Optimized Midterm Preventive Maintenance Outage Scheduling of Thermal Generating Units

1354 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 3, AUGUST 2012

Optimized Midterm Preventive Maintenance OutageScheduling of Thermal Generating Units

Amir Abiri-Jahromi, Student Member, IEEE, Mahmud Fotuhi-Firuzabad, Senior Member, IEEE, andMasood Parvania, Student Member, IEEE

Abstract—This paper addresses the midterm preventive main-tenance outage scheduling problem of thermal generating unitswhich is becoming increasingly important due to the aging ofpower generation fleet. In this context, a novel midterm preventivemaintenance outage scheduler is proposed based on decision treeand mixed integer linear formation which explicitly considers thethermal units agingmomentum in terms of failure rate. This allowsthe system operators to determine the thermal units’ maintenanceoutage window based on the cost/benefit analysis of preventivemaintenance tasks while optimizing the time interval betweenconsecutive maintenance tasks. Additionally, the division of theyear-longmidterm horizon into several time blocks in the proposedmodel provides a unique opportunity for parallel processing andcomputational saving. The proposed approach is tested on theIEEE Reliability Test System (IEEE-RTS). The results presentedreveal the accuracy and efficiency of the proposed approach.

Index Terms—Aging process, midterm preventive maintenancescheduling, mixed integer linear programming, resource allocationand optimization.

NOMENCLATURE

Constants

Duration of the th maintenance task(hour) for the th thermal unit.

Duration of period in hour.

Budget for the preventive maintenancein period .

Available labor in period .

Operating cost at hour of weekwhen all generating units are available.

Operating cost at hour of week inscenario .

Total cost of labor and materialassociated with repairing the thfailure mode of the th thermal unitin period .

Manuscript received April 28, 2011; revised August 19, 2011 and November15, 2011; accepted December 19, 2011. Date of publication January 31, 2012;date of current version July 18, 2012. Paper no. TPWRS-00388-2011.The authors are with the Center of Excellence in Power System Control and

Management, Electrical Engineering Department, Sharif University of Tech-nology, Tehran, Iran (e-mail: [email protected]; [email protected]; [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.2011.2182362

Cost of one working hour necessaryfor repairing the th failure mode ofthe th thermal unit in period .

Price of materials for repairing the thfailure mode of the th thermal unitin period .

Production cost function of unit athour at weekly interval .

Total cost of labor and materialsassociated with the th preventivemaintenance task of the th thermalunit in period .

Cost of one working hour necessaryfor performing the th maintenancetask of the th thermal unit in period .

Price of materials for performingthe th maintenance task on the ththermal unit in period .

Expected outage cost associated withthe th failure mode of the th unit inperiod .

Expected outage cost associated withthe th preventive maintenance task ofthe th unit in period .

Commitment state of unit at hourat weekly interval .

Initial value of the th decoupledfailure rate of the th thermal unit.

th stair wise step of Weibulldistribution utilized to model the thdecoupled failure rate function of theth thermal unit.

Number of hours necessary forrepairing the th failure mode of theth thermal unit.

Number of hours necessary forperforming the th preventivemaintenance task of the th thermalunit.

Probability of scenario in whichsome units including the th thermalunit are on outage.

0885-8950/$31.00 © 2012 IEEE

ABIRI-JAHROMI et al.: OPTIMIZED MIDTERM PREVENTIVE MAINTENANCE OUTAGE SCHEDULING OF THERMAL GENERATING UNITS 1355

Probability of scenario in whichsome units including the th thermalunit are on outage and failure rate ofthe th thermal unit is considered timevarying.

Probability of scenario in whichsome units including the th thermalunit are on outage without consideringthe th thermal unit failure probability.

Maximum number of units that can bemaintained in period .

Number of thermal units that are onoutage in scenario .

Number of in service thermal units inscenario .

Number of scenarios that include theoutage of the th thermal unit.

Number of decoupled failure rates ormaintenance tasks.

Number of thermal units.

Number of hours at each weeklyinterval.

Number of intervals of the stair wisefailure rate function of the th thermalunit.

Number of weeks in each period understudy.

Real power generation of unit athour at weekly interval .

Maximum capacity of unit .

Highest incremental cost of energyproduction of unit .

Expected cost associated with thescenarios that include the th unitoutage.

Expected cost associated with thescenarios that include the th unitoutage while failure rate of the thunit is considered time varying.

Startup cost of unit at hour atweekly interval .

Shutdown cost of unit at hour atweekly interval .

Lead time .

Number of preventive maintenancescheduling periods.

Constant failure rate of thermal unit inthe base period (per hour).

