Probabilistic Wind Energy Modeling in Electric Generation System Reliability Assessment

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 3, MAY/JUNE 2011 1507

Probabilistic Wind Energy Modeling in ElectricGeneration System Reliability Assessment

Yi Zhang, Senior Member, IEEE, A. A. Chowdhury, Fellow, IEEE, and D. O. Koval, Fellow, IEEE

Abstract—Power grid reliability impacts could be significantwhen a large amount of variable wind generation is integratedwith the electric power system. The widely used determinis-tic reliability assessment method is invalid when modeling theintermittency of wind energy sources. The energy-based proba-bilistic reliability assessment models are required in system re-liability impact assessment in order to consider the stochasticcharacteristic of wind resources. This paper investigates differentstochastic characteristics in wind energy integration, includingresource availability, generation facility outage, and transmissionavailability. A probabilistic framework of reliability modeling forrenewable resource integration such as wind energy conversionsystem is proposed in this paper. Using the proposed reliabilitymodels and framework, the cost of wind energy integration withthe power grid for maintaining system adequacy and reliabilitycan be evaluated realistically. The IEEE Reliability Test System isutilized to demonstrate the developed models and methods. Themethodology can be used for modeling the reliability of industrialand commercial facilities being serviced by wind farms and trans-mission lines.

Index Terms—Cost, outage rate, planning, reliability, transmis-sion availability, wind energy.

I. INTRODUCTION

R ENEWABLE energy resources, such as wind and solarenergy conversion systems, play an important role to

eliminate reliance on fossil fuels, as well as in reducing thegreenhouse gas emissions. With the wind energy technologyadvancements in the past couple of decades, it is expected that alarge amount of electric energy supply requirements will be metby nonconventional energy sources, such as wind, solar, andgeothermal technologies. Many countries have adopted aggres-sive Renewable resource Portfolio Standard (RPS) targets in or-der to reduce their reliance on imported oil and environmentallyharmful fossil fuels. For example, in the state of California,a 33% RPS target by 2020 is under consideration [1]. Wind

Manuscript received January 18, 2010; accepted May 17, 2010. Date ofpublication March 14, 2011; date of current version May 18, 2011. Paper2010-PSEC-015, presented at the 2010 IEEE/IAS Industrial and Commer-cial Power Systems Technical Conference, Tallahassee, FL, May 9–13, andapproved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLI-CATIONS by the Power Systems Engineering Committee of the IEEE IndustryApplications Society.

Y. Zhang and A. A. Chowdhury are with California Independent System Op-erator, Folsom, CA 95630 USA (e-mail: [email protected]; [email protected]).

D. O. Koval, deceased, was with the University of Alberta, Edmonton, ABT6G 2E1, Canada.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIA.2011.2127435

resource integration with the power system has received in-creased attention by power system researchers and engineersin both planning and operation phases. Intermittency and vari-ability of energy production associated with any renewabletechnologies need to be reflected and accurately modeled insystem reliability performance assessments.

The inability of modeling the stochastic characteristics ofpower system is not a new problem for widely deterministicmethods; however, it becomes a serious problem when consid-ering the integration of wind resources with the power system.For example, in the current practice of system planning, thedeterministic method is used in generation interconnection toidentify and resolve the stability issues [2]. The transmissionupgrades identified based on the worst case scenarios may beunderutilized if the capacity factor of wind resource is low. Asolution that has been used in deterministic study is to adopt aderated capacity as the target capacity of transmission upgrade[3]. The selection of the derated target capacity is normallybased on the average of historical data or field measurements.The deterministic reliability assessment is a snapshot studythat is difficult to cover all possible scenarios. The systemaddition identified by deterministic methods cannot adequatelymodel power system capability to accommodate different typesof generation technologies including intermittent sources. Theprobability of loss of load may increase when wind resourcepenetration and system load increase [4] and [5].

Probabilistic reliability techniques are required to model theimpacts of wind energy resources on system reliability andadequacy. The energy-limited and intermittent characteristics ofwind generation, particularly wind generation, have been stud-ied using the probabilistic reliability assessment techniques.The capacity state probability model of energy-limited gener-ation in probabilistic reliability assessment has been developedin [6] and [7]. The capacity state probability model of windgeneration output is dependent on wind speed and wind tur-bine outage [8], [9]. The impacts on system reliability fromwind generation have been investigated based on probabilisticreliability assessment from different viewpoints [4], [5], [10],[11]. It has been recognized that the system reliability maybe degraded when wind generation penetration increases inpower system, because of the intermittent characteristic of windresource. The requirements of additional conventional capacitymay increase in order to maintain system reliability [5]. Notethat the deterministic approach is favored in calculating theoperating limit and transmission capability, which are neededas inputs to probabilistic reliability assessments.

