Optimal Transmission Switching Considering Voltage Security and N-1 Contingency Analysis

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

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.


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)


(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)


(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.


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.


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.


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.

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