Variables

Binary variable that is equal to 1 ifthe minor preventive maintenance isperformed on the th unit in periodand 0 otherwise.

Binary variable that is equal to 1 ifthe major preventive maintenance isperformed on the th unit in periodand 0 otherwise.

Binary variable that is equal to 1 ifthe th preventive maintenance task isperformed on the th unit in periodand 0 otherwise.

Failure rate of the th thermal unit inperiod (per hour).

th decoupled failure rate of the ththermal unit in period (per hour).

Decoupled minor failure rate of theth thermal unit in period (per hour).

Decoupled major failure rate of theth thermal unit in period (per hour).

Decoupled minor failure rate of theth thermal unit in period whenth periods elapsed since the lastassociated maintenance activity (perhour).

Decoupled major failure rate of theth thermal unit in period whenth periods elapsed since the lastassociated maintenance activity (perhour).

I. INTRODUCTION

M AINTAINING the availability of generating units in anacceptable level is of great importance to the reliability

of power systems. Accordingly, preventive maintenance outagescheduling in aging power systems becomes critical. Further-more, reducing costs, while enhancing the reliability, has putdecision makers in a classical dilemma of conflicting objectives.For that reason, the power industry is looking for more efficientand accurate tools to support decisions on preventive mainte-nance outage scheduling [1], [2].Most generating unit maintenance outage scheduling tech-

niques ignore cost/benefit analyses of preventive maintenancetasks and consider a predefined set of generating units for pre-ventive maintenance while minimizing the impact of generatingunit outages [3]–[9]. Also the existing approaches enforce apredefined maintenance window as a constraint to the mainte-nance problem without optimizing the interval between consec-utive maintenance tasks. In recent years, with advances in con-dition monitoring, information processing, fault detection, andartificial intelligence technologies, it is possible to monitor andforecast the condition of aging equipment and use the available


operation data to estimate failure rates on periodic basis [10].Thus, preventive maintenance optimization approaches that cananalyze the cost/benefit associated with each preventive main-tenance task while optimizing the time interval between con-secutive maintenance tasks are much more applicable to powersystem operations [11], [12].This paper introduces an innovative midterm maintenance

scheduler for thermal generating units based on decision treeand mixed integer linear formation which explicitly considersthe thermal units aging momentum in terms of failure rate. Thisallows the system operators to determine the optimal thermalunits’ maintenance outage window based on the cost/benefitanalysis of preventive maintenance tasks. In this context, theoptimal unit maintenance outage window is determined suchthat system costs are minimized while maintaining the systemreliability independently of any power producer. Accordingly,the power producers’ interest and attitude toward risk are nottaken into account. Once the midterm maintenance window isdetermined using the proposed model, each power producer cannegotiate the exact outage time of its units in the correspondingmidterm maintenance window, e.g., 8-week midterm mainte-nancewindowor requesting an alternativemaintenancewindow.Note that the midterm maintenance scheduler introduced in thispaper just locates the optimal midterm time block in which thepreventive maintenance should take place while the exact timeof maintenance outage would be determined by a short-termmaintenance scheduler which is out of the scope of this paper.In the proposed approach, the impact of generating unit un-

availability, due to failure or preventive maintenance outages, isquantified in terms of the expected outage costs and the requiredlabor and material costs. First, a credible set of generating unitoutage scenarios is considered. In this paper, the contingenciesare selected based on the N-2 criterion; however, any otherapproaches can be used by operator to obtain a credible set ofcontingencies. Second, an hourly network-constrained unitcommitment (NCUC) simulator is developed. Third, the NCUCoutput associated with each scenario is weighted by the corre-sponding probability to calculate the expected cost associatedwith each generating unit outage. Finally, the expected costassociated with the unit outages is considered together with therequired labor and material costs and optimized. These steps aredepicted in Fig. 1. The proposed approach will schedule preven-tive maintenance outages for minimizing the impact on gener-ating unit availability considering equipment, system, budgetand labor constraints. The output of the proposed approach couldbe used for short-term maintenance outage scheduling.The main contribution of this paper is to introduce a midterm

preventive maintenance outage scheduling model for thermalgenerating units that explicitly considers the units’ aging mo-mentum in terms of failure rate and optimizes the cost/benefitassociated with each maintenance task from power system oper-ator’s perspective. Additionally, the proposedmethodology pro-vides a great flexibility to the user in terms of the computationburden management and selection of the midterm maintenancetime horizon and the associated duration.The rest of this paper is organized as follows. Section II pro-

vides a detailed description of the proposed midterm preven-tive maintenance model. In Section III, thermal unit preven-

Fig. 1. Midterm preventive maintenance outage scheduler for thermal gener-ating units.