A new approach to reliability cost assessment is presentedin this paper, which is an extension of the model developed

0093-9994/$26.00 © 2011 IEEE

1508 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 3, MAY/JUNE 2011

in [5]. The impacts of wind resource on system reliability canbe quantified by the cost of additional conventional capacity.Several reliability modeling issues, which may affect the ac-curacy of probabilistic reliability assessment for wind resourceintegration, are investigated in this. As an extension of [10], theimpact of wind turbine outage on system reliability is analyzedfirst. Then, the correlation between the wind capacity factor andthe outage rate of wind turbine is discussed. Another modelingissue is related to the capacity of transmission system. It isassumed that the transmission capacity has been obtained ina deterministic study. An equivalent probabilistic reliabilitymodel is developed to represent the composite system of trans-mission and wind generator. Using the developed model, theimpact of transmission upgrade on system reliability can beassessed when different target capacity of transmission upgradeis adopted. The outages of transmission line and other facilitiescan also be incorporated into the developed model. Based onthe proposed models and methods, a framework of identify-ing appropriate target capacity of transmission upgrades andadditional generation capacities can be developed. The IEEEReliability Test System (IEEE-RTS) is used to illustrate thedeveloped probabilistic models.

II. MODELING WIND RESOURCE IN GENERATION

SYSTEM ADEQUACY EVALUATION

A. Reliability Index, EENS

Different reliability indices can be used to quantify thesystem reliability. Loss-of-load expectation (LOLE), loss-of-load probability, and expected energy not supplied (EENS)have been widely used in probabilistic reliability assessmentin power system reliability evaluations. Similar to that in [10],EENS is used in this paper as the reliability index. It has beenverified that the reliability assessment results using EENS inthis paper are consistent with the results using hourly LOLE.Only the results using EENS are presented. According toBillinton and Allan [6], EENS can be calculated as

EENS =n∑

k=1

EkPk (1)

where n is the number of system capacity states, Pk is theprobability of a capacity state, and Ek is the energy curtailedwhen the capacity is at state k. EENS has energy unit such asMWh or GWh.

B. Capacity States of a Wind Farm

Assuming that there is no energy storage facility associatedwith the wind energy conversion system, the wind generationcan be modeled as a conventional generation with multiplecapacity states with corresponding probability reflecting theenergy availability at various levels [7]. The capacity states ofwind generation can be sampled from the historical profiles ofwind generation. The philosophy of using the historical profilesof wind generation is that both wind energy availability andwind turbine availability have been reflected in the historicalprofiles. In the absence of live data, the wind generation output

is normally calculated based on the wind speed of the locationwhere the wind turbine is installed and the wind turbine tech-nology [8], [10], [11].

In a wind farm that has many wind turbines, the availabilityof individual wind turbines is another factor that may affectthe output of the wind farm. A joint capacity state method hasbeen developed in [8] and [9] to calculate the capacity statesof wind farm, considering the availability of both wind energyand wind turbine. This model is further employed in generationsystem reliability assessment for wind generation integrationin [10]. The same idea is extended in this paper to investigatethe correlation of the wind turbine outage and the wind farmcapacity factor.

The capacity factor of a wind farm is the ratio between theaverage capacity and the maximum capacity in the study period,which normally is a calendar year. A large wind capacity factorimplies that the probabilities of high wind conditions are large.Capacity factor can be calculated as

Capacity factor =Average capacity of study period

Maximum capacity. (2)

In order to calculate the joint states of a wind farm, twocapacity state tables need to be created first. One is the statetable of available wind. It can be represented as a pair ofavailable wind capacity and its probability (Cwnd

j , Pwndj ), for

j = 1 to s; s is the number of wind capacity states. The windcapacity availability and its probability can be obtained fromthe historical or field-measured wind profiles. The other statetable is for the capacity of available wind turbines and itsprobability. The state table for the wind turbine capacity can becalculated using the forced outage rate (FOR) of wind turbines.The method is the same as that used for conventional generator[10]. Then, the probability of a given wind farm output Ck canbe obtained by

P (Ck) =n∑

i=1

⎛⎝Pwtg

i ×s∑

j=1

Pwndj × U

(Ck

i− Cwnd

j

)⎞⎠

(3)

where n is the number of states of wind turbine availability,Pwtg

i is the probability of the wind turbine availability at statei, and U(•) is a step function.

