IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 2, JUNE 2004 435

Cost-Effective Wind Energy Utilizationfor Reliable Power Supply

Rajesh Karki, Member, IEEE, and Roy Billinton, Life Fellow, IEEE

Abstract—Environmental concerns and fuel cost uncertaintiesassociated with the use of conventional energy sources have re-sulted in rapid growth of wind energy applications in power gen-erating systems. It is important to assess the actual cost and ben-efit of utilizing wind energy in a power system. Such assessmentsrequire realistic cost/reliability evaluation methods and quantita-tive indices. This paper presents a simulation technique that gener-ates probabilistic indices that can help determine appropriate windpower penetration in an existing power system from both the reli-ability and economic aspects.

Index Terms—Monte Carlo simulation, power generatingcapacity, power system planning, power system reliability, windenergy, wind power.

I. INTRODUCTION

WIND energy sources have the potential to significantlyreduce fuel costs, greenhouse gas emissions, and natural

habitat disturbances associated with conventional energy gen-eration. Wind turbine generators (WTGs) are an ideal choice indeveloping countries where the most urgent need is to supplybasic electricity in rural or isolated areas without any power in-frastructure. Active public awareness of the need to save the en-vironment has encouraged many industrialized nations to pro-mote wind energy. Many large industrial companies have mademassive investments in the development of wind technology. Asa result, wind energy has become competitive with conventionalforms of energy. Power system deregulation has opened oppor-tunities for many private energy producers. Wind energy is apotential choice for smaller energy producers due to relativelyshort installation times, easy operating procedures, and differentavailable incentives for investment in wind energy.

The environmental benefits of using renewable energy arewell perceived. Wind application also offsets fuel costs that canbe relatively high in some generating plants. It is evident thatlimitations in the energy available in wind and its intermittentbehavior degrade system reliability. A comprehensive evalua-tion of cost and reliability is required to analyze the actual ben-efits of utilizing wind energy. The reliability aspects of utilizingwind energy have largely been ignored in the past due the rela-tively insignificant contribution of these sources in major powersystems, and consequently due to the lack of appropriate tech-niques. Increasing application of wind energy can create signif-icant impacts on system cost and reliability.

Manuscript received November 5, 2002.The authors are with the Power Systems Research Group, Department of

Electrical Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9Canada (e-mail: Rajesh_Karki@engr.usask.ca; Roy_Billinton@engr.usask.ca).

Digital Object Identifier 10.1109/TEC.2003.822293

Power utilities apply different reliability evaluation methodsdepending on their system sizes, and their conventional prac-tice. Probabilistic risk indices, such as loss of load expectation(LOLE) or loss of energy expectation (LOEE) [1], are used inmany large power systems. Small isolated systems normallyapply deterministic techniques, such as the loss of the largestunit (LLU) [2] to determine capacity requirements. Thesetechniques associate fixed capacity outputs to generating unitsand cannot be extended to include wind energy sources thathave highly fluctuating capacity levels. On the other hand,although conventional probabilistic methods [1] recognizerandom system behavior, they do not provide any informationon the available system capacity reserves, and have not beenreadily accepted by small system planners who are used tocapacity planning based on physical and observable reservemargins.

This paper presents a well-being approach [3] that incorpo-rates a deterministic criterion in a probabilistic framework andprovides probabilistic reliability indices useful to both the smalland large system planners. This paper also introduces proba-bilistic indices that can be used to evaluate the energy costs andutilization efficiency of WTG. The applications of these indicesin planning wind energy utilization in power systems are illus-trated with practical examples. This paper also presents the eval-uation model developed to obtain these indices.

II. WIND ENERGY AND RELIABILITY INDEXES

In the well-being approach, a power system is considered toreside in one of the three states shown in Fig. 1. A system op-erates in the healthy state when it has enough capacity reserveto meet a specified deterministic criterion such as the LLU. Thedegree of comfort associated with operating the system withinthe accepted deterministic criterion is given by the probability ofresiding within the healthy state or the healthy state probability

. The system violates the deterministic criterion withoutcausing any load curtailment in the marginal state. The loadexceeds the available capacity in the at risk state. Thecan be used as a useful reliability criterion in system adequacyevaluation.

The expected wind energy supplied (EWES) is a useful en-ergy index for a power system containing wind power. It mea-sures the conventional fuel energy offset by wind applicationand can be used to assess fuel cost and emission penalty costsavings.