Fig. 2. Three state Markov diagram of deterioration process.

tive maintenance costs and benefits are quantified mathemati-cally. In Section IV detailed display of midterm thermal unitmaintenance formulation using mixed integer linear program-ming is presented. Numerical results are given and discussed inSection V. Finally, the conclusion is presented in Section VI.

II. PROPOSED MIDTERM PREVENTIVE MAINTENANCE MODEL

Equipment failures are divided into random and deteriorating(aging) failures. Random failures are modeled by exponentialdistribution functions and are characterized by constant failurerates, while deteriorating failures are modeled by Weibulldistribution, normal distribution, etc. Since the rate of randomfailures is constant, preventive maintenance outages would notimprove random failures. However, failure rates originatedfrom deterioration are time varying and any preventive mainte-nance could bring about improvements to deteriorating outages[13]–[15].The failure rate of thermal power plants represents turbine

failures, generator failures, cooling system failures, auxiliaryequipment failures, etc. The decoupling of deterioration failurerates (1), based on such factors and maintenance requirements,would provide quantitative factors on reliability:

(1)

Accordingly, a method is developed to link power system op-erations, maintenance, reliability, and the associated costs. Theexisting models for linking these concepts almost all employ aMarkov model to represent the effect of preventive maintenanceon deteriorating equipment. This model is illustrated in Fig. 2.


Fig. 3. Maintenance decision tree of the th thermal unit in period .

The Markov model represents the deterioration process by asequence of states of increasing wear and tear, which would fi-nally lead to equipment failure. Deterioration is a continuousprocess in time and, only for the purpose of modeling, is con-sidered in discrete steps using the Markov model. Moreover,the model assumes that the residing time in each state is ex-ponentially distributed. These two assumptions in conjunctionwith the complexity of this model would limit its applicationto multiple pieces of equipment simultaneously. Moreover, theMarkov model does not provide a long-term dynamic overviewbecause individual periods are considered separately.A decoupled state transition model which links maintenance,

reliability, and cost was introduced for distribution systems [16].This model revised and utilized in this paper provides an effi-cient decision making tool for the preventive generation main-tenance outage scheduling.The state of each generating unit in each period is defined

by decoupled failure rates in this paper, e.g., minor and majorfailure rates. The minor and major failure rates stand for shortduration outages of auxiliary equipment and long duration out-ages of main equipment such as turbine failure, generator failureor cooling system failure respectively. We define a set of minorand major preventive maintenance tasks in accordance with de-coupled failure rates. A decision tree is formed in Fig. 3 and itis assumed that each maintenance activity will affect the corre-sponding decoupled failure rate [16]. In Figs. 3 and 9, 14 periodshave been elapsed from the last time, minor and major mainte-nance tasks were performed on the unit accordingly. As illus-trated in Fig. 3, a set of decoupled failure rates,and is identified for the thermal unit in each pe-riod and each maintenance task reduces the corresponding de-coupled failure rate to its initial value [16].Therefore, the number of possible preventive maintenance

scenarios for a thermal unit in each period is representingminor and major maintenance tasks. The transition rates be-tween different states of this model are equal to the sum of totalcosts of preventive maintenance tasks performed and the ex-pected costs that would be imposed on the system for the gen-erating unit failure. A set of binary decision variables in eachperiod, i.e., and , would determinethe maintenance scenario selected for thermal units.Utilizing the proposed model, a thermal unit state at a given

period will introduce new states in the following periodwhere represents the number of possible preventive main-tenance tasks. The transition rate from one state to another is

defined by the total cost of preventive maintenance tasks andthe expected cost of failures and repairs.The proposed model has four distinguishing features. First,

this approach provides a dynamic overview of how each preven-tive maintenance task would affect the system cost in midtermperiods as the states are discriminated by failure rates, and thestate transition rate is based on cost. Second, failure rates origi-nated from deterioration can be modeled byWeibull distributionwhich proven to be the most flexible distribution for failure ratemodeling [13]. Third, any number of equipment can be consid-ered simultaneously without adding much complexity. Further-more, the benefits of preventive maintenance outage schedulingand its costs are optimized simultaneously. In the following sec-tion, the costs and benefits of preventive maintenance are quan-tified.

III. THERMAL UNIT PREVENTIVE MAINTENANCECOST/BENEFIT ASSESSMENT

In order to assess costs and benefits associated with thethermal unit preventive maintenance outages, the consequencesof failure (forced outage) and preventive maintenance outageshould be quantified mathematically.The consequence of thermal unit failure may be quantified as

the sum of the following terms:1) expected outage cost associated with the thermal unitfailure scenarios;

2) expected labor and material costs for repairing the failedthermal unit;

3) expected security cost imposed to system accounting for athermal unit failure.