From (3), it can be seen that the probability of wind capacityis the weight of the probability of wind turbine availability incalculating the probability of the joint capacity. Then, a largewind capacity factor implies that the wind turbine availabilityhas large impact on the probability of the joint capacity, partic-ularly under high wind conditions. Therefore, it is necessary toevaluate and revise the wind profile by incorporating the windturbine availability when the wind capacity factor is large.

C. Joint Capacity of Wind Generation and Transmission

Interconnecting wind generation to the grid may need longdistance lines since the wind resources are normally locatedat remote areas. The transmission path between the windgeneration and the main grid may consist of one or multiple

ZHANG et al.: WIND ENERGY MODELING IN ELECTRIC GENERATION SYSTEM RELIABILITY ASSESSMENT 1509

Fig. 1. Example of wind farm interconnection.

transmission lines and reactive power support devices. Nor-mally, the capacity of the transmission path is a function ofthe availability of transmission lines and the status of the reac-tive power compensation devices. The deterministic reliabilityassessment normally identifies the transmission upgrade basedon a derated capacity instead of the full capacity of wind farm.The target capacity of transmission upgrade that is often used incurrent practice is the average megawatt value on hourly windprofile during the peak-load or off-peak-load hours, dependingon which scenario is selected for the deterministic study. Insome wind resource areas, the average wind capacity duringsummer peak-load hours may be 60% of the wind farm capacityand even lower; during the off-peak hours, it can be as high as80% [3]. It is important to select the target capacity appropri-ately so that both the system reliability and the utilization ofgreen energy will be economically optimized.

Probabilistic reliability models can permit the selection of theoptimal target capacity of transmission upgrade. In this section,a probabilistic reliability model of the composite system ofwind generation and transmission lines is developed basedon reliability mathematics [12]. A typical wind generationinterconnection is shown in Fig. 1, where a wind farm isconnected to the system through two transmission lines. Thewind generation and its associated transmission upgrades canbe modeled as a system in series connection from the reliabilityassessment standpoint.

The series-connection system is shown in Fig. 2. The inputand output of the series system are wind capacity and thedelivered power to the main grid, respectively. The capacityof the wind farm, transmission lines, and the output of thecomposite system are denoted by x, y, and z, respectively. Inthis series-connection system, the output z is the minimum of xand y, i.e.,

z = min(x, y). (4)

The probabilities of x and y are denoted by Px and Py,respectively; hence, the probability of the composite systemoutput Pz can be obtained by

Pz(z) = Px(z) ×∑y≥z

Py(y) + Py(z) ×∑x≥z

Px(x). (5)

The capacity state pair (x, Px) of the wind farm can be obtainedby the method discussed in Section II-B. The derivation ofcapacity states of transmission lines, denoted by y, is discussedin the following.

If the forced outages of transmission lines are ignored, thetransmission path has two capacity states, namely, path rating

Fig. 2. Series-connection system.

and zero. The probabilities of these two capacity states areone and zero, respectively. Considering line forced outages,each transmission line still has two capacity states, but theprobability of capacity states needs to be revised according tothe outage rate of the line. For the transmission path with twoparallel lines, as shown in Fig. 1, its capacity states can beobtained by convoluting the capacity states of two lines. Thealgorithm is the same as for calculating the capacity states ofgeneration system with multiple units, which is not repeatedhere; instead, the reader is referred to [6].

The transmission capacity of the transmission path is alsoaffected by the status of the reactive power devices, such asshunt capacitors or series compensators. If some reactive powerdevices are out of service, the transmission capacity may needto be derated. The capacity states considering the outages ofreactive power devices can be calculated using the series-connection system model, as shown in Fig. 2. For simplicity,only the line outage is considered in this paper. Note that theavailable capacity of the transmission path between the windgeneration and the main grid is determined separately, normallyby deterministic reliability assessment method.

The FOR of a two-terminal transmission line can be calcu-lated by the following [13]:

FORL = (λL × L × rL + 2λT × rT )/T (6)

whereλL the frequency of line-related failure; in occurrences,

years, or miles but is normally given in per 100 miles;L the length of a line; in miles;rL the mean duration of line-related failure, in hours or

occurrences;λT the frequency of terminal-related failure; in occur-

rences or years;rT the mean duration of terminal-related failure; in hours

or occurrences;T the hours of a cycle, e.g., 8760 hours of a year.

