operates in the VIM mode
and maintains the difference between post-contingency
voltages at PB and SB, and , respectively, at
its pre-contingency level (i.e., ) So
(53) The post-contingency injections of SS, and
, are calculated using (40), (49), (50), and (53)
The post-contingency injections of PS and SS, that is,
calculated by solving (49)–(51) and (53)
REFERENCES
[1] Y.-H Song and A T Johns, Flexible AC Transmission Systems
(FACTS), ser Inst Elect Eng Power Ser 30. London, U.K.: Inst.
Eng Technol Press, 2000.
[2] C D Schauder, L Gyugyi, M R Lund, M R , D M Hamai, T.
R Rietman, D R Torgerson, and A Edris, “Operation of the unified
power flow controller (UPFC) under practical constraints,” IEEE Trans.
Power Del., vol 13, no 2, pp 630–639, Apr 1998.
[3] S Y Kim, B Y Kim, J S Yoon, B H Chang, and D H Baek, “The
operation experience of KEPCO UPFC,” Electrical Machines and
Sys-tems 2005, pp 1–6, ICEMS.
[4] R Billinton, M Fotuhi-Firuzabad, S O Faried, and S Aboreshaid,
“Impact of unified power flow controllers on power system reliability,”
IEEE Trans Power Syst., vol 14, no 1, pp 410–415, Feb 2000.
[5] F Aminifar, M Fotuhi-Firuzabad, and R Billinton, “Extended
relia-bility model of a unified power flow controller,” Proc Inst Elect Eng.,
Gen Transm Distrib., vol 1, no 6, pp 896–903, Nov 2007.
[6] A Rajabi-Ghahnavieh, M Fotuhi-Firuzabad, and R Feuillet,
“Evalu-ation of UPFC impacts on power system reliability,” in Proc IEEE/
Power Eng Soc Transm Distrib Conf Expo., Apr 21–24, 2008, pp.
1–8.
[7] B Fardanesh, “Optimal utilization, sizing, and steady-state perfor-mance comparison of multiconverter VSC-based FACTS controllers,”
IEEE Trans Power Del., vol 19, no 3, pp 1321–1327, Jul 2004.
[8] H I Shaheen, G I Rashed, and S J Cheng, “Optimal location and parameters setting of unified power flow controller based on
evolu-tionary optimization techniques,” in Proc IEEE Power Eng Soc
Gen-eral Meet., Jun 24–28, 2007, pp 1–8.
[9] G K Venayagamoorthy, “Optimal control parameters for a UPFC in a
multimachine using PSO,” in Proc 13th Int Conf Intelligent Systems
Application to Power Systems, Nov 6–10, 2005, pp 1–6.
[10] M A Abdel-Moamen and N P Padhy, “Optimal power flow
incor-porating FACTS devices—Bibliography and survey,” in Proc IEEE
Transm Distrib Conf Expo., Sep 7–12, 2003, vol 2, pp 669–676.
[11] S Arabi and P Kundur, “A versatile FACTS device model for power
flow and stability simulations,” IEEE Tran Power Syst., vol 11, no 4,
pp 1944–1950, Nov 1996.
[12] S An;, J Condren, and T W Gedra, “An ideal transformer UPFC model, OPF first-order sensitivities, and application to screening for
optimal UPFC locations,” IEEE Trans Power Syst., vol 22, no 1, pp.
68–75, Feb 2007.
[13] R Billinton and R N Allan, Reliability Evaluation of Power Systems,
2nd ed New York: Plenum, 1996.
[14] P M Anderson and A A Fouad, Power System Control and Stability,
2nd ed New York: Wiley, 2003.
[15] IEEE Reliability Test System Task Force, “IEEE reliability test
system,” IEEE Trans Power App Syst., vol PAS-98, no 6, pp.
2047–2054, Nov./Dec 1979.
A Rajabi-Ghahnavieh (GSM’08) was born in Iran
in 1981 He received the B.Sc degree in electrical engineering from Isfahan University of Technology, Isfahan, Iran, in 2002 and the M.Sc degree in electrical engineering from Sharif University of Technology, Tehran, Iran, in 2004, where he is currently pursuing the joint Ph.D degree in elec-trical engineering with the Elecelec-trical Engineering Laboratory of the Institute National Polytechnique
de Grenoble, Grenoble, France.
His areas of interest are reliability assessment of power systems.
M Fotuhi-Firuzabad (SM’99) was born in Iran.
He received the B.S degree in electrical engineering from Sharif University of Technolog in 1986, the M.S degree in electrical engineering from Tehran University in 1989, and the M.S and Ph.D degrees
in electrical engineering from the University of Saskatchewan, Saskatoon, SK, Canada, in 1993 and
1997, respectively.
He joined the Department of Electrical Engi-neering at Sharif University of Technology in 2002 Currently, he is a Professor and the Head of the Department of Electrical Engineering, Sharif University of Technology Prof Fotuhi-Firuzabad is a member of the Center of Excellence in Power System Management and Control at Sharif University of Technology, Tehran, Iran.
M Shahidehpour (F’01) is Carl Bodine Professor
in the Electrical and Computer Engineering Depart-ment at the Illinois Institute of Technology, Chicago.
He is an Honorary Professor at Sharif University
of Technology and the North China Electric Power University.
Dr Shahidehpour was the recipient of the 2009 Honorary Doctorate from the Polytechnic University
of Bucharest He is the Vice President of Publications for the IEEE Power and Energy Society.
Trang 101979 and 1991, respectively.
He has been a Professor at the Ecole Nationale Supérieure d’Ingénieurs Electriciens de Grenoble and the Laboratoire d’Electrotechnique de Grenoble since 1998, where he was Deputy-Director in charge
of industrial relations from 1997 to 2002 His research activities include power system security, new technologies to enhance power system control and monitoring, and large
power-system management.