A Decomposition Approach for Solving Seasonal Transmission Switching

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IEEE TRANSACTIONS ON POWER SYSTEMS 1

A Decomposition Approach for Solving SeasonalTransmission Switching

Masood Jabarnejad, Jianhui Wang, Senior Member, IEEE, and Jorge Valenzuela

Abstract—Economic transmission switching has been proposedas a new control paradigm to improve the economics of electricpower systems. In practice, the transmission switching operationitself is a disruptive action to the system. Frequently switching linesinto or out of service can create undesirable effects on the securityand reliability of power systems and may require new investmentsin the automation and control systems. In this paper, we formulatean economic seasonal transmission switching model where trans-mission switching occurs once at the beginning of a time period(season) and then the transmission topology remains unchangedduring that period. The proposed seasonal transmission switchingmodel is a large-scale mixed integer programming problem. Theobjective of the optimization model is to minimize the total energygeneration cost over the season subject to loads and N-1 reliabilityrequirements. We develop a novel decomposition method that de-composes the seasonal problem into one-hour problems which arethen solved efficiently. We demonstrate our model and the decom-position approach on the 14-bus, 39-bus, and 118-bus power sys-tems and show potential cost savings in each case.

Index Terms—Decomposition, mixed integer programming,power generation dispatch and economics, seasonal transmissionswitching (STS).

NOMENCLATURE

Indices

Transmission lines.

Generators.

Buses.

Origin bus for line .

Destination bus for line .

Hours.

Bins.

Contingency scenarios.

Sets

Set of lines consuming power from bus .

Manuscript received September 20, 2013; revised January 22, 2014, May 16,2014; accepted July 15, 2014. Paper no. TPWRS-01219-2013.M. Jabarnejad and J. Valenzuela are with the Department of Industrial and

Systems Engineering, Auburn University, Auburn, AL 36849 USA (e-mail:[email protected]; [email protected]).J. Wang is with Argonne National Laboratory, Argonne, IL 60439 USA

(e-mail: [email protected]).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/TPWRS.2014.2343944

Set of lines injecting power to bus .

Set of in-service lines in transmissiontopology .

Set of generators at bus .

Set of buses with load.

Parameters

Number of transmission lines.

Number of generators.

Number of buses.

Number of hours.

Number of bins.

Operation cost of generator .

Net load at bus at hour .

Representative load at bus in bin .

Peak load at bus in the planning season.

Number of load vectors in bin .

Electrical susceptance of transmission line .

Min and max capacity of generator .

Min and max voltage angle at bus .

Thermal Capacity of transmission line .

State of line under scenario .

State of generator under scenario .

Sufficiently large number.

Optimal generation cost under topology atload vector .

Variables

Power generated by generator at hourunder contingency scenario .

Voltage angle at bus at hour undercontingency scenario .

Real Power flow transmitted by line at hourunder contingency scenario .

Load variable for bus .

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2 IEEE TRANSACTIONS ON POWER SYSTEMS

Objective function in the load lower-boundand load upper-bound problems.

Binary decision variable representingswitching state of line (0 out of service, 1in service).

Transmission topology .

I. INTRODUCTION

T HE transmission-line network is usually considered to bea static structure when determining the optimal economic

dispatch of power generators. However, it has been pointedout in [1] that switching transmission lines into/out of servicehas multiple benefits. The hourly-based optimal transmissionswitching (TS) problem was first introduced in [2]. It is mod-eled as a mixed integer program (MIP) based on the traditionaldc optimal power flow (DCOPF) problem. The objective of theoptimization model is to minimize the energy generation costfor one hour subject to supplying the load at that hour. Theoptimal TS problem was extended in [3] to include N-1 relia-bility requirements. Constraining the transmission switching to

requirements ensures that the line on and off plan meetsthe NERC’s single contingency reliability standard for powersystems. A transmission switching model that includes unitcommitment and constraints has been proposed in [4].All of these studies have reported noticeable savings in powergeneration costs when using transmission switching.Different aspects of the optimal TS problem have been re-

ported in the literature [5]–[11]. A just-in-time concept has beenadded to the optimal TS problem in [5] to improve the effi-ciency of a power system by removing inefficient lines fromservice and only using those lines in unusual situations. The ef-fects of transmission switching on electricity markets were in-vestigated in [6]. The study showed that transmission switchingmay result in considerable variability in nodal prices, generatorpayments, and load payments. The authors concluded that thetransmission topology planning should be controlled and man-aged by unbiased and independent agencies with no interest inthe financial outcomes of the switching decisions. In [7], the au-thors developed a disjunctive programming model to enhancethe static security of transmission switching operations. Trans-mission switching has also been applied in capacity expansionplanning ([8], [9]) and in security constrained unit commitment([10], [11]).The formulated MIP for the hourly-based optimal TS is

difficult to solve [2], [4], [12]. In [12], the authors show that thesymmetry, which is the presence of more than one transmissionline with the same impedance, thermal rating, and terminalbuses, can adversely affect the computational requirementfor solving the optimal TS problem. They introduce sym-metry-breaking constraints and branching methods to deal withthe symmetry in lines. To solve the optimal TS problem muchfaster, some heuristics have been proposed. A heuristic methodhas been reported in [13]. The method is based on a line-rankingparameter calculated using primal and dual solutions of the