D. Benefit/Cost Assessment of Derated Transmission Upgrade

The benefit of using derated transmission mainly is thesaving on transmission investment. From the standpoint of sys-tem reliability, however, the derated transmission upgrade mayreduce the contribution of wind generation to system reliabilityimprovement. A benefit/cost assessment is therefore needed todetermine the optimal capacity of the transmission upgradefor wind generation interconnection. The cost may includeadditional conventional capacity that is needed to maintainsystem reliability and the additional wind capacity to meet themandatory RPS target. Additional transmission upgrade for the


TABLE IWIND ENERGY AVAILABILITY AND THE PROBABILITY

Fig. 3. EENS increases as the wind penetration and peak load increase.

higher capacity may also be needed. The reliability approachproposed in this paper can be used to identify the cost of deratedtransmission upgrade, which will be discussed in detail in thefollowing section.

III. RELIABILITY ASSESSMENT OF WIND RESOURCE

A. Reliability Cost of Wind Integration

The IEEE-RTS [13] is used in this paper to demonstratethe reliability modeling of wind energy integration using theproposed models and methods. In this section, a wind farm,as given in [10], is added into the system. The wind capacityavailability of this wind farm is shown in Table I. The windcapacity factor is 83%. The capacity of the wind farm isadjusted so that the consumed wind energy is 6% of the totalconsumed energy. This reflects the 6% RPS target. Assume thateach wind turbine generator has 2-MW capacity and 10% FOR.The base case scenario has 2400 MW of peak load and 0 MWof wind generation. The EENS of this base case scenario isused as the reliability criterion of the system. For any otherstudied scenarios, if the EENS is less than the EENS of thebase case scenario, then the studied scenario is deemed reliable;otherwise, it is not reliable.

Fig. 3 shows that the EENS increases rapidly as the loadincreases. In order to maintain system reliability, conventionalcapacity is added into the system. In this example, assume thatthe capacity of the additional units is 25 MW and the FOR is6.3%. The addition of wind generation and conventional capac-ity that are needed to meet the 6% RPS target and to maintainthe system reliability is shown in Fig. 4. It can be seen in this

Fig. 4. Addition of new conventional capacity to improve system reliability.

Fig. 5. Wind penetration change along with peak load increases.

example that the addition of conventional capacity increasesrapidly and will be more than the new wind generation whenthe peak load exceeds a certain level. This implies that the windpenetration is limited for a particular system, depending on thepeak load, which is shown in Fig. 5.

Similar studies have been performed using different windcapacity factors. The same conclusions can be made, althoughthe results are not shown here because of space limitation. Notethat the size and FOR of the additional thermal units that areused in the earlier assessments will affect the total capacityneed of additional thermal units, but the conclusion will stillbe valid. In order to meet the RPS goal and to maintain thesystem reliability, close coordination between the developmentsof wind resource and conventional capacity is always needed inwind resource integration.

The additional conventional capacity causes reliability ca-pacity cost of wind resource integration, which can only beadequately determined using the probabilistic reliability mod-els. The reliability capacity cost can be obtained given the costof additional thermal units. This cost needs to be added withother cost in the economic assessment for wind integration.Assuming that the cost of thermal unit in this example is$0.3 million/MW, the reliability capacity cost of wind integra-tion is shown in Fig. 6. It can be seen that the reliability capacitycost increases quickly as the peak load increases, in order tomeet the 6% RPS target. The method presented in this sectiona simple and easy-to-use practical model that can be utilized inlarge system assessments.


Fig. 6. Cost of capacity addition of wind integration.

Fig. 7. EENS for different wind farms with different capacity factors.

B. Effect of Wind Capacity Factor

In this section, the test system is modified such that thepeak load is 2850 MW. A 570-MW wind farm is added intothe system to replace the 570 MW of existing generation thathas higher FOR. The EENS for scenarios with different windcapacity factors is computed, as well as the need of additionalconventional capacity. The results are shown in Fig. 7, wherethe EENS is illustrated by the wide columns and the need foradditional conventional capacity is illustrated by the narrowcolumns. As expected, the wind farms with low capacity factorhave less contribution to the system reliability than the windfarms with high capacity factor. This is reflected in Fig. 7 in thatthe EENS decreases when the wind capacity factor increases.It is also shown that more additional conventional capacity isneeded for the wind farms with low capacity factor than thewind farms with high capacity factor.