Another useful index is the expected surplus wind energy(ESWE), which is defined in this paper as the amount of en-ergy that was available but not utilized. A high value of this

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436 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 2, JUNE 2004

Fig. 1. System well-being model.

index indicates an inefficient use of wind power. The ESWEindex also provides useful information in determining storagecapacity when considering energy storage options, and batterycharging and discharging patterns can be estimated using thehourly distribution of this index.

The EWES and ESWE indices can be combined to create anindex designated as the wind utilization factor (WUF). This isthe ratio of EWES to the total wind energy harvested by WTG.The EWES, ESWE, and WUF are useful indices containing con-siderable information.

III. EVALUATION MODEL

The adequacy evaluation model for a power system con-taining wind power is shown in Fig. 2. The overall generatingsystem is divided into subsystems of WTG and conventionalgenerators. The power output generated from the wind systemis combined with the capacity of the conventional system tocreate the generation model for the entire power system.

The power output of a WTG depends on the stochastic na-ture and chronological variability of the wind velocity. Wind ishighly variable, site-specific, and terrain specific. There is also anonlinear relationship between the available wind speed and theelectric power generated by a WTG. The reliability evaluationconsists of three consecutive steps–wind data modeling, WTGpower evaluation, and system adequacy assessment.

A. Wind Data Modeling

The first step involves the modeling of the time-varying windspeed that dictates the amount of energy that can be extractedfrom the wind at the system location. Historical wind speed dataare required for the specific site, from which hourly data canbe predicted using a time series model [4]. The model parame-ters are determined from actual wind data records at the site inquestion.

The simulated wind speed can be obtained from themean wind speed and its standard deviation at time tusing (1)

(1)

The data series is used to establish the wind speed timeseries model in (2)

(2)

Fig. 2. Wind-conventional system model.

Fig. 3. Power curve of a WTG.

where and are theautoregressive and moving average parameters of the model,respectively.

An appropriate wind model should be selected to representthe wind characteristics at a particular site [4]. A computer pro-gram has been developed to implement an ARMA [4, 3] modeland utilize annual site-specific hourly data for mean wind speedand standard deviation and generate hourly wind speed data fora desired number of yearly samples.

B. WTG Power Evaluation

The second step involves the interaction of the hourly windspeed data generated in the first step with the WTG design pa-rameters in order to evaluate the electrical power generated as afunction of time.

A power curve based on the WTG design is a plot of outputpower against the average wind speed as shown in Fig. 3. Windturbines are designed to start generating at the cut-in wind speed

. Fig. 3 shows that the power output increases nonlinearly asthe wind speed increases from to the rated wind speed .The rated power is produced when the wind speed variesfrom to the cut out wind speed at which the WTG willbe shut down for safety reasons. The electrical power generatedhourly is calculated from the wind speed data using the powercurve of the WTG.

C. System Adequacy Assessment

The hourly power generated by the WTG is combined withthe outputs of other existing conventional generating units in thesystem. Monte Carlo simulation is used to resolve the system

KARKI AND BILLINTON: COST-EFFECTIVE WIND ENERGY UTILIZATION FOR RELIABLE POWER SUPPLY 437

complexity by simulating the wind conditions and the corre-sponding system operation while recognizing the chronology ofthe actual events as they occur. Generating unit up and down res-idence times are assumed to be exponentially distributed and canbe calculated using the unit mean times to failure and repair [1].

The outage histories of all the generating units are combinedto create the generation model, which is compared with thehourly load and the accepted deterministic criterion to identifythe healthy, marginal, and the at risk states. The simulation pro-ceeds chronologically from one hour to the next for repeatedyearly samples until specified convergence criteria are satis-fied. The number of healthy states , marginal states ,and risk states , and their durations arerecorded for the entire N simulation years. The well-being in-dices are evaluated using (5)–(7) [5]

Healthy State ProbabilityYear in hours

(5)

Marginal State ProbabilityYear in hours

(6)

Loss of Load ProbabilityYear in hours

(7)

The inclusion of WTG in a power system introduces ad-ditional system stability problems. The power imbalances insupply and demand that are normally caused by load variationstend to accelerate or retard the rotating generators, causingfrequency and voltage fluctuations. Conventional units, suchas diesel generators, respond to these stability problems bychanging the supply power to match the demand throughexcitation and governor controls, respectively. The WTG units,however, cannot provide the proper power balance since theirpower supply fluctuates randomly and often at a higher raterelative to the load variations. On the contrary, the rapid fluc-tuations in the WTG supply become the root cause for powerimbalance rather than the load variations in a conventionalsystem. A common practice to solve this problem is to imposean operating constraint which limits the wind system to aspecified fraction of the total demand.

The wind system generation model, therefore, depends on theload due to the operating constraint applied. A wind energy toconventional energy dispatch ratio (W:G ratio) has been usedas an operating constraint in building the generation model forthe wind system. The load is shared jointly by the wind andconventional systems in the specified ratio, always dispatchingwind energy to allow a maximum of its share. In this way, theuseful capacity of the wind system is calculated and added to theavailable capacity of the conventional generating units in orderto create the generation model.

The saving in fuel energy is the total expected energy sup-plied by all of the WTG units in a power system. If and

are the total available wind and conventional generating ca-pacity, respectively, and the load in hour i, the EWES can

be calculated using (8) when the simulation is run for N sampleyears with a W:G ratio of x

EWESWLi

N(8)

where

for and

for and

and for load curtailment conditions

for and

for and

The ESWE, the energy harvested from wind which cannot besupplied to the load, is calculated using (9)

ESWEWi WLi

N(9)

The WUF is the ratio of the EWES to the total wind energyharvested by WTG, and can be calculated using (10)

WUFEWES

EWES ESWE% (10)

The simulation model described in this section assumeshourly events with WTG outputs dictated by hourly mean windspeed variations. The model is, therefore, not intended fortransient analyses of wind power fluctuations. The simulationmodel is appropriate for system planning studies which requiresystem performance analyses over an extended period of timein the future.

A software tool named SIPSREL has been developed bythe authors which implements the evaluation model describedin this section, and can be used to generate the mean values andthe distribution of the indices discussed above. The software wasused to obtain the results of the studies in Section V.

IV. CAPACITY FACTOR VERSUS WIND UTILIZATION FACTOR

Capacity factor (CF) is a familiar term in wind power tech-nology, and is the WTG’s actual energy output for the year di-vided by the energy output if the machine operated at its ratedpower output for the entire year. Although a large CF is gener-ally preferred, it may not always be an economical advantage.For example, it may be of advantage to use a larger generatorwith the same rotor diameter in a very windy location. Thiswould lower the CF, but it may substantially increase annualenergy production [6].

CF depends on the intermittent nature of the wind regime,and on the relative turbine rotor and generator capacities. Onthe other hand, the WUF introduced in this paper depends onthe system operating policies, and on how well the system loadvariations follow the wind variation pattern.

WTG capacity decisions based merely on CF, lack informa-tion on the actual wind utilization that is important for relia-bility/cost assessment. The CF and WUF can be combined to

438 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 2, JUNE 2004

Fig. 4. System reliability and fuel offset with increasing wind capacity.

obtain an index designated as the wind utilization efficiency(WUE), which can be calculated using (11)

WUE CF WUF (11)

This index indicates the amount of return from investment inWTG, and therefore, provides useful information on deciding anappropriate level of wind energy penetration in a power system.The lower the value of WUE for a power system, the lower willbe the benefits of utilizing wind energy in that system.

V. WIND ENERGY UTILIZATION STUDIES AND RESULTS

Case study results on a typical small power generating systemare presented in order to illustrate how an appropriate level ofwind energy utilization can be determined. Such studies andtechniques can also be applied to larger systems where a sig-nificant proportion of wind power is anticipated.

The example system has three diesel generating units with5% FOR (MTTF h, MTTR h) that are rated at 720,1000, and 1400 kW, respectively. The geographic location of thesystem has wind conditions that can be represented by the SwiftCurrent, Saskatchewan, Canada, data. The system peak load is1540 kW with hourly chronological load shape of the IEEE-RTS[7]. A typical operating constraint of limiting the wind energyto 40% of the system load (W:G ratio of 0.67) is considered.

The healthy state probability with a LLU criterion is 0.901and is taken as the accepted adequacy criterion in this example.This criterion should, however, be determined from a reliabilitycost and worth analysis, or from planning experience, as is thecase with most conventional probabilistic risk criteria acceptedby major power utilities. The expected fuel energy consumptionfor this system is 8258 MWh/yr. The resulting emissions willconsist of about 7510 tons of CO , 180 tons of No , 9 tons ofSO , including other gases and hazardous waste oils. A heat rateof 3.2 kWh/l for diesel fuel is assumed in these calculations.

This study considers the addition of different amounts of windcapacity to determine a reasonable wind penetration level. A 4%FOR (MTTF h, MTTR h) is assumed for theWTGs, with 5, 18, and 25 m/s as the cut-in, rated, and cut-outwind speeds, respectively.

Fig. 5. Wind utilization with increasing wind capacity.

Fig. 6. Cost comparison with increasing wind capacity.