Besides, the effects of thermal unit preventive maintenanceoutage may also be expressed in terms of:1) expected outage cost reduction due to the reduced failurerate of the thermal unit;

2) expected cost that would be imposed to system during thethermal unit preventive maintenance outage;

3) labor and material costs associated with thermal unit pre-ventive maintenance.

These terms are formulated and discussed next.

A. Quantification of Thermal Unit Failure Consequences

The generating unit availability is of great importance foreconomic and reliability purposes. In order to quantify the im-pact of suffering an unplanned thermal unit outage, the expectedoutage cost associated with the credible thermal unit failure sce-narios is required. Thus, a midterm NCUC simulator is devel-oped which calculates the weighted increased operation cost foreach failure scenario as follows:

(2)

(3)


Here, represents the probability of the occurrence ofscenario containing the failure of the th generating unit.The difference between and representsthe increased operation cost due to the occurrence of sce-nario . The two cost terms and

are evaluated by the NCUC simulatorover an week period using the objective functions (4)and (5), respectively. The objective functions are subject toprevailing unit commitment and DC power flow constraints.The number of available units is in (4) while the numberof available units in (5) is :

(4)

(5)

Considering the fact that the proposed approach is not de-pendent on the method utilized for calculating the operatingcost, any preferred technique would be utilized in (4) and (5),[17]–[21].In (2) and (3), generating units aging momentum is assumed

to be zero. Thus, the failure rate is constant over time and equalto that of a thermal unit when it is in the as good as new condi-tion. In the following, the effect of th generating unit aging isadded to the formulation. Thus, the failure rate of the th gener-ating unit is considered to be time varying and factorized. Theexpected outage cost associated with the failure scenario isrewritten in the following:

(6)

(7)

(8)

Here, is the th decoupled failure rate of the th thermalunit in period which depends on the time of the last th pre-ventive maintenance. Fig. 4 shows a typical Weibull distribu-tion which is utilized to model the generating unit deteriorationin this paper. Here, the time span for preventive maintenanceis discretized into fixed periods, e.g., . Hence, thefailure rate is discretized in Fig. 4. The discretized decoupled

Fig. 4. Stair-wise failure rate using Weibull distribution.

failure rates of thermal units can be asymptotically approxi-mated by a stair-wise function shown in Fig. 4 and substitutedin (8).Next, the formulation (6)–(8) will be used for calculating the

expected outage cost associated with thermal unit failure sce-narios taking into account the units aging momentum.1) Expected Outage Cost Associated With the Thermal Units

Failure Scenarios: Using the term (6), the expected cost of suf-fering a thermal unit failure scenario is formulated as follows.The unique characteristic of the following formulation is theembodiment of the th thermal unit aging momentum in termsof :

(9)

(10)

2) Expected Labor and Material Costs for Repairing FailedThermal Units: The other costs that would incur due to thefailure of a thermal unit include the labor and material costs. Ingeneral, the average number of hours and the average amountof materials required for repairing any failures are pre-specified.Thus, the labor and material costs of repairing a failed thermalunit can be quantified as follows. Note that the labor and ma-terial expenses are weighted by the probability of equipmentfailure over period in order to account for the probabilistic na-ture of failure incident:

(11)

(12)


3) Expected Security Cost Accounting for a Thermal UnitFailure: Expected security cost represents the cost of correctiveactions, such as the deployment of reserve, required for compen-sating possible loss of a thermal unit. This term is quantified bya penalty factor equal to the highest incremental cost of energyproduction by a unit multiplied by the maximum capacity andfailure rate of the unit in each period as follows:

(13)

(14)

B. Quantification of Thermal Unit Preventive MaintenanceConsequences

In order to achieve a complete understanding of thermal unitpreventive maintenance effects, one should consider the fol-lowing terms:1) Thermal Unit Failure Rate Reduction Due To Preventive

Maintenance: The benefit of thermal unit preventive mainte-nance is quantifiable in terms of the unit failure rate reductionwhich results in reduced quantity of terms (9)–(14) associatedwith thermal unit failure. Amixed-integer linear formulation formodeling the effect of preventive maintenance on failure rate isgiven in Section IV.2) Expected Cost Associated With the Thermal Unit Preven-

tiveMaintenance Outage: Mathematically, the effect of preven-tive maintenance outage of a generating unit can be modeledanalogously to the generating unit’s failure outage by modifying

with two respects. First, the generating unitcannot fail during the maintenance outage which can be ful-filled by dividing the by unit’s failure rate,i.e., . Second, calculated by (9)should be nullified in the periods that maintenance takes placefor the duration of preventive maintenance. Thus, the expectedcost imposed to system due to the generating unit’s preventivemaintenance outage can be formulated as follows:

(15)

3) Labor and Material Costs Associated With Thermal UnitsPreventive Maintenance: The final costs that would incur dueto the preventive maintenance of a thermal unit include the laborand material costs. In general, the average number of hours andthe average amount of materials required for performing pre-ventive maintenance are pre-specified. Thus, the cost of the thpreventive maintenance task of unit over the period is rep-resented as

(16)

Next, the midterm preventive maintenance of thermal units isformulated by utilizing the formulation developed in Section IIIand implementing it in the model developed in Section II.

IV. PREVENTIVE MAINTENANCE FORMULATION USING MILP

The proposed thermal unit midterm preventive maintenancescheduling problem is formulated in this section using theMILPmethod (17)–(22). In the objective function (17), and

represent the costs of preventive maintenance tasks.These terms are multiplied by the corresponding binary deci-sion variable, i.e., . , , and

represent the costs associated with thefailure mode of each thermal unit over the scheduling horizon.The decision variable embedded in these terms is whichdepends on the time of the last th preventive maintenance ofcomponent . Constraints (18) represents the labor constraint.Constraint (19) ensures that minor andmajor preventive mainte-nances would not be performed simultaneously on a generatingunit. Finally, constraint (20) would limit the maximum numberof units that would be maintained in each period. Additionalthermal unit constraints could be added to the optimization [7],[9]:

(17)

(18)

(19)

(20)

The term in the objectivefunction contains the product of binary variableand the bounded continuous variable which makes theproblem nonlinear. In order to remove this nonlinearity and keepthe formulation as MILP, this product is substituted by a new bi-nary variable which is subjected to the followinglinear inequalities [22]:

(21)

(22)

The preventive maintenance optimization proposed in(17)–(22) is a MILP problem but its dependence on the last


preventive maintenance is not formulated yet. In the following,an MILP approach is utilized to formulate the relation betweenpreventive maintenance and failure rate suitable for commercialsoftware applications [23], [24].Here, the time span utilized in the preventive maintenance

model is discretized into fixed periods, e.g., .Hence, the failure rate can also be discretized as shown inFig. 4. The discretized decoupled failure rates of deterioratingthermal units are asymptotically approximated by a stair-wisefunction shown in Fig. 4. We propose a MILP formulationfor decoupled stair-wise failure rates of thermal units over thescheduling horizon. This formulation links the generating unitfailure rate to the last preventive maintenance task:

(23)

(24)

In the above formulation, the decoupled failure rate ofthermal units with a Weibull distribution is replaced bysteps . Each in Fig. 4 is constant which is equalto the stair-wise value of the Weibull distribution in period .Subsequently, a set of MILP constraints (23), (24) are definedwhich restricts the failure rate decision variable based onthe last preventive maintenance. Detailed discussion of thisformulation is given in [16].In summary, (17)–(24) describe a MILP formulation for the

midterm preventive maintenance scheduling of thermal units.The formulation would only require a set of binary variables

and , and positive continuous vari-ables .

V. STUDY RESULTS

The proposed approach for the preventive maintenanceoutage scheduling of thermal units is applied to the IEEE-RTSwithout hydro generation [25]. This system is composed of 26thermal units, 20 load points, 24 buses, and 38 transmissionlines. Some of the required data such as generating units andtransmission lines data are given in [25]. Other data such asdecoupled deteriorating failure rates of each unit, averageduration of unit outages, average number of working hoursnecessary to perform preventive maintenance or repair, whichare not given in [25], are defined subjectively and accessible inhttp://ee.sharif.edu/~parvania/GenPaperData.pdf. Also, all thetransmission lines are considered to be fully reliable.An optimization horizon of 6 periods is considered, con-

sisting of 48 weeks in which each period consist of 8 weeks.The peak load is 2100 MW and the hourly load profile of thefirst 48 weeks of the IEEE-RTS [25] is utilized to achieve thesystem hourly load curve.The expected outage cost associated with thermal unit failure

in each period is evaluated based on NCUC and the proposal inSection III. Here, all single and double contingencies are takeninto consideration which consists of 351 cases. The simulationof 352 NCUC problems, including the base case, for the whole

Fig. 5. Preventive maintenance outage schedules: Study 1.

optimization horizon is computationally demanding. The divi-sion of the midterm preventive maintenance horizon into sev-eral periods in the proposed approach provides a unique oppor-tunity to perform the simulations on several processors simul-taneously. This feature also provides a user flexibility to selectthe number and the duration of midterm preventive maintenanceperiods subjectively. Furthermore, the similarity of thermal unitlocation and size in power system would further reduce thenumber of required simulations and computation burdens. Forinstance, two identical 76 MW generating units are located atbus 1 of the IEEE-RTS. It was seen in simulations that units withsame locations and sizes have a similar . Anothersalient feature of the proposed method is that NCUC solutionsare completely separated from the preventive maintenance op-timization. Therefore, available data or estimates about the ex-pected cost of thermal unit outages can also be used in the finalpreventivemaintenance optimization problem in order to reducethe computation burden on NCUC.In this paper, minor and major failure rates of thermal units

are modeled by a 13-interval stair-wise linear function calcu-lated from the Weibull distribution. The optimization problemintroduced in Section IV is coded in the GAMS environment[26] and solved using the MILP solver CPLEX 12.0 [23] ona PC equipped with 3.2-GHZ processor and 2 GB of RAMmemory. To reveal the features of the proposed model, four dif-ferent studies are conducted on the system as follows. In all fourstudies, the maximum number of units on maintenance in eachperiod is limited to 4.

A. Study 1: Basic Simulation

This study presents the basic simulation associated with theproposed preventive maintenance scheduler of thermal gener-ating units. The aim of this study is to demonstrate that thethermal unit size, location, aging momentum and commitmentfrequency are the decisive parameters which affect the preven-tive maintenance outage schedules in the proposed model. Theunit commitment frequency is dependent on operating cost andsystem load. The unit aging momentum is also characterizedby Weibull distribution and parameters. Fig. 5shows minor and major preventive maintenance outage sched-ules of thermal units obtained by the proposed model for thefailure data calculated from the Weibull distribution with andparameters defined in Table I. The CPLEX execution was

stopped at 12 min when the objective function was within the0.1% of the optimal system cost of $2 389 524. The proposed


TABLE IWEIBULL DISTRIBUTION PARAMETERS FOR FAILURE RATE

TABLE IIAMOUNT OF LABOR AND OBJECTIVE FUNCTION

VALUE IN EACH PERIOD: STUDY 1

case study contains 312 binary variables, 312 continuous vari-ables, and 4531 constraints. Table II shows the labor and thevalue of objective function in each period of Study 1.It can be seen from Fig. 5 that 76-MW, 100-MW, and

350-MW units with the highest major failure rate aging mo-mentum are scheduled for major preventive maintenance. The155-MW units with the highest minor failure rate aging mo-mentum are scheduled for minor preventive maintenance. Thelargest units maintained including 350-MW and 155-MW unitsare scheduled for outage during period 2 which has the lowestload level. Furthermore, the units 1, 2, 5, 6, and 12–19 arenot scheduled for preventive maintenance in the optimizationhorizon as these units have relatively low commitment fre-quency and aging momentum in terms of and .For instance, and parameters of 20-MW and197-MW units are close to 1 which means that the aging mo-mentum of these units are almost zero. Therefore, preventivemaintenance would not provide a tangible improvement to theirfailure rate. Furthermore, units 15–19 are expensive units thatare only committed in certain peak hours of the year. Therefore,their outage would cause a minor impact on system operatingconditions. Another point is that the 400-MW units with ahigh parameter are not scheduled for major preventivemaintenance. This is because the 400-MW units supply thebase load and their preventive maintenance outage will imposea high cost on the system.

B. Study 2: Impact of Aging Momentum on Midterm PreventiveMaintenance Schedules

In this study, three cases are considered to investigate the im-pacts of aging momentum on midterm maintenance schedules.The impacts of aging momentum variation on the maintenanceschedules of 400-MW and 155-MW thermal units are first in-vestigated once at a time. Subsequently, the impacts of simulta-neous change of thermal units’ major failure rates are examined.In Case 1, the impact of aging momentum of 400-MW units onthe preventive maintenance outage scheduling is investigated.In order to assess this point, the parameter of 400-MWunits was increased by 0.1 steps from that given in Table I,i.e., 1.5. It was seen that the 400-MW units are scheduled fora major preventive maintenance when the parameter of

Fig. 6. Preventive maintenance outage schedules: Study 2—Case 1.

TABLE IIIAMOUNT OF LABOR AND OBJECTIVE FUNCTIONVALUE IN EACH PERIOD: STUDY 2—CASE 1


these units reached 1.9. This shows that the expected cost of400-MW units failure surpasses the major preventive mainte-nance outage cost of these units at equal to or higher than1.9. The minor and major preventive maintenance task sched-ules obtained in this case are summarized in Fig. 6. The dis-cussion on preventive maintenance outage schedules in Study1 is also valid for this case. For instance, the largest units in-cluding the 400-MW and 350-MW units are scheduled for pre-ventive maintenance outages during period 2 with lowest loadlevel. The optimal system cost in this case is $3 054 609 whichis executed in 15 min. The higher system cost in this case, incomparison with Study 1, is due to the increased failure proba-bility of 400-MW units. Table III shows the labor and the valueof objective function in each period of this case.In Case 2, the parameter of 155-MW units was de-

creased by 0.1 steps from that given in Table I, i.e., 1.5. It wasseen that the 155-MW units are removed from minor preven-tive maintenance list when the parameter of these unitsreached 1.3. This shows that the minor preventive maintenanceoutage cost of these units surpasses the expected failure costof these units at equal to or less than 1.3. The minorand major preventive maintenance task schedules obtained inthis case are summarized in Fig. 7. The optimal system cost inthis case is $2 342 411 which is executed in 14 min. The lowersystem cost in this case, in comparisonwith Study 1, is due to thedecreased failure probability of 155-MW units. Table IV shows


TABLE IVAMOUNT OF LABOR AND OBJECTIVE FUNCTIONVALUE IN EACH PERIOD: STUDY 2—CASE 2


TABLE VAMOUNT OF LABOR AND OBJECTIVE FUNCTIONVALUE IN EACH PERIOD: STUDY 2—CASE 3

the labor and the value of objective function in each period ofthis case.In Case 3, the impacts of simultaneous change of thermal

units’ major failure rates are examined. Accordingly,parameter of all units is increased simultaneously by 20 per-cent from that given in Table I. The minor and major preventivemaintenance task schedules obtained in this case are summa-rized in Fig. 8. The optimal system cost in this case is $3 388 752which is executed in approximately one hour. The increasedcost and computation burden of this case originates from the in-creased number of maintenance task candidates as a result of theincreased aging momentum of the thermal units. It can be seenform Fig. 8 that 100-MW and 350-MW units with very highmajor failure rate aging momentums are scheduled twice formajor maintenance. Additionally, the 20-MW and 76-MW unitsare scheduled once for major maintenance and 155-MW unitsare scheduled for minor maintenance. It is noteworthy that the76-MW units with high parameter are scheduled oncefor major preventive maintenance. This is due to the fact that the76-MW units have a relatively high commitment frequency asthese units are inexpensive and their outages require the com-mitment of more expensive units. Table V summarizes the laborand the value of objective function in each period of this case.

C. Study 3: Impact of Labor Resource Shortage on MidtermPreventive Maintenance Schedules

In order to assess the impact of labor resource shortage onmidterm preventive maintenance schedules, upper bound onlabor constraint is considered in each period to be 250 h, inthis study. Furthermore, generating unit’s aging momentum is

Fig. 9. Preventive maintenance outage schedules: Study 3.

TABLE VIAMOUNT OF LABOR AND OBJECTIVE FUNCTION

VALUE IN EACH PERIOD: STUDY 3

Fig. 10. Intuitive yearly time-based preventive maintenance outage schedule.

TABLE VIIOBJECTIVE FUNCTION VALUE FOR DIFFERENT MAINTENANCE STRATEGIES

considered to be similar to Study 1. The minor and major pre-ventive maintenance outage schedules are shown in Fig. 9. Theexecution time of the model in this study was approximately36 min and the total cost was $2 445 326. Fig. 9 illustratesthat the number of preventive maintenance task schedules arereduced due to labor shortages. Also, for the same reason,some of preventive maintenance outages are scheduled inperiods 4 and 5 which have higher load levels. Consequently,the system cost is increased when the preventive maintenancetask schedules are delayed which would increase the expectedcost of unit failures. Table VI shows the labor and the value ofobjective function in each period of Study 3.


TABLE VIIIMINOR AND MAJOR FAILURE RATES VARIATION IN DIFFERENT MAINTENANCE STRATEGIES

D. Study 4: Comparative Study

In order to demonstrate the superiority of the solution foundby the proposed approach, the results obtained in Study 1 andStudy 2, Case 3, are compared with two time-based mainte-nance strategies. In the time-based maintenance strategy, allmaintenance activities are performed in fixed time intervalssuch as once per year, once per two years and so on. Here,the no maintenance strategy and a yearly maintenance strategyare compared with the proposed approach. In the yearly main-tenance strategy, an intuitive approach is used to schedulea set of thermal units for maintenance outage as shown in

Fig. 10. As shown in Fig. 10, the largest units are assumed tobe scheduled in the periods with the lowest peak load level.Also, the units with high major failure rate are considered formajor maintenance and units with the high minor failure rateare considered for minor maintenance. In addition, we assumethat the 12-MW units do not undergo maintenance as theircommitment frequency and aging momentum are low. Themaximum number of maintenance tasks in each period is alsolimited to 4 similar to other studies. Table VII summarizes thetotal costs obtained by the proposed approach and the othertwo intuitive time-based maintenance strategies. The resultsshow that optimizing the maintenance task intervals based on


cost/benefit analysis would result in significant saving. Thetotal cost obtained by the proposed approach in Study 1 is, re-spectively, $192 671 and $503 747 less than the costs associatedwith the no maintenance and yearly time-based maintenancestrategies. The total cost obtained by the proposed approachin Study 2, Case 3 is also $694 452 and $249 896 less than thecosts obtained for the no maintenance and yearly time-basedmaintenance strategies. This study indicates that the proposedmethod is more efficient than the existing time-based mainte-nance scheduling approaches as it considers the cost/benefitassociated with each maintenance task.The variations of minor and major failure rates of thermal

units in the three maintenance strategies discussed above forStudy 1 are summarized in Table VIII. As it can be seen, thefailure rates are reduced to their initial values in the periodswhen the units are maintained and increased in other periodsbased on the Weibull distribution.

VI. CONCLUSIONS

This paper incorporates the aging momentum in terms offailure rate into the midterm preventive maintenance scheduleof thermal units. In contrast to the conventional generatingunit preventive maintenance schedulers, the proposed MILPapproach optimizes the cost/benefit of performing or de-laying preventive maintenance tasks. The salient feature ofthe proposed methodology is the utilization of the decoupledfailure rate model in conjunction with the decision tree andmixed-integer linear formulation which optimizes the preven-tive maintenance task schedules considering the deteriorationprocess. The impact of generating unit repair or preventivemaintenance is quantified based on the expected outage costthat would be imposed on the system due to generating unitoutages and the costs of material and labor which are neededto repair the failures or to perform preventive maintenancetasks. The proposed approach provides the ability to evaluatethe effectiveness of each preventive maintenance scenarioin midterm periods which was not possible in conventionalschemes. The proposed model has been successfully tested onthe IEEE-RTS thermal units which revealed the accuracy andefficiency of the proposed method.

ACKNOWLEDGMENT

The authors would like to thank Prof. M. Shahidehpour ofIllinois Institute of Technology for his valuable comments anddiscussions during the preparation of the paper.

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Amir Abiri-Jahromi (S’10) received the B.Sc. de-gree in electrical engineering from Shiraz University,Shiraz, Iran, in 2003 and the M.Sc. degree in energysystems engineering from Sharif University of Tech-nology, Tehran, Iran, in 2007. He is currently pur-suing the Ph.D. degree at McGill University, Mon-treal, QC, Canada.He was a Research Assistant in the Electrical

Engineering Department of Sharif University ofTechnology from 2008 to 2010. He was also aResearch and Development Engineer with UIS

Company, Dubai, United Arab Emirates, from 2008 to 2010. His researchinterests are asset management and automation as well as operation andoptimization of smart electricity grids.


Mahmud Fotuhi-Firuzabad (SM’99) received theB.Sc. degree in electrical engineering from SharifUniversity of Technology, Tehran, Iran, in 1986,the M.Sc. degree in electrical engineering TehranUniversity, Tehran, Iran, in 1989, and the M.Sc.and Ph.D. degrees in electrical engineering fromthe University of Saskatchewan, Saskatoon, SK,Canada, in 1993 and 1997 respectively.Currently, he is a Professor and Head of the De-

partment of Electrical Engineering, Sharif Universityof Technology, Tehran, Iran. He is also an Honorary

Professor in the Universiti Teknologi Mara (UiTM), Shah Alam, Malaysia.Dr. Fotuhi-Firuzabad is a member of the Center of Excellence in Power

System Management and Control. He serves as an Editor of the IEEETRANSACTIONS ON SMART GRID.

Masood Parvania (S’09) received the B.S. degreein electrical engineering from Iran University ofScience and Technology (IUST), Tehran, Iran, in2007, and the M.S. degree in electrical engineeringfrom Sharif University of Technology, Tehran, Iran,in 2009, where he is currently pursuing the Ph.D.degree.His research interests include power system reli-

ability and security assessment, as well as operationand optimization of smart electricity grids.

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Optimized Midterm Preventive Maintenance Outage Scheduling of Thermal Generating Units