DCOPF problem. The line-ranking is used to detect lines thatcarry power flows from buses with high marginal cost to buseswith low marginal cost. The detected lines are switched out ofservice. In [14], four transmission switching criteria are intro-duced to detect the switchable set of candidate lines. Anotherheuristic has been developed in [15]. The method uses twoprescreening strategies to reduce the number of to-be-examinedtransmission lines for the optimal TS problem.The economic transmission switching studies in [2]–[6] con-

sider hourly TS for reducing costs. However, TS operation itselfis a disruptive action, and frequently switching lines into or outof service can create undesirable effects on the security and re-liability of power systems [7]. In this paper, we formulate aneconomic seasonal transmission switching (STS) model wherethe economic TS operation occurs once at the beginning of atime period (e.g., season), and then the transmission topologyremains unchanged during that period. The objective of our STSmodel is to minimize the total generation cost over the seasonsubject to loads and reliability requirements. We want toemphasize that the season can be defined to be a week, a month,or any other desired time period. It should be mentioned that pe-riodic switching of transmission lines has been used for mainte-nance ([16], [17]), and also for making trade-offs between pro-tecting against potential contingencies in winter versus avoidingpotential overloads in summer [1]. Our seasonal TS focuses onthe economics of switching for cost reductions. The contribu-tions of this paper are summarized as follows.1) The proposed STS model is unique in terms of consideringthe economic switching action once in a multiple time pe-riod which is studied for the first time in this paper.

2) The STS model is very large in size compared with earlierTS models. The load lower bound and upper bound ap-proaches, proposed in this paper, significantly reduce thetime required for solving the STS problem.

3) The decomposition approach introduced in this paper is anovel method that enables breaking the seasonal probleminto one-hour problems which can be solved in a reason-able time.

This paper is organized as follows. Section II describes theSTS model. To solve the STS model efficiently, a decompo-sition approach is developed in Section III. Sections IV–VIare devoted to conduct experiments of the STS model and theproposed decomposition approach on the 14-bus, 39-bus, and118-bus power systems. Section VII analyzes the saving dif-ferences between the hourly and the seasonal TS. Section VIIIgives the conclusions.

II. STS SWITCHING MODEL

The optimal TS problem in [2] is modeled as a mixed-integerlinear program where the transmission topology is assumed tobe flexible. Here, we model the economic STS problem as amixed-integer linear program where the transmission topologycan change only once in a multiple time period. Our model alsoincludes the reliability requirements as in [18] and thevariability of loads throughout the season. Since ourmodel is forthemidterm seasonal planning purposes, we ignore the temporal


JABARNEJAD et al.: DECOMPOSITION APPROACH FOR SOLVING SEASONAL TRANSMISSION SWITCHING 3

constraints for the units such as ramping limits. The STS modelis described by

(1a)

(1b)

(1c)

(1d)

(1e)

(1f)

(1g)

The objective function (1a) minimizes total electricity genera-tion costs over the planning season when the system is operatingwithout any contingency. Meeting all loads over the planningseason is satisfied by constraints (1b). In the power balance con-straints (1b), a net load (i.e., the forcasted load minus theforecasted wind) at each hour is considered. The physical rela-tions between voltage angles of connected buses and the powerflow in connecting lines are represented by constraints (1c) and(1d). In constraints (1c) and (1d), the state of binary variablesdenotes that throughout the season line is either in service

or switched out of service . The is thedisjunctive parameter. By setting the value of to be suffi-ciently large, the inequality constraints (1c) and (1d) will be re-dundant when the corresponding line is switched out of service.Efficiently tuning the disjunctive parameter is discussed in[19]. In this paper, we use a fixed value of for

which was also used in [2]. Transmission thermal limits areenforced by constraints (1e), generators’ capacity by (1f), andvoltage angle limits by (1g). The left- and right-hand sides ofconstraints (1e) are multiplied by binary variables to ensurethere is no power flow in lines that are out of service. The bi-nary parameters and are used in the model to includethe contingency scenarios such as

(2a)

(2b)

A value of means that line is under contingency andtherefore it is not working. Similarly, a value of meansgenerator is not working. The noncontingency scenario (i.e.,the normal operation without any contingency) is representedby constraints (1b)–(1g) with to ensure that the system isfeasible (reliable) at every hour when there is no contingency.The contingency scenarios are represented by constraints(1b)–(1g) with .