Fig. 4 shows the increase in system reliability when an in-creasing number of 720-kW-rated WTGs are added to the basesystem. It is not necessary to expand the system capacity as faras system adequacy is concerned since it is assumed that thebase system reliability is acceptable. However, the addition ofwind energy offsets conventional fuel consumption which notonly reduces environmentally harmful emissions but also lowersoperating costs. Fig. 4 also shows the amount of fuel energyoffset by the wind. It may be economically advantageous to in-stall wind power at a time when the system adequacy may bewell above the acceptable level. This can be determined by com-paring the cost savings resulting from fuel offset against the in-stallation and operating costs of WTGs.

There is normally a linear increase in investment cost withan increasing number of WTGs; whereas the increase in relia-bility tends to saturate as seen in Fig. 4. It is important to assessboth the reliability benefit and the costs associated with addingWTGs in determining appropriate wind capacity expansion in apower system. The relative amount of wind energy that can beactually utilized by the system load decreases with increasingwind capacity installation as shown in Fig. 5. This figure alsogives an indication of how the return in wind investment de-clines with increasing investment.

Fig. 6 compares the investment cost and the fuel cost savingswith increasing WTG installation. All monetary values are inCanadian dollars. A WTG unit, installation, and maintenancecost of $120/kW/yr is assumed in calculating the investmentcost. Fuel cost of $0.55/l is assumed for the diesel units in cal-culating the fuel cost savings. Additional installations of up tothree WTG units are justified by the cost comparison analysisin Fig. 6. In practice, the cost analysis should also include anysubsidies received for wind installations, penalty costs for emis-sions, and other conventional unit operation cost offset, etc.

KARKI AND BILLINTON: COST-EFFECTIVE WIND ENERGY UTILIZATION FOR RELIABLE POWER SUPPLY 439

Fig. 7. WTG capacity required to maintain reliability.

The vertical line in Fig. 6 indicates the amount of wind ca-pacity installation for which the investment cost and savings areequal. Further increase in wind capacity is not economically jus-tified. This vertical line corresponds to 8% WUE in Fig. 5. Thispaper recommends the use of a WUE criterion in conjunctionwith a reliability criterion to help determine the appropriate levelof wind penetration in a system.

Consider a situation where capacity expansion is being con-sidered in order to meet increasing demand. The rising curvein Fig. 7 shows the amount of wind capacity required to main-tain the specified system reliability criterion for different peakload levels. The falling curve shows the WUE at those capacityadditions.

It can be seen from the capacity curve in Fig. 7 that the de-sired reliability cannot be achieved by adding any amount ofwind capacity if the peak load exceeds 2060 kW. The verticalline L2 shows the maximum load growth that can be met at theacceptable reliability level by adding wind power. The verticalline L1 indicates the maximum load that can be supplied with aneconomic advantage by installing wind power. A WUE of 8%is taken as the acceptable criterion in this case. The acceptableWUE criterion is a managerial decision based on cost analysesthat should foresee anticipated variations in cost parameters upto the planning horizon. Capacity expansion strategy shouldconsider conventional generating units if the anticipated peakload exceeds this limit. For a lower load, say 1700 kW, the re-quired WTG capacity should be at least 900 kW to meet therequired reliability criterion, and should not exceed 2500 kWfor the WUE criterion, as shown in Fig. 8. An appropriate pene-tration level can be determined by comparing the costs and ben-efits represented by the two curves within the two vertical linesin Fig. 8.

It should be noted that the WTG used in the example has typ-ical rotor design parameters suitable for a more windy locationthan swift current which has a mean wind speed of 6.2 m/s. Op-timum wind utilization requires proper matching of wind tur-bine characteristics with installation site wind data. Studies asillustrated above can be done to compare different turbine char-acteristics to obtain the appropriate wind penetration level.

Fig. 8. WTG capacity requirement criteria.

VI. DISCUSSION OF RESULTS

This section highlights some interesting findings from the re-sults of the studies illustrated in the previous section.

New units are usually brought into service just before thesystem adequacy level falls below the accepted criterion in con-ventional capacity expansion. The study results show that ca-pacity expansion dates should not be determined by the relia-bility criterion alone when considering WTG. There may be asignificant economic advantage in adding WTG at a time whenthe system adequacy is relatively high.

A specified reliability criterion can always be obtained byadding appropriate conventional generating capacity. Since thepower supply reliability of WTG is dictated by the intermittentnature of wind availability, addition of any amount of wind ca-pacity in a power system may not provide the specified systemadequacy. Capacity expansion should then be considered byadding conventional generating units.