C. Impacts of Wind Turbine Availability

A large wind farm normally includes many energy collectionfacilities, e.g., hundreds of wind turbines in a wind farm. Thissection will discuss the impact of wind turbine availabilityon the system reliability. The correlation of the wind turbineavailability and the wind capacity factor will be analyzed.

Fig. 8. Ratio of EENS change between 4% and 20% wind turbine FORs.

The same modified test system as considered inSection III-B is used. Two wind turbine outage rates,namely, 4% and 20%, are compared. The changes of EENSthat are resulted from the increase of wind turbine outage rateare shown in Fig. 8.

It can be seen that the increase of wind turbine outage ratehas limited impact on system reliability if the wind capacityfactor is low. The impact of wind turbine outage may becomesignificant in the cases of high wind capacity factor. The resultsof reliability assessment may be unrealistic if the wind profiledoes not incorporate the wind turbine availability.

Note that the availability of wind turbines is affected not onlyby the wind turbine outage but also by the outage of collectorsystem and the auxiliary facilities in the wind farm. The outagerate of collector system in the wind farm is normally small sinceunderground cable is often used. On the other hand, the impactof collector system outage may not be small since a collectorfeeder outage will result in all wind turbines on the samefeeder unavailable. The test result of the impact of collectorsystem outage is not presented in this paper because of lackof outage data of collector system. Still, the joint capacity statemodel of wind generator and transmission line, which has beenpresented in Section II-C, can be used to create the capacitystate probability model of a wind farm considering collectorsystem outage.

D. Target Capacity for Transmission Upgrade

Assume that a 570-MW wind farm is interconnected withthe system via the plan of interconnection shown in Fig. 1.Three scenarios of transmission upgrades are compared withdifferent transmission capacities. Normally, the upgrade is de-cided by deterministic criteria that are widely used in trans-mission system planning. In the first scenario, the capacity ofthe transmission upgrade is based on the full capacity of thewind farm, which is assumed to be 570 MW when two linesare in service and 285 MW when one line is in service. Aremedial action scheme of tripping wind generation may beneeded when only one line is in service. The second scenario isthat the transmission upgrade can deliver 80% of the nameplatecapacity of the wind farm, which are 456 MW when two linesare in service and 228 MW when one line is in service. In the


TABLE IITYPICAL INDUSTRY DATA FOR LINE OUTAGE

TABLE IIIPROBABILITY OF LINE CAPACITY

TABLE IVEENS COMPARISON FOR 40% WIND CAPACITY FACTOR

third scenario, the transmission upgrade is based on 60% ofwind capacity, which are 342 and 171 MW when two lines arein service and when one line is in service, respectively.

The probabilistic reliability models proposed in Section II-Care used in system reliability assessment. Line outage data aregiven in Table II, which are the typical outage data of 230-kVlines used in some utilities in North America. Further assumethat the length of the transmission lines is 200 miles to reflectthe long distance of the wind interconnection. The outage rateof each line can be obtained by (6), and the capacity states ofthe two-line transmission system can be calculated using themethod discussed in Section II-C. The capacity states of thetransmission system with two parallel transmission lines areshown in Table III.

First, assume that a 570-MW wind farm with 40% windcapacity factor is interconnected. The EENSs of the threescenarios of transmission upgrades are illustrated in Table IV.In the first column of Table IV, “Full capacity” means thatthe target capacity of transmission upgrade is based on the fullcapacity of the wind farm; “80% capacity” and “60% capacity”mean that the target capacities are 80% and 60% of the windfarm capacity, respectively; “plus outage” means that the lineoutage is modeled. Also listed in Table IV is the ratio of theconsumed wind energy and the total consumed energy. It canbe seen from Table IV that the availability of transmissioncapacity does impact the system reliability and the consumedwind energy but not significantly. The outage of transmission

TABLE VEENS COMPARISON FOR 60% WIND CAPACITY FACTOR

lines between the wind farm and the main grid has a slightimpact on the system reliability and the utilization of windenergy.

For the 570-MW wind farm with 40% capacity factor in thisexample, it may be appropriate to build the transmission lineswhose capacity is 60% of the wind farm capacity from theprobabilistic reliability standpoint. The transmission upgradebased on the full capacity of the wind farm does not providemuch more benefit to the system than the upgrade based on60% capacity.