III. DECOMPOSITION APPROACH

The hourly-based TS problem is an NP-Hard problem [6].The STS problem (1) is much larger than the hourly TS problembecause it includes multiple time periods and reliabilityconstraints. Directly solving the STS problem using CPLEX isdifficult for small power systems and impossible for larger sys-tems. To overcome this challenge, we develop a decompositionapproach. First, a few definitions are introduced, and two prop-erties of the STS problem are explored and proved. Then thedecomposition approach is described in detail.Given a load vector at hour , its total load is defined as

the sum of its bus loads which is equal to . The loadvectors in a season are sorted with respect to their total loads indescending order. Therefore, in the set of sorted load vectors,the load vector with sort index 1 has the highest total load, theload vector with sort index 2 has the second highest total load,and so on. By the sort index of a load vector we mean the po-sition of that load vector in the set of sorted load vectors, andnot the hour that the load vector is forecasted. The sorted loadvectors are grouped into bins. If bin is not the last bin (i.e.,

), then that bin includes load vectors with sortindexes to . If bin is the last bin(i.e., ), then it includes load vectors with sort indexes

to . Grouped load vectors in bin arerepresented by the representative load vector which has thehighest total load in bin , that is,and . In our decomposition approach,the goal is to find a transmission topology that minimizes thecost for supplying the representative load vectors and ensuressupplying other load vectors in the planning season. The numberof grouped load vectors in a bin is used as a weight to esti-mate the total generation cost for that bin. The user of our modelcan change the number of bins in the model and make atrade-off between the amount of achieved cost reduction andthe amount of time it takes to solve the problem. For exampleif a user sets , then the STS model will include all loadvectors in the season and the decomposition approach will findthe optimal solution with the lowest generation cost. But it willtake the longest time to solve the problem. Now consider thefollowing problem:

(3a)

(3b)

(3c)

(3d)

(3e)

(3f)

(3g)

(3h)

Problem (3) is a modified DCOPF problem in which the trans-mission network is fixed to the topology . As problem (3) is for



one hour, we dropped the hour index from all variables andparameters. The problem (3) is a minimax problem where wewant to minimize the maximum ratio of the bus load to the peakload at all buses, i.e., . The value of thevariable represents the largest ratio of the load variables to thepeak loads. Constraints (3b) implement the minimax structureof the problem. The (3c) ensure that the net power balance ateach bus meets the load variable . The power flow equations,thermal ratings, generators’ capacity, and voltage angle boundsare represented by constraints (3d)–(3g), respectively. The goalof the problem (3) is to find the lowest load vector that can besupplied under the fixed topology . We call the problem (3) theload lower-bound (LLB) problem. The load upper-bound (LUB)problem is obtained from the LLB problem where we maximizethe variable instead of minimizing it and we change the signin constraints (3b) to .Property 1: Let and denote optimal load solutions

to the LLB and LUB problems, respectively. Then any loadvector in the set

satisfies the constraints (3c)–(3h).Proof: Assume that denotes the solution space for con-

straints (3c)–(3h). Because constraints (3c)–(3h) are linear, theis a convex polyhedron. This means that the solutions inside

or on the edge of satisfy constraints (3c)–(3h). As constraints(3c)–(3h) in both LLB and LUB problems are the same, the loadsolutions and are inside or on the edge of . All loadvectors in the set are between load solutions andand therefore inside or on the edge of the which concludesthat any satisfies constraints (3c)–(3h).Property 1 indicates that, for checking the feasibility of a

topology in a season, it is sufficient to check the feasibilityof at load vectors . We call a transmission topology asglobal feasible if that topology satisfies constraints (1b)–(1g) forall hours . Also, we call a topology global optimalat load vectors if that topology is the optimalsolution to the problem (1) with load vectors .Now, assume that, instead of solving the STS problem (1) withall representative load vectors, we solve the problem with oneparticular load vector. The following property holds for the STSproblem (1) with one-hour load.Property 2: Assume and are global feasible and optimal

topologies at load vectors and , respectively. Also assumethat is the global optimal topology at load vectorsand . Then the inequality

holds. Note that denotes the optimal ob-jective function value (generations cost) under topology atload vector .

Proof: This property is proved by contradiction. As-sume that the inequality

does not hold. This means eitheror holds. The

inequality is not satisfied as itviolates the optimality of the topology at load vector .On the other hand, the topology is optimal at load vectorand its objective function value is the lowest satisfying

. By adding two inequali-ties and

Fig. 1. Pseudocode for proposed decomposition algorithm: part I.

we have. This means topology is a better

solution at load vectors and than topology whichviolates the assumption that topology is the global op-timal at load vectors and .Property 2 indicates that, for finding the global optimal

topology at load vectors and it is enough to enumeratethe candidate topologies with generation costs in the range

. Properties 1 and 2 are used todevelop a decomposition algorithm. First the STS problem isdecomposed into one-hour load problems. The algorithm solvesthe STS problem with load vector and finds the optimaltopology at . Based on Property 2, the algorithm moves tothe STS problem with load vector and finds the global op-timal topology at and . Then the algorithm moves to loadvector and finds the global optimal topology at , and. The algorithm continues to iterate until all considered load

vectors are enumerated. Property 1 is used at each iteration toefficiently check the global feasibility of candidate topologies.The pseudocode of the proposed decomposition algorithm is

provided in Figs. 1 and 2. In the main code in steps 4)–7), thelines are switched out of service one at a time, and the feasi-bility and generation cost of the resulting transmission networkis examined. Using the obtained information, a heuristic is usedin steps 8)–120 to construct an initial topology that is feasibleand also results in less generation cost than the full topologywithout transmission switching. The constructed topology is de-noted in the code as . In steps 13)–15), the is used to find



Fig. 2. Pseudocode for proposed decomposition algorithm: part II.

Fig. 3. 14-bus power system.

the initial global optimal topology considering the con-straints. First, the optimal topology at the first representativeload without considering constraints is found in step 13).In step 14), the candidate topologies with generation cost lowerthan or equal to the cost of and higher than or equal to the costof are collected in the set . The function “EnumTopols()”is used in step 15) to find the best topologies in and reportas the initial global optimal topologies. The function “Enum-Topols()”, defined in Fig. 2 in steps 23)–35), enumerates inputtopologies and finds the best one(s) in terms of global feasibilityand least generation cost over all representative load vectors. Inthe second part of the main code [steps 16)–22)], the decompo-sition approach is applied to find the global optimal topologies.In the loop in steps 16)–21), the remaining representative loadvectors are enumerated and the global optimal topologies areupdated. Finally, global optimal topologies and total generationcost are reported in step 22).In the following sections, all experiments are conducted on

a computer with Intel Celeron CPU 1005M @ 1.90 GHz and4 GB of RAM memory. The decomposition algorithm is codedin C programming language. The CPLEX Version 12.5 is usedto collect candidate topologies and to solve the LPs and MIPs.

TABLE I14-BUS POWER SYSTEM

Fig. 4. Total load in different hours of summer.

Also, a value of 0.6 radians is considered for minimum/max-imum voltage angles at all buses.

IV. EXPERIMENTAL RESULTS ON THE 14-BUS SYSTEM

The 14-bus power system1 has five generators, 20 lines, and11 loads, as shown in Fig. 3. As the thermal capacities of trans-mission lines in the 14-bus system are not provided, we confinedthe maximum limit of power flow in every transmission line to150 MW. For each generator, the quadratic cost function, takenfromMatpower [20], is replaced with one straight-line segment,and the slope of the line is considered as the linearized cost co-efficient for that generator. The 14-bus system is summarizedin Table I. To generate the seasonal loads, first we normalizethe hourly load data from [21] for the regions PJME, PJMW,and COMED and for the summer season (Jun 01–August 31) ofthe year 2012 which is hours of data for eachregion. We assume that, in the 14-bus system, the normalizedload profile for buses 1 through 3 are the same with the nor-malized load profile for region PJME, for buses 4–6 the samewith region PJMW, and for buses 7–14 the same with regionCOMED. The normalized load data in each region is multipliedby 1.6 times the corresponding system load at the 14-bus systemto generate different loads at every hour. The 1.6 times the loadat the 14-bus system represents the extreme power consumptionin a typical hot summer. The generated seasonal load profile isdepicted in Fig. 4. We limit the maximum number of switchableline candidates to 1 and 2, respectively, and compare it with thecase where no limit on the maximum number of switchable linesexists. Then we analyze the resulting impacts of the switchingon the total generation cost and reliability requirements in theseason.1) Switching One LineOut of Service: The transmission lines

in the 14-bus system are switched out of service one at a time

1[Online]. Available: http://www.ee.washington.edu/research/pstca/



TABLE IIEXPERIMENTS WITH ONE LINE OUT OF SERVICE

and the reduction or increase in costs are calculated. In the cal-culation of costs, the 2208 hours of load data is used. The re-sults are summarized in Table II, where the rows are sorted inascending order of total cost in the season. The results show thatswitching one of the lines 3, 4, 5, 8, 9, 15, 16, or 17 out of ser-vice can decrease total generation costs. Switching line 4 outof service results in the lowest generation cost of $20 061 606,which is $194 752 or 0.96% saving. Switching line 3 or 5 out ofservice also results in considerable savings of 0.69% and 0.95%respectively. Switching any of lines 12, 18, and 19 out of ser-vice has the least impact on generation costs in the consideredseason. The worst impact on costs occurs when line 1 or 2 isremoved from service, which results in 4.45% increase in costs.The power system without one of the lines 1, 2, 4, 5, 7, 8, 9, 10,13, or 15 still remains reliable. Switching line 4 out ofservice noticeably decreases the cost and preserves thereliability requirement.2) Switching Two Lines Out of Service: Experiments with

two lines out of service are conducted. There are 190 pair-wisecombinations of the 20 lines in the 14-bus system. The N-1 re-liability status is preserved in only 39 of the 190 pairs with twolines out of service. For those 39 pairs of lines with status,the percentages of cost savings are summarized in Table III. Inthis table, L4 means line 4 is out of service, L5 means line 5 isout of service, and so on. The values in Table III indicate the per-centages of change in the generation cost if the correspondinglines in the very top and right are switched together. The highestsaving of 2.83% results from switching lines 4 and 5 out of ser-vice. When compared with seasonal generation cost with fulltopology operation, this is a $572 395 reduction in the cost. Thesecond highest saving occurs when lines 5 and 15 are removed

TABLE IIISAVINGS (%) WITH TWO LINES OUT OF SERVICE

from the service which results in 1.05% or $212 939 saving. Theworst case occurs when one of lines 1 or 2 is switched alongwithany of lines 4, 5, 7, 8, 9, 10, 13, or 15 where it results in 4.45%increase in the generation cost.3) Finding the Optimal Seasonal Switching Solution: In

the third case, we do not limit the number of lines that canbe switched out of service. In other words, any number oflines can be removed from service. The bin number is set to100 and the representative load vectors are calculated in thesame way explained in Section III. After running the decom-position algorithm using the representative loads, it finds thatthe global optimal topology is to switch lines 4, 5, and 15 outof service. The total generation cost of the found solution inthe whole season with 2208 hours of loads is $19 682 878,while if no-switching is allowed, the generation cost increasesto $20 256 358. The implementation of this solution gives a2.83% reduction in cost ($573 480 saving). The seasonal savingis consistent with the findings of experiments with one line andtwo lines out of service. The STS problem is solved by the de-composition algorithm with (i.e., with all 2208 loadvectors) to validate the found optimal solution with(i.e., with 100 representative load vectors). The solution with

is the same with the findings of the model with. The decomposition algorithm solves the problem

with in one and a half minutes and the problem within 3 hours and 58 minutes. Hence, modeling the

problem with representative loads reduces the computationaltime significantly and offers the same quality solution at thesame time. We also applied CPLEX on the same problem with2208 h of loads. After 6 hours of running time, CPLEX couldnot find a transmission switching solution. The differences ingeneration costs between the global optimal topology and thefull topology are depicted in Fig. 5(a) and (b) on the daily basisand the total load basis, respectively. Fig. 5(a) shows that thehighest cost saving occurs during day 48 which corresponds toJuly 18. The results in Fig. 5(a) are fairly consistent with thedata in Fig. 4, in which the severe peak-load hours are expe-rienced in month of July. The relationship between peak-loadtimes and saving amounts are better shown in Fig. 5(b), inwhich the total loads for different hours are sorted from thelowest to the highest. As this figure indicates, there are positivecost differences at total loads 214 to 406 MW/h meaning thatswitching lines 4, 5, and 15 results in less generation cost



Fig. 5. Generation cost difference between the full topology and the switchedtopology (a) in different days and (b) in different total loads.

TABLE IV39-BUS POWER SYSTEM

at those total load levels. Nevertheless, switching the men-tioned lines has no economic benefit at total loads 147 to 213MW/h. The switching practice cumulatively outperforms thenon-switching practice for the season because the generationcosts are lower for higher total loads.

V. EXPERIMENTAL RESULTS ON THE 39-BUS SYSTEM

The 39-bus power system is a generally representative net-work of the New England 345 KV system and the data for thispower system is taken fromMatPower [20]. The system is com-prised of ten generators, 46 lines, and 21 loads and is summa-rized in Table IV. Generation quadratic costs are linearized inthe same way explained in previous experiments. After initialexaminations, it is noticed that the 39-bus system is not re-liable when the system load is considered. However, the systemis reliable to single contingencies when 0.72 times of the systemload or less is applied. Hence, for this power system a time pe-riod with moderate loads is considered to preserve re-liability requirements. To generate the seasonal loads, first wenormalize the hourly load data from [21] for the regions DOM,FE, and DEOK and for the time period from October 1 to De-cember 31, 2012. We assume that the normalized load profilefor buses 1–13 are the same with the normalized load profilefor region DOM, for buses 14–26 the same with region FE, andfor buses 27–39 the same with region DEOK. The normalizedload data is multiplied by the corresponding system load at the39-bus system to generate seasonal load data. Again for effi-ciency, we bin 2208 hours of loads into 100 representative loadvectors in the same way explained before. We also decrease thepower flow limit of the line (2–25) from 500 to 250 MW tocreate congestion.We assume all lines can be switched and the optimization re-

sults show that removing lines 4, 10, and 13 from service andkeeping the others in service is the optimal network configu-ration. The total generation cost of the found solution in theentire season is $48 233 701. If no transmission line is switched,

TABLE VIEEE 118-BUS SYSTEM

TABLE VIELEMENTS IN THE 118-BUS SYSTEM REMOVED FROM THE

CONTINGENCY LIST

the total generation cost is $49 301 768. This optimal networkconfiguration for the 39-bus system saves $1 068 067 in threemonths while respecting requirements. This saving is2.17% of total generation costs. The decomposition algorithmsolves this problem in less than 7 min. The optimality of thefound solution is validated by solving the problem by the de-composition algorithm with . The topology solutionobtained from the decomposition algorithm with isthe same with the topology solution of the decomposition algo-rithm with . The decomposition algorithm solves theproblem with in 6 h and 22 min. Therefore, similarto the 14-bus system, binning the loads preserves the optimalsolution and significantly reduces the computational time. TheCPLEX gets out-of-memory when it is used to solve the STSproblem on the 39-bus system with 2208 h of loads.

VI. EXPERIMENTAL RESULTS ON THE 118-BUS SYSTEM

Data for the IEEE 118-bus power system is downloaded fromthe University ofWashington, where generators’ capacity, gen-eration costs, transmission network, and line characteristics aretaken from [22]. The 118-bus system is summarized in Table V.We use the normalized load data used in the experiments on the14-bus system. We assume that the normalized load profile forbuses 1–40 are the same with the normalized load profile for re-gion PJME, for buses 41–80 the same with region PJMW, andfor buses 81–118 the same with region COMED. The normal-ized load data in each region is multiplied by the correspondingsystem load at the 118-bus system to generate different loads atevery hour. The radial transmission lines are not considered inthe FERC’s reliability standards [18]. Therefore, those elementsare removed from the contingency list. The IEEE 118-bussystem is not reliable to the single contingency scenarios if oneof the generators or nonradial lines in Table VI is lost. To makethe system survive in scenarios, the generators and trans-mission lines listed in Table VI are removed from thecontingency list. The studies in [2] and [23] show that limitingthe number of out-of-service lines to a smaller number preservesthe majority of the cost savings from transmission switchingwhile it improves the computational efficiency. To speed up the



process, the number of out-of-service transmission elements islimited to 5 lines and the number of bins is set to 10. We applythe decomposition algorithm on the system with modifiedcontingency constraints. The decomposition algorithm finds theseasonal transmission solution to switch out of service the lines77, 123, 132, 133, and 172. With those five lines switched out ofservice at the beginning of the season, total generation cost over2208 hours of loads is $1 426 286 where without switching anyline, total generation cost is $1 463 476. Therefore, $37 190 issaved in whole season which is 2.54% reduction in total gener-ation cost. The decomposition algorithm solves the problem in5 h and 52 min. The CPLEX runs out of memory when it is usedto solve the STS problem on the 118-bus system with 2208 h ofloads.

VII. COST SAVINGS

Here, we compare the cost reductions of the hourly transmis-sion switching (HTS) and the seasonal transmission switching(STS) on the 14-bus, 39-bus and 118-bus systems. In the 14-bussystem with the HTS, the total generation cost in the season is$19 681 464 which is a 2.83% reduction in the cost. The HTSsaves $1414 (or 0.007%) more in the season when it is com-pared to the STS. In the 39-bus system, the total generation costwith the HTS is $48 225 435 which is $8266 lower than the totalgeneration cost with the STS. This is a 0.017% improvement inthe cost saving. Solving the TS problem on the 118-bus systemwith contingency scenarios is computationally difficulteven for one hour load [3]. In the previous section, we limitedthe number of out-of-service transmission elements to five linesand considered ten representative load vectors for the 118-bussystem to decrease the computational time of the STS. We con-sider the same limitation on maximum number of switchablelines (five lines) and the same ten representative load vectors forthe HTS. The total generation cost in the considered 10 hourswith the HTS is $7169 while with the STS the cost is $7414.With no transmission switching, the cost increases to $7640,which results in 6.16% saving by HTS and 2.96% saving bySTS, respectively. As the HTS has more flexibility in changingthe transmission topology, when compared with the STS, in gen-eral, it is expected that the HTS provides more cost reduction.More research is needed for a thorough evaluation of the costreductions provided by HTS and STS methods.

VIII. CONCLUSION

Seasonal transmission switching can be an alternativeapproach to hourly-based transmission switching when new in-vestments are undesirable and excessive transmission switchingis avoided. We show that despite one-time switching at thebeginning of the season, the seasonal transmission switchingmodel can noticeably reduce generation costs. A seasonaldecision such as the STS problem probably would not haveto be solved within a short time period which is required inthe hourly TS problem. However, efficiently solving the STSproblem is important because of two reasons: The STS modelis itself a difficult problem to solve and efficiency becomesnecessary when the size of the problem increases. Also, thelong-term investment projects normally require simulation

of various future scenarios where computational efficiencyfor such problems is required. The CPLEX could not find acost-reducing solution to the 14-bus system after running for6 hours. The CPLEX also gets out-of-memory when it is usedto solve the STS problem on the 39-bus and 118-bus systems.The developed decomposition algorithm in this paper signif-icantly reduces the time required to solve the problem. Thesolution time is further decreased by binning thousands of loadvectors into tractable number of representative load vectors.More research is needed to be conducted on power systems toinvestigate the sensitivity of good solutions to bin numbers andfinding better criteria for effective data reduction for the STSproblem. We used dc power flow and deterministic net-loadprofiles in our STS model. Future research should include thedevelopment of an AC-OPF STS model and the uncertaintiesespecially in wind, which are two important extensions to ourcurrent deterministic model.

ACKNOWLEDGMENT

The authors wish to thank the anonymous referees for severalsuggestions that improved this paper.

REFERENCES

[1] K. Hedman, S. Oren, and R. O’Neill, “A review of transmissionswitching and network topology optimization,” in Proc. IEEE Powerand Energy Soc. Gen. Meeting, July 2011, pp. 1–7.

[2] E. Fisher, R. O’Neill, andM. Ferris, “Optimal transmission switching,”IEEE Trans. Power Syst., vol. 23, no. 3, pp. 1346–1355, Aug. 2008.

[3] K. Hedman, R. O’Neill, E. Fisher, and S. Oren, “Optimal transmissionswitching with contingency analysis,” IEEE Trans. Power Syst., vol.24, no. 3, pp. 1577–1586, Aug. 2009.

[4] K. Hedman,M. Ferris, R. O’Neill, E. Fisher, and S. Oren, “Cooptimiza-tion of generation unit commitment and transmission switching withn-1 reliability,” IEEE Trans. Power Syst., vol. 25, no. 2, pp. 1052–1063,May 2010.

[5] K. Hedman, R. O’Neill, E. Fisher, and S. Oren, “Smart flexible just-in-time transmission and flowgate bidding,” IEEE Trans. Power Syst., vol.26, no. 1, pp. 93–102, Feb. 2011.

[6] K. Hedman, R. O’Neill, E. Fisher, and S. Oren, “Optimal transmissionswitching—Sensitivity analysis and extensions,” IEEE Trans. PowerSyst., vol. 23, no. 3, pp. 1469–1479, Aug. 2008.

[7] C. Liu, J. Wang, and J. Ostrowski, “Static switching security in multi-period transmission switching,” IEEE Trans. Power Syst., vol. 27, no.4, pp. 1850–1858, Nov. 2012.

[8] A. Khodaei, M. Shahidehpour, and S. Kamalinia, “Transmissionswitching in expansion planning,” IEEE Trans. Power Syst., vol. 25,no. 3, pp. 1722–1733, Aug. 2010.

[9] J. Villumsen and A. Philpott, “Investment in electricity networkswith transmission switching,” Eur. J. Oper. Res., vol. 222, no. 2, pp.377–385, 2012.

[10] A. Khodaei and M. Shahidehpour, “Transmission switching in secu-rity-constrained unit commitment,” IEEE Trans. Power Syst., vol. 25,no. 4, pp. 1937–1945, Nov. 2010.

[11] A. Khodaei and M. Shahidehpour, “Security-constrained transmissionswitching with voltage constraints,” Int. J. Electr. Power Energy Syst.,vol. 35, no. 1, pp. 74–82, 2012.

[12] J. Ostrowski, J. Wang, and C. Liu, “Exploiting symmetry in transmis-sion lines for transmission switching,” IEEE Trans. Power Syst., vol.27, no. 3, pp. 1708–1709, Aug. 2012.

[13] J. Fuller, R. Ramasra, and A. Cha, “Fast heuristics for transmission-lineswitching,” IEEE Trans. Power Syst., vol. 27, no. 3, pp. 1377–1386,Aug. 2012.

[14] P. Ruiz, J. Foster, A. Rudkevich, and M. Caramanis, “Tractabletransmission topology control using sensitivity analysis,” IEEE Trans.Power Syst., vol. 27, no. 3, pp. 1550–1559, Aug. 2012.

[15] C. Liu, J. Wang, and J. Ostrowski, “Heuristic prescreening switchablebranches in optimal transmission switching,” IEEE Trans. Power Syst.,vol. 27, no. 4, pp. 2289–2290, Nov. 2012.



[16] M. K. C. Marwali and S. M. Shahidehpour, “Long-term transmis-sion and generation maintenance scheduling with network, fuel andemission constraints,” IEEE Trans. Power Syst., vol. 14, no. 3, pp.1160–1165, 1999.

[17] H. Pandzic, A. Conejo, I. Kuzle, and E. Caro, “Yearly maintenancescheduling of transmission lines within a market environment,” IEEETrans. Power Syst., vol. 27, no. 1, pp. 407–415, 2012.

[18] U.S. Fed. Energy Regulatory Comm., “Mandatory reliability standardsfor the bulk power system,” Order 72 FR 16416, 2007.

[19] S. Binato,M. V. F. Pereira, and S. Granville, “A new benders decompo-sition approach to solve power transmission network design problems,”IEEE Trans. Power Syst., vol. 16, no. 2, pp. 235–240, May 2001.

[20] R. T. R. D. Zimmerman and C. E. Murillo-Sanchez, “Matpower:Steady-state operations. Planning and analysis tools for power systemsresearch and education,” IEEE Transactions on Power Systems, vol.26, p. 1219, 2011.

[21] “PJM Hourly Load Data,” [Online]. Available: http://www.pjm.com/markets-and-operations/energy/realtime/loadhryr.aspx

[22] S. Blumsack, “Network topologies and transmission investment underelectric-industry restructuring,” Ph.D. dissertation, Dept. Eng. andPublic Policy, Carnegie Mellon Univ., Pittsburgh, PA, USA, 2006.

[23] C. Barrows and S. Blumsack, “Transmission switching in the RTS-96test system,” IEEE Trans. Power Syst., vol. 27, no. 2, pp. 1134–1135,May 2012.

Masood Jabarnejad received the B.S. degree inindustrial engineering from Bu-Ali Sina University,Hamedan, Iran, in 2003, the M.S. degree in industrialengineering from Middle East Technical University,Ankara, Turkey, in 2010, and the M.I.S.E degreein industrial and systems engineering from AuburnUniversity, Auburn, AL, USA, in 2012, where heis currently working toward the Ph.D. degree in theDepartment of Industrial and Systems Engineering.He also teaches an undergraduate course on the

engineering economy at Auburn University, Auburn,AL, USA. His research interests include operations research and its applicationsin the optimization of the electric power systems.Mr. Jabarnejad is a member of INFORMS and IIE.

Jianhui Wang (M’07–SM’12) received the Ph.D.degree in electrical engineering from Illinois Insti-tute of Technology, Chicago, IL, USA, in 2007.Presently, he is a Computational Engineer with

the Decision and Information Sciences Division, Ar-gonne National Laboratory, Argonne, IL, USA, andan Affiliate Professor at Auburn University, Auburn,AL, USA. He is also the editor of Artech HousePower Engineering Book Series. He is an associateeditor of the Journal of Energy Engineering andApplied Energy

Dr. Wang is the chair of the IEEE Power and Energy Society (PES)power system operation methods subcommittee. He is an editor of the IEEETRANSACTIONS ON POWER SYSTEMS, the IEEE TRANSACTIONS ON SMARTGRID, and the IEEE POWER AND ENGINEERING SOCIETY LETTERS. He wasthe recipient of the IEEE Chicago Section 2012 Outstanding Young EngineerAward.

Jorge Valenzuela received the Ph.D. degree in in-dustrial engineering at the University of Pittsburgh,Pittsburgh, PA, USA, in 2000.His research interests are applied and theoretical

stochastic modeling and optimization. His recent re-search involves stochastic models for the economicsof wind power, optimization of electric powergeneration, and cybersecurity. He is a Professor andChair with the Department of Industrial and SystemsEngineering, Auburn University, Auburn, AL, USA,where he teaches courses on stochastic operations

research and information technology.Dr. Valenzuela is member of INFORMS and IIE.

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