The WUE is the ratio of the actual energy utilized to the totalenergy based on rated WTG capacity. This index, therefore, re-flects the ratio of the cost savings from fuel offset to the totalinvestment on WTG. The WUE criteria can be significantly dif-ferent for different systems depending on various factors suchas wind regime, system composition, fuel costs, and operatingpolicies. A wind penetration level that falls below the specifiedWUE criterion is not justified from cost considerations. Con-ventional generating units should be considered during capacityexpansion if WTG does not meet the WUE criterion.

Turbine design characteristics should be selected to matchthe available wind data at the installation site for optimum CF.This will usually increase the WUF and provide better systemavailability. Any increased investment costs for custom designshould, however, be included in the analysis.

The reliability and cost criteria indicated above can be usedjointly to obtain an acceptable range of wind penetration levels,as shown in Fig. 8, when considering wind energy applicationin a power system. Analyses as shown in this figure can helpthe system planner compare the costs and benefits at differentwind capacities within the acceptable range to determine an ap-propriate penetration level.

440 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 2, JUNE 2004

VII. CONCLUSION

Determining the right amount of wind penetration in a powersystem is becoming increasingly important, as the applicationof this relatively new form of energy is expected to grow muchfaster than other existing forms. The main difficulty arises dueto the highly fluctuating power output capacity of WTGs in con-trast to the stable power capacity of conventional generatingunits. Some planners use capacity factors to estimate the equiv-alent power rating of WTG. A realistic method to determinean appropriate wind penetration level should, however, includeboth cost and reliability analyses based on actual utilization ofwind energy in a power system.

This paper presents a reliability/cost evaluation model usingMonte Carlo simulation to obtain probabilistic quantitative in-dices that recognize the random nature of wind, load variation,unit failures and repairs, and system operation. The healthy stateprobability measures system adequacy based on specified deter-ministic criteria. Wind utilization efficiency indicates how muchof the total investment in WTG is actually being utilized. Thispaper illustrates the use of these two indices in specifying reli-ability and cost criteria to help determine an appropriate windpenetration level in a power system.

REFERENCES

[1] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems,2nd ed. New York: Plenum, 1996.

[2] Isolated Systems Generating Planning Practices; A Survey of CanadianUtilities, Nov. 1995.

[3] R. Billinton and R. Karki, “Capacity reserve assessment using systemwell-being analysis,” IEEE Trans. Power Syst., vol. 14, pp. 433–438,May 1999.

[4] R. Billinton, H. Chen, and R. Ghajar, “Time-series models for reliabilityevaluation of power systems including wind energy,” Microelectron. Re-liab., vol. 36, no. 9, pp. 1253–1261, 1996.

[5] R. Billinton and R. Karki, “Application of Monte Carlo simulation togenerating system well-being analysis,” IEEE Trans. Power Syst., vol.14, pp. 1172–1177, Aug. 1999.

[6] The Danish Wind Industry Association website, “Wind Energy Refer-ence Manual” [Online]. Available: www.windpowr.org

[7] Reliability Test System Task Force of the Application of ProbabilityMethods Subcommittee, “IEEE Reliability Test System,” IEEE Trans.Power App. Syst., vol. PAS-98, pp. 2047–2054, Nov./Dec. 1979.

Rajesh Karki (M’02) received the B.E. degree from Burdwan University,Durgapur, India, and the M.Sc. and Ph.D. degrees from the University ofSaskatchewan, Saskatoon, SK, Canada.

Currently, he is an Assistant Professor in the Department of ElectricalEngineering at the University of Saskatchewan. He was a Lecturer forTribhuvan University, Kathmandu, Nepal. He was also an Electrical Engineerwith Nepal Hydro & Electric, Butwal, Nepal; Udayapur Cement Industries,Udayapur, Nepal; Nepal Telecommunications Corporation, Kathmandu, Nepal;and General Electric Canada, Peterborough, ON.

Roy Billinton (LF’01) received the B.Sc. and M.Sc. degrees from the Universityof Manitoba, Winnipeg, MB, Canada, and the Ph.D. and D.Sc. degrees from theUniversity of Saskatchewan, Saskatoon, SK, Canada.

Currently, he is a Professor Emeritus in the Department of ElectricalEngineering at the University of Saskatchewan. He joined the University ofSaskatchewan in 1964. He was also with Manitoba Hydro, Winnipeg, MB,Canada, in the System Planning and Production Divisions. He is FormerlyActing Dean of Graduate Studies, Research and Extension of the College ofEngineering at the University of Saskatchewan. He is also an author of powersystem analysis, stability, economic system operation, and reliability papers.

Dr. Billinton is a Fellow of the EIC and the Royal Society of Canada.