The wind farm capacity factor may affect the selection of thetarget capacity of transmission upgrade. Assume that a windfarm with 60% capacity factor is integrated with the powersystem, while all other assumptions are the same as those inthe previous example. Table V shows the reliability assessmentresults. It can be seen that, when the transmission capacityis 60% of the wind capacity, the system reliability and theutilization of wind energy reduced significantly compared tothe 80% capacity and full-capacity scenarios. The reliabilitycapacity cost can be evaluated based on the addition of thermalunits. Assume that the FOR of the additional thermal units is0.12. The 60% capacity scenario needs 30 MW of additionalthermal capacity to achieve the same reliability level as inthe full-capacity scenario. It is also noticed that extra windgeneration capacity may be needed for the derated transmissionupgrade scenarios, depending on the RPS target.

IV. CONCLUSION

Wind resource integration has significant impacts on sys-tem reliability. Although the deterministic reliability study isoften used in generation interconnection studies, it lacks thecapability of considering the stochastic characteristics of windresources. It is necessary to complement the deterministic ap-proach with probabilistic models in system reliability assess-ments to identify the system upgrade and the associated cost.

Probabilistic reliability assessment has been applied to windresource integration in this paper. It has been demonstrated thatthe deployment of wind generation needs to be coordinatedclosely with the deployment of conventional capacity. Theprobabilistic reliability assessment can identify the reliabil-ity capacity cost for wind resource integration. The reliabil-ity capacity cost can be estimated based on the addition ofthe conventional capacity that is needed to maintain systemreliability.


Several modeling issues of wind resource integration inprobabilistic reliability assessment have been discussed usingseveral wind generation scenarios. The availability of windturbines in the wind farm has impact on the wind generationoutput and the system reliability. The joint capacity state modelof wind farm that considers wind capacity availability and windturbine availability has been investigated. It is recommendedthat incorporating wind turbine availability in wind integrationreliability assessment, particularly when the wind capacity fac-tor is high, is absolutely necessary. Another important issue thathas been discussed is the derated transmission upgrade in windinterconnection. System reliability will be degraded when der-ated transmission upgrade is adopted. A joint capacity model ofwind generation and transmission has been proposed in order toidentify the appropriate target capacity of transmission upgrade.The reliability cost of using derated transmission upgrade canbe calculated by the proposed method and framework presentedin this paper. In conclusion, the probabilistic reliability modelsand methods presented in this paper are simple and easy to useand can be applied to practical large power systems to inves-tigate the system reliability impacts from large wind energypenetration.

ACKNOWLEDGMENT

This paper does not reflect in any form and manner theposition of the California ISO. Any errors and omissions arethe sole responsibilities of the authors.

REFERENCES

[1] “2007 Integrated energy policy report,” California Energy Commission,Sacramento, CA, CEC-100-2007-008-CMF, p. 101, 2007.

[2] A. A. Chowdhury, Y. Zhang, H. Liu, S. Zhu, and D. Le, “Practice of largewind generation interconnection study in CAISO,” in Proc. IEEE PESGen. Meeting, Calgary, AB, Canada, Jul. 26–30, 2009, pp. 1–7.

[3] CAISO, RETI Phase II—Conceptual Transmission Planning, 2009.[4] R. Karki, R. Billinton, and G. Bai, “Risk based equivalent wind capacity in

power generation systems,” in Proc. 8th Int. Conf. Probabilistic MethodsPower Syst., Ames, IA, Sep. 12–16, 2004, pp. 463–469.

[5] Y. Zhang and A. A. Chowdhury, “Reliability assessment of windgeneration in planning and operating phases in generation system,” inProc. IEEE PES Gen. Meeting, Calgary, AB, Canada, July 26–30, 2009,pp. 1–7.

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

[7] R. Billionton and P. Harrington, “Reliability evaluation in energy limitedgenerating capacity studies,” IEEE Trans. Power App. Syst., vol. PAS-97,no. 6, pp. 2076–2085, Nov. 1978.

[8] P. Giorsetto and K. F. Utsurogi, “Development of a new procedure forreliability modeling of wind turbine generators,” IEEE Trans. Power App.Syst., vol. PAS-102, no. 1, pp. 134–143, Jan. 1983.

[9] X. Wang, H. Dai, and R. Thomas, “Reliability modeling of largewind farms and associated electric utility interface systems,” IEEETrans. Power App. Syst., vol. PAS-103, no. 3, pp. 569–575,Mar. 1984.

[10] A. A. Chowdhury, “Reliability models for large wind farms in generationsystem planning,” in Proc. IEEE PES Annu. Gen. Meeting, San Francisco,CA, Jun. 12–16, 2005, pp. 1926–1933.

[11] R. Billinton, H. Chen, and R. Ghajar, “Time-series models for reliabil-ity evaluation of power systems including wind energy,” Microelectron.Reliab., vol. 36, no. 9, pp. 1253–1261, Sep. 1996.

[12] A. Papoulis, Probability, Random Variables, and Stochastic Processes,3rd ed. New York: WCB McGraw-Hill, 1991.

[13] “IEEE reliability test system,” IEEE Trans. Power App. Syst., vol. PAS-98,no. 6, pp. 2047–2054, Nov. 1979.

Yi Zhang (SM’09) received the M.S. degree fromTianjin University, Tianjin, China, and the Ph.D.degree from Washington State University, Pullman.

He was with the Electric Power Research Insti-tute, Beijing, China, where he worked mainly onthe development and implementation of the Distrib-ution Management System, Supervisory Control andData Acquisition/Energy Management System, andPower Market. He is currently with the Departmentof Regional Transmission, California IndependentSystem Operator, Folsom, CA. His interests include

power system stability and reliability assessments, power system economicassessment, renewable integration, and comprehensive transmission planning.

A. A. Chowdhury (F’05) received the MBA de-gree from St. Ambrose University, Davenport, IA,the M.Sc. degree (with honors) in electrical engi-neering from Belarus Polytechnic Institute, Minsk,Belarus, and the M.Sc. and Ph.D. degrees in elec-trical engineering with specialization in power sys-tems reliability and security from the University ofSaskatchewan, Saskatoon, SK, Canada.

He is currently the Director of Planning andInfrastructure Development with the California In-dependent System Operator, Folsom, CA. He has

approximately 30 years of electric utility industry, electric equipment manufac-turing industry, consulting experience, and teaching, research, and developmentin power system reliability and security assessments, planning, and analysis.He is actively involved in the development of probabilistic models, criteria,and software for use in power system planning, operating, and maintenance.He has given invited lectures on the theory and applications of power systemreliability and value-based planning nationally and internationally. He has per-formed original work on power system reliability and value-based assessments,designed and conducted customer interruption cost surveys, and developedpractical system models for use in reliability cost/reliability worth assessmentsin the emerging competitive electricity market. He coauthored (with Dr. DonKoval) the book Power Distribution System Reliability—Practical Methods andApplications and has authored and/or coauthored approximately 150 technicalpapers on power system analysis, planning, and reliability published in differentpeer-reviewed engineering journals in Asia, Europe, Australia, Africa, andNorth and South Americas.

Dr. Chowdhury a Fellow of the Institution of Engineering and Technology,U.K., a Chartered Engineer in the U.K., and a Registered Professional Engineerin the State of Texas and in the Province of Alberta, Canada. He was therecipient of five best prize paper awards from the IEEE, the InternationalInstitute for Advanced Studies in Systems Research and Cybernetics, andthe 8th International Conference on Probabilistic Methods Applied to PowerSystems. He was also the recipient of the IEEE Region 4 2003 OutstandingEngineer of the Year Award for his contributions to the science of power systemreliability evaluation; the 2005 IEEE Technical Working Group RecognitionAward for his contribution to the revision and expansion of the IEEE Standard762-2005: Standard Definitions for Use in Reporting Electric Generating UnitReliability, Availability, and Productivity; and the IEEE Regional ActivitiesBoard 2005 Achievement Award for his outstanding leadership and contri-butions and to IEEE and Engineering profession. He has been listed in theInternational Biographical Center’s (Cambridge, U.K.) 2004 Living Legends,the 2008/2009/2000 Outstanding Scientists of the World, Marquis’ Who’s Whoin America, Who’s Who in the World, Who’s Who in Finance and Business, andWho’s Who in Science and Engineering.


D. O. Koval (S’64–M’65–SM’78–F’90) was a Dis-tribution Special Studies Engineer with B.C. Hydroand Power Authority, Vancouver, BC, Canada, for12 years, and for two years, he was a Subtrans-mission Design Engineer with Saