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542 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY
2013
Optimal Transmission Switching Considering VoltageSecurity and
N-1 Contingency AnalysisMojtaba Khanabadi, Hassan Ghasemi, Senior
Member, IEEE, and Meysam Doostizadeh
AbstractIn power system operation, transmission congestioncan
drastically limit more economical generation units from
beingdispatched. In this paper, optimal transmission switching as a
con-gestion management tool is utilized to change network
topologywhich, in turn, would lead to higher electricity market
efficiency.Transmission switching (TS) is formulated as an
optimizationproblem to determine the most influential lines as
candidatesfor disconnection. In order to relieve congestion without
vio-lating voltage security, TS is embedded in an optimal power
flow(OPF) problem with AC constraints and binary variables, i.e.,
amixed-integer nonlinear programming (MINLP) problem, solvedusing
Benders decomposition. Also, a methodology is presentedwhich
provides a guideline to the system operator showing theorder of
switching manoeuvres that have to be followed in orderto relieve
congestion. It is also shown that TS based on DC optimalpower flow
(DCOPF) formulation as used in the literature mayjeopardize system
security and in some cases result in voltagecollapse due to the
shortcomings in its simplified models. In orderto evaluate the
applicability and effectiveness of the proposedmethod, the IEEE
57-bus and IEEE 300-bus test systems are used.
Index TermsBenders decomposition, optimal power flow(OPF) and
N-1 contingency, transmission congestion, transmis-sion switching
(TS).
NOMENCLATURE
Indices:
, Index for bus.
Index for contingency.
, , , Number of buses, generators, loads and
lines,respectively.
Variables:
, Voltage magnitude and angle at Bus .
, Active and reactive power generation at Busin p.u.
Active power flow at Line in p.u.
Rective power flow at Line in p.u.
Apparent power flow at Line in p.u.
Marginal value in violation with increasegeneration for unit
.
Manuscript received January 13, 2012; revised May 10, 2012 and
June 18,2012; accepted June 30, 2012. Date of publication July 30,
2012; date of currentversion January 17, 2013. Paper no.
TPWRS-00044-2012.The authors are with the School of Electrical and
Computer Engineering,
University of Tehran, Tehran, Iran (e-mail:
[email protected];[email protected];
[email protected]).Digital Object Identifier
10.1109/TPWRS.2012.2207464
Marginal value in violation with changing instate of Line .
Binary variable which represents the state ofLine (0: open, 1:
closed).
Total generation cost in $/h.
, Active and reactive power mismatches at Busin p.u.
, Voltage magnitude and angle mismatches at Bus.
Supply bidding price from generator at Bus .
Parameters:
, Lower and upper limits for voltage angle at Bus.
, Lower and upper limits for voltage magnitudeat Bus .
, Lower and upper limits for active powergeneration at Bus .
, Lower and upper limits for reactive powergeneration at Bus
.
, Lower and upper limits for active power flow atLine in
p.u.
, Lower and upper limits for apparent power flowat Line in
p.u.
, Active and reactive power demand at Bus inp.u.
Maximum number of line switchings allowed.
Big positive multiplier.
Number of iteration.
Matrices:
Admittance matrix.
Susceptance matrix.
Conductance matrix.
Admittance angle matrix.
, , , Sub-matrices of Jacobian matrix.
0885-8950/$31.00 2012 IEEE
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KHANABADI et al.: OPTIMAL TRANSMISSION SWITCHING CONSIDERING
VOLTAGE SECURITY AND N-1 CONTINGENCY ANALYSIS 543
I. INTRODUCTION
T HE open access transmission plays a vital role in compet-itive
electricity markets. As in these markets, it is alwaysdesirable to
transmit power to all parts of network without vio-lating system
security constraints. The electrical power that canbe transmitted
between two locations in a network is limitedby several security
criteria such as voltage limits, lines thermallimits and stability
limits. When power cannot be transmittedto a part of network
because of violating one or more of thementioned security criteria,
the system is said to be congestedand consequently market power
problem is likely to occur [1].When congestion occurs, the most
economical generation unitscannot be fully dispatched to meet the
demand. Thus, expensivegenerators have to be dispatched instead
which would leadto market inefficiency. Therefore, congestion
problem in atransmission system should be addressed, which is
typicallyhandled by means of transmission congestion
managementschemes. These schemes are mostly based on
conventionaloptimal power flow (OPF) with objective functions such
as [2]: minimizing the number of control actions; minimizing the
cost of re-dispatch [3]; minimizing the deviations between pre and
post-dispatchsystems.
As one of the important and suitable solutions for con-gestion
management, optimal network reconfiguration hasbeen employed by
operators to improve operating conditions.Generally, two types of
switches are used for this purpose;sectionalizing switches and tie
switches, which are normallyclosed or normally open, respectively.
From time to time, thenetwork operators change the state of these
switches in orderto enhance system security. The network switching
can beclassified into two main categories [4]: 1) opening or
closingbranches and 2) substation switching.Since 1980, some
research work has been conducted on using
switching for network reconfiguration. Switching was first
in-troduced in [5], in which it was used as a tool for preventive
con-trol actions. The authors in [6] have used corrective
switchingto relieve line overloading. Switching actions such as
load shed-ding and network switching are formulated as a
mixed-integerproblem (MIP) [7]. In [8], DC load flow and line
outage distribu-tion factors have been used to determine the line
switching thatwould eliminate network congestions without making
overloadsin other parts of the system. The busbar reconfiguration
is alsoutilized to solve the branch overload problem [9]. The
z-matrixmethod is employed in [10] for finding the most influential
linesto be switched to resolve overloading problems.The authors in
[11] have employed the fuzzy set algorithm to
construct preventive and corrective switching actions in
distri-bution network. In [12], in order to reconfigure and balance
loadat a distribution system, a heuristic algorithm is used. In
[13], asensitivity matrix is used to find which line(s) switching
has thehighest impact on overloaded line(s). A discrete
optimizationalgorithm has been employed in [14] to find optimal
switchingactions which alleviate overloads while avoiding potential
over-voltage conditions. In [15], the authors have proposed a
methodwhich uses analytical equivalence of corrective switching for
asystematic search to enhance system security. Reference [16]
provides a comprehensive review about concept of
correctiveswitching actions.The application of TS in transmission
expansion planning is
demonstrated in [17] where switching actions are employed
aspowerful tools for respecting system security and decreasingtotal
operation cost. TS in security-constrained unit commit-ment (SCUC)
is discussed in [18] where the SCUC problem isdivided into the unit
commitment (UC) master problem and theTS subproblem; TS subproblem
uses the master problems so-lutions to find optimal dispatch of
generation units consideringthe system constraints.The authors in
[19] and [20] have proposed an approach based
on DC optimal power flow (DCOPF) which utilizes TS in orderto
remove congestion. They have also used TS to relieve con-gestion
with contingency analysis where problem is formulatedas an MIP and
solved based on DCOPF [21].However, they have not examined the
impact of switching on
important system variables such as bus voltages and
transmis-sion losses. A DCOPF followed by an ACOPF is used in
[22]which alleviates congestion and takes into consideration the
im-pacts of switching on mentioned variables. In each search
trialof the proposed procedure in [22], only one switching is
per-formed and this cycle will continue until no further optimal
TScan be found. Since the optimal TS is selected based on a
DCmodel, the output of this optimization problemmight not be
fea-sible in an AC model. Therefore, the algorithm in [22] may
notbe able to alleviate congestion in all conditions.It is good to
mention that other aspects of opening a line and
what consequences it can have in a power system should alsobe
considered; e.g., some unstable transients may get triggeredand/or
the voltage stability margin for the post-switching systemmay not
meet the criteria specified by the system
operationalrequirements.In this paper, an optimal TS based on an
ACOPF is used
which does not suffer from the mentioned shortcomings in
themethod in [22] and is also able to respect voltage security
cri-teria in the TS problem which has not been addressed in
pre-vious literature work. The resulted mixed integer nonlinear
pro-gramming (MINLP) problem is formulated such that efficientand
robust Benders decomposition algorithm is utilized to solveit. This
would ensure that the solution is not trapped at a locallyoptimal
point which can be encountered in famous solvers suchas BARON and
DICOPT.This paper is structured as follows: Section II provides
a
background on optimal TS based on an ACOPF in full
details.Section III represents solution method used to solve the
cor-responding MINLP problem using Benders decomposition.Section IV
represents the results of applying the proposedmethod in the IEEE
57-bus test system. Also, the results of TSbased on DCOPF are
provided and are compared to the onesof TS with AC constraints. The
impact of using tighter voltagebands is discussed and analyzed in
Section IV-C. Section Vproposes a method to find the order of
switchings that have tobe followed by the system operator. In
Section VI, the result ofTS with AC constraints based on priority
method in the IEEE300-bus test system is discussed. Section VII
summarizes themain findings of this work.
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544 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY
2013
Fig. 1. Block diagram of master problem procedure.
II. OPTIMAL TRANSMISSION SWITCHING BASED ON ACOPF
Figs. 1 and 2 show the presented outline of the optimal TS
tosolve transmission congestion problem in the system. Here,
thenumber of switching actions in the search trial of procedurecan
be greater than one and is not limited. However, the numberof
switching actions in a real power system is restricted due tothe
reliability of power system. Thus, one may enter a maximumfor
number of switching actions as shown in (9).As shown in Fig. 1, an
ACOPF with no switching is first run.
If no congestion occurs, no switching is required and the
resultsdo not need to be changed. In case of encountering
congestion,some line flows would reach their limits and
consequently eco-nomic supply offers would not be fully
dispatched.The system operator can use switching to fully or
partially
alleviate congestion problem. The output of this
optimizationproblem would identify line(s) that have to be outaged
so thatthe congestion can be relieved. Note that since AC
constraintsare used here, it is possible that no optimal TS is
found due tothe fact that opening lines may result in insecure
voltage levels.Within the context of TS based onDCOPF [19][21],
some linesmaybe identified as candidate lines for switching to
remove con-gestion but in a real power system these TS may lead to
busvoltages that do not respect voltage security requirements.
Thisfact has been demonstrated in the test system results used
inSection IV.In this paper, first, optimal TS problem is formulated
as an
MINLP. The main purpose is to minimize the overall cost
ofgeneration with regards to physical system constrains such asline
thermal and bus voltage limits. For example, the bus an-gles across
the system have to be maintained between upper andlower limits or
bus voltages across the system should not exceed
Fig. 2. Block diagram of subproblems.
certain levels. The line or lines that should be switched are
de-termined by means of an ACOPF:
(1)
s.t.
(2)
(3)
(4)(5)(6)(7)(8)(9)
where the voltage angle at each bus could change betweenand .
Also, , and is ob-
tained from following equations:
(10)
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KHANABADI et al.: OPTIMAL TRANSMISSION SWITCHING CONSIDERING
VOLTAGE SECURITY AND N-1 CONTINGENCY ANALYSIS 545
(11)
(12)
The results of this optimization problem determine which lineor
lines have to be outaged.
III. SOLUTION METHODThe TS problem formulated in the previous
section is an
MINLP problem. It should be noted that available solvers
forMINLP problems, in particular BARON and DICOPT, donot perform
well to solve the proposed problem, in terms ofcomputational time
and convergence characteristics [23]. Also,in this case, the
solution might not be a global one. To avoidthis issue, more
practical search algorithms such as Bendersdecomposition [24] have
to be employed. Therefore, Bendersdecomposition approach which has
been used widely [25][29]is applied here to solve the MINLP
problem.The first stage in Benders decomposition is a mixed
integer
linear problem denoted as master problem and the second oneis a
nonlinear subproblem. The master problem determinessystem
configuration and active power generation of each unit(Fig. 1).
Although line active power flow limits are checkedin the master
problem, bus voltage limits and reactive powerdistribution in power
system are not considered in the masterproblem. Therefore, the
subproblem checks the feasibilityof the master problem solution
from the viewpoint of ACconstraints. Then, violations could be
relieved by adjusting thepower generation of existing units or
modifying the list of linesto be switched previously determined in
the master problem.It should be noted that this approach is
incapable of finding
TS actions which are feasible and provide cost saving in
ACOPFperspective while being infeasible and/or not providing
costsaving in the DCOPF formulation. Note that these indicate
thecases that for instance, in the AC model, one line is loadedvery
close to its limit while being overloaded in the DC model.System
operators usually use security margins, e.g., 5% to ac-count for
errors in models and data; therefore, these cases wouldbe likely to
be filtered out. The TS subproblem consists of twomain blocks as
shown in Fig. 2. The TS feasibility check exam-ines the master
problem solution to find whether a feasible TSsolution can be found
in the base case. Furthermore, the sub-problem performs security
analysis for contingencies.More details about master problem and
subproblems are pro-vided in the following subsections.
A. Master Problem FormulationThe objective of the master problem
seeks to minimize the
overall operation system cost which is given in (13). The
masterproblem formulation is as follows:
(13)
s.t.
(14)(15)
(16)
(17)(18)(19)
(20)
(21)
where is the subproblem cost at iteration; and are the fixed
values calculated by masterproblem at iteration ; and in (18) and
(19) is a largepositive multiplier greater than or equal to[21].
Note that when , the value of is not importantwhereas would impose
a zero power flow on Line(17) while allowing different angles on
lines both ends using(18) and (19).The first term of the objective
function (13) represents the
operation cost. The second one means, through the real variable,
the feasibility cost due to an underestimation of the sub-
problem cost (system losses). The (21), referred to as
Benderslinear cut, couples master problem and subproblem by
updatingthrough and at each iteration. The formulation uses
binary variables specifying which line or lines have to
beoutaged from the test system to relieve congestion. Besides,
inorder to keep the system reliability on an acceptable level,
thenumber of lines connected to each bus is restricted to be
higherthan or equal to two after any switching action. Note that
for abus with only two connections, losing a connection would
dras-tically reduce its reliability. Mathematically, one has
(22)
in which is the set of lines connected to Bus .
B. Subproblem FormulationAs it was discussed earlier, TS
subproblem consists of two
stages, TS feasibility check and security analysis:1)
Feasibility Check: It tests the feasibility of master
problem solution. This stage is an NLP problem and its
objec-tive function is
(23)
s.t.
(24)
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546 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY
2013
(25)(26)(27)
where and are positive slack variables. andare the fixed value
calculated by master problem. The other
constraints for this optimization problem are the same as (3)
and(5)(12). Note that the solution obtained for the NLP problemmay
not be a global solution due to the non-convex, non-linearnature of
the problem. Also, if the solver is not able to finda solution, it
does not necessarily means that the problem isinfeasible.The
solution to the subproblem provides Lagrangian coeffi-
cients and dual values in the current itera-tion. Then, and are
used in the benders cuts formulationin the following iteration
(21). In this subproblem, transmissionflow and bus voltage
violations are relieved by adjusting activeand reactive power
injections. When , Benders cut (21)will be formed and added to
Master problem. The subproblemcuts are updated in each iteration
leading to an update in themaster problem solution; this iterative
procedure continues untilconverged solution is obtained. The
problem convergence cri-terion is defined as follows:
(28)
where is a small positive number adjusted by the user. Thelower
the , the higher the accuracy and the program extra time.2)
Security Analysis: The solution of TS feasibility check
subproblem has to be checked from the viewpoint of
systemsecurity. At this stage, AC security criteria are tested for
the
contingencies. The criteria include voltage levels andAC line
flows. For this purpose, a binary parameter isintroduced to model
each transmission lines status in Contin-gency . represents the
loss of Line in Contingency:
ifif (29)
This binary parameter is multiplied by admittance matrix
andconsequently transmission line outages have been modeledusing a
for loop over set of lines.The objective of this stage is to solve
a set of power flow
problems. This can be done based on Newton-Raphson methodby
minimizing real and reactive power mismatches while rep-resenting
voltage and flow limits. The feasibility cost is thusminimized
based on notation used in [26]:
(30)
where , , , and are positive slackvariables which model
fictitious generation in each bus in orderto make the power flow
equations feasible. The correspondingconstraints are
(31)
(32)(33)
where and are the bus voltage and apparent power flowafter
applying contingency , respectively.Here, (30)(33) represent an LP
problem which are used in
an iterative method yielding power flow solution. The
iterativemethod is as follows:Step 1) Calculate Jacobian
sub-matrices and the initial bus
mismatches and based on the valuescalculated in the previous
subproblem.
Step 2) Use an LP solver to minimize the objective function(30)
subject to the corresponding constraints.
Step 3) Update , , , and using calculatedand .
Step 4) Stop the process, if the objective function is
smallerthan a threshold and the mismatches are less than aspecified
value. Otherwise, go to Step 2.
If for a specific contingency, the objective function (30)
ishigher than the specified threshold after several iterations,
itmeans that the contingency does not pass the security anal-ysis
check. Therefore, the set of identified lines for switchingis
invalid and should be removed from the search space. Thiscan be
done by adding a new inequality constraint (34) to themaster
problem. This new constraint prevents the program fromgiving the
previously identified invalid set of candidate lines
forswitching:
(34)
where is the set of candidate lines leading to insecure
systemconditions. In rare conditions, it is possible that by
opening oneor more lines in addition to the lines in , the
contingencywould pass the security analysis check. However, from
prac-tical point of view, the system operator has to open one line
at atime (not all identified lines simultaneously). Therefore,
sinceopening the set of lines would lead to an insecure condi-tion,
they should be removed from the search space which isaddressed by
(34).
IV. IEEE 57-BUS TEST SYSTEM
The feasibility of the mentioned method has been tested in
theIEEE 57-bus test system. System data for this test system is
pro-vided in [30] and bid information is given in the Appendix.
Inthis system, there are 7 generators along with 80
transmissionlines. Also, the system provides 1250.8 MW active power
toserve the loads. Here, both Gen. 1 and Gen. 8 have lower
mar-ginal prices compared to other generation units. Hence,
thesegenerators are economical generation units and it is
desirableto fully dispatch without violating any security criteria.
In thissection, first, based on the gathered bid information from
gen-erators, an ACOPF is run to identify the transmission
conges-tion in the system. The results indicate that Lines 115, 89
and729 are congested resulting in utilizing more expensive
gener-ators to meet the demand. In order to relieve congestion, the
TSproblem has been utilized in two different forms: TS based
onDCOPF and TS based on proposed method with AC constraints.The TS
based on DCOPF has been used widely in the literature;therefore, we
here used it as well to demonstrate its shortcomingand the
necessity of checking AC constraints.
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KHANABADI et al.: OPTIMAL TRANSMISSION SWITCHING CONSIDERING
VOLTAGE SECURITY AND N-1 CONTINGENCY ANALYSIS 547
Fig. 3. Bus voltages for TS with AC constraints; the IEEE 57-bus
test system.
TABLE IDISPATCH RESULTS FOR PRE AND POST-TS SYSTEMS BASED
ON DCOPF; THE IEEE 57-BUS TEST SYSTEM
A. TS Based on DCOPF
The problem is formulated as an MIP with binary variables[19],
[20] and is solved in BARON. The results indicate thatLines 115,
729, 89, 2238, and 4849 are selected as can-didate lines that have
to be switched (opened) to remove trans-mission congestion problem.
The results of opening these linesare provided in Table I. By
opening the mentioned lines, thecheaper generators are dispatched
to higher levels. Therefore,the total generation cost has been
decreased from $19 021/h to$14 835/h. Also, the LMP at some buses
will be lower com-pared to the case that congestion exist. Although
this methodsuccessfully removes congestion and dispatches as more
eco-nomical units as possible, the system security is jeopardized.
Byopening the identified lines in an AC power flow program,
theresults show that this system would experience a voltage
col-lapse, i.e., the solution diverges, which is not acceptable
fromthe viewpoint of the system operator.
B. TS With AC Constraints
In this part, TS is formulated as described in Section III and
issolved using Benders decomposition method. The results yieldthat
Lines 115 and 34 are identified as the ones to be outagedin order
to remove congestion while respecting security and ACconstraints
across the system. The impact of TS is investigatedby means of some
system variables such as generation dispatch,system losses, LMP
variations and voltage profile. Note thatonly two lines (as opposed
to five lines in the DCOPF case)are selected as candidate lines for
switching since opening morenumber of lines would lead to insecure
system.1) Generation Dispatch and Losses: Table II shows the
re-
sults of generation dispatch and total generation cost before
and
TABLE IIDISPATCH RESULTS FOR PRE AND POST-TS SYSTEMS WITH
AC CONSTRAINTS; THE IEEE 57-BUS TEST SYSTEM
opening lines. As a result of opening two identified lines,
thetotal generation cost has been decreased and cheaper
generatorsare dispatched to higher levels; however, cost reduction
in thiscase is not as much as DCOPF case (17.5% compared to
22%reduction). The active and reactive system losses have been
in-creased in post-switching system as expected [31].2) Voltage
Profile: Fig. 3 demonstrates the voltage magni-
tude at load buses in the IEEE 57-bus test system before
andafter opening the mentioned transmission lines. The resultsshow
that as a consequence of opening lines, most bus voltagesincrease
while a few decrease. However, the average of busvoltages increases
from 1.03 p.u. to 1.04 p.u. Also, in thepre-switching system, the
minimum voltage is 0.98 p.u. at Bus31; after opening the
transmission lines the minimum voltagehas been increased to 0.99
p.u. Note that by including ACconstraints, the minimum voltage
criterion has been respectedand all the voltages are above 0.9
p.u.3) LMP: Fig. 4 and Table III display the impact of opening
identified lines on LMP at system load buses. Note that, be-fore
switching, the LMP fluctuations across the system is sig-nificant;
the maximum and minimum LMP are $209/MWh and$10/MWh, respectively.
On the other hand, the maximum andminimum LMP for post-switching
system have been changedto $18.1/MWh and $12.9/MWh, respectively.
Also, the averageLMP across the system has been decreased from
$78.7/MWh to$16.4/MWh. The maximum LMP deviation occurred at Bus
29where the LMP has been decreased from $209/MWh to $16.5/MWh.
Since after TS, the LMP variations across the systemis not as high
as pre-switching system, the congestion rent hasbeen decreased from
$23 594 to $834.
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548 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY
2013
Fig. 4. LMP variations at some load buses; the IEEE 57-bus test
system.
TABLE IIILMP VARIATIONS; THE IEEE 57-BUS TEST SYSTEM
C. Impact of Using Tighter Voltage Bands
As mentioned before, for the IEEE 57-bus test system, withTS
based on DCOPF, five lines were identified as the ones tobe
outaged. Also, in TS with AC constraints with asallowed voltage
band, only two switching actions were allowed.Here, voltage band is
restricted to . As a result ofapplying a tighter voltage band, only
one switching action isallowed (Line 115) in this case. Also, less
economic units aredispatched here to respect system voltage
security, thus resultingin higher total generation cost (cost
decreases from $20 156.6/hto $18 969.5/h, 5.9% reduction). Note
that in this case, the cost ishigher for both pre- and
post-switching systems and congestionis partially relieved which
was not the case for the TS based onDCOPF. Therefore, by using
tighter voltage bands in operation,congestion may not be completely
removed.
V. DETERMINING A PRIORITY LIST FOR LINES TO BE OPENED
By using the TS based on the proposed method, one can findthe
candidate lines that have to be opened to relieve congestion.The
system operator would also require a priority list for theselines
since line switchings in a real power system have to beperformed
one at a time and not simultaneously. In this section,a method is
proposed to find a priority list for opening identifiedlines.
Therefore, the master problem is formulated by limitingthe number
of switching actions to one . The blockdiagram for this method is
shown in Fig. 5. This procedure isrepeated until congestion is
fully or partially removed while foreach switching actions, and
voltage security criteria arerespected as well. Using this method,
the priority list for twoidentified lines in the previous section
is found as Line 115(1st, i.e., to be opened) and Line 34
(2nd).Table IV shows the impact of sequential TS on system
vari-
ables such as generation dispatch and losses. Note that after1st
TS, the total generation cost has dropped significantly from$19
021/h to $15 957.8/h (16.1% reduction) and does not change
Fig. 5. Block diagram to find a priority list for opening
candidate lines.
TABLE IVGENERATION DISPATCH; THE IEEE 57-BUS TEST SYSTEM
WITH VOLTAGE BAND BEING
much for the following TS action. Nevertheless,
transmissioncongestion in test system cannot totally relieved and
transmis-sion line between Bus 8 and Bus 9 is congested. Moreover,
thedrop in average LMP is also significant for 1st TS action.
Inother word, 1st TS has improved significantly both total
gener-ation cost and LMP variation. On the other hand, the 2nd
TSmarginally decreases total generation cost while
transmissioncongestion is totally relieved from the system. If only
one cor-rective switching can be performed and total generation
cost isimportant from the viewpoint of system operator, it may not
berequired to perform the 2nd TS.
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KHANABADI et al.: OPTIMAL TRANSMISSION SWITCHING CONSIDERING
VOLTAGE SECURITY AND N-1 CONTINGENCY ANALYSIS 549
TABLE VSYSTEM DISPATCH RESULTS; THE IEEE 300-BUS TEST SYSTEM
VI. IEEE 300-BUS TEST SYSTEMThe IEEE 300-bus test system as a
more realistic and larger
test system is used here. It consists of 69 generators, 411
trans-mission lines with total load of 23 525.8 MW and 7788
MVAr.Data for this system are available in [32]. The initial
ACOPFresults show that Lines 11628, 108109, and 28116 are
con-gested. Based on the method presented in Section V, the
pro-posed method is used here to identify which line or lines
haveto be outaged to solve transmission congestion problem. As
itwas discussed in previous section, the system operator needs
apriority list for performing TS. Therefore, the problem is
for-mulated with in each path of the algorithm in Fig. 5.The
required switching actions are identified and reported in
Table V. The first switching action (Line 108109) would re-duce
the total cost by 1.95%. It is worth mentioning that Line11628 is
removed from the candidate lines since by openingthis line,
reliability criterion (22) will be violated. Ignoring (22)would
result in selecting Line 11628 as the second switchingaction and
total generation cost would decrease to $337 855/h.In the second
run of the search trail in Fig. 5, Line 80104 is
identified as the second line to be opened which would reducethe
cost by 3.61% with respect to the base case. LMP varia-tions over
system buses has also been reduced after applyingthe switching
actions.Eventually, in the third run of search trail, Line 177 is
iden-
tified. Here, cost reduction is not significant and is mostly
dueto small reduction in active losses. The fourth run of search
trialin Fig. 5 cannot identify another line to be outaged. Note
thatthe congestion is not completely relieved since opening a
newline would jeopardize system security and thus it is not
allowedby the program.The case is tested on a 2.8-GHz, 16-Gb Ram
personal com-
puter. Note that the execution time highly depends on
systemconditions and the initial values given for the
optimizationproblem. For instance, the initial conditions for s can
be pro-vided based on our operation experience and system
conditions.This can significantly affect the execution time. The
executiontime for identifying the first TS action from ten
candidate linesand 340 contingencies is about 5 min. Contingencies
leading tosplitting the system to two islands have been ignored.
However,without providing candidate lines, the CPU time would
increasesignificantly (about 150 min).
VII. CONCLUSIONSIn this paper, transmission congestion
management using
transmission switching (TS) considering and voltage se-curity
criteria is presented and discussed. The TS is formulated
TABLE VISUPPLY BIDDING INFORMATION; THE IEEE 57-BUS TEST
SYSTEM
as an MINLP problem and decomposed into smaller problems,which
are solved using Benders decomposition, determiningthe most
effective lines to be opened in order to relieve con-gestion. Any
switching action which would violate voltagesecurity and/or
security criteria is deleted from the listof candidate lines for
TS. In some cases, maybe more thanone TS action is required for
transmission congestion relief.Therefore, a methodology is also
proposed to find a priority listproviding a guideline for operators
in taking switching actions.The results of TS with AC constraints
is also compared to thoseof TS based on DCOPF showing that DCOPF is
inadequateand may give results that can jeopardize system security
or insome cases may lead to voltage collapse. The effect of
voltagebands on TS with AC constraints is also discussed; with
tightervoltage bands, the number of TS actions that respect voltage
se-curity would decrease and consequently TS cannot
completelyremove congestion.The main contributions of this paper
are summarized as
follows: Transmission switching with AC constraints
(includingvoltage and security criteria) is formulated andused to
reduce extra generation costs imposed due totransmission
congestion.
Benders decomposition is employed to effectively solvethe
resulted MINLP problem.
A methodology is introduced providing the system oper-ator with
a priority list for performing switching actions.
APPENDIX
Table VI provides the supply bidding information for theIEEE
57-bus test system.
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Mojtaba Khanabadi received the B.Sc. degree fromthe University
of Qazvin, Qazvin, Iran, and the M.Sc.degree from the University of
Tehran, Tehran, Iran, in2009 and 2012, respectively.He has the
experience of working at Besat substa-
tion and the Caspian company. His interests includepower system
operation and optimization, electricitymarkets, and smart
grids.
Hassan Ghasemi (S01M07SM11) receivedthe B.Sc. and M.Sc. degrees
from the University ofTehran, Tehran, Iran, in 1999 and 2001,
respectively,and the Ph.D. degree in electrical engineering fromthe
University of Waterloo, Waterloo, ON, Canada,in 2006.He worked for
the market and system operation
division at the independent electricity system oper-ator (IESO),
Ontario, Canada, from 20062009. Cur-rently, he is an Assistant
Professor in the School ofElectrical and Computer Engineering,
University of
Tehran. His main research interests are power system operation
and control, en-ergy systems, electricitymarkets and system
identification applications in powersystems.
Meysam Doostizadeh received the B.Sc degree inelectrical
engineering from the University of ShahidChamran, Ahwaz, Iran, in
2009. He is currently pur-suing the M.Sc degree at the University
of Tehran,Tehran, Iran.His research interests are power system
optimiza-
tion, demand response programs, and integration ofdistributed
energy resources to smart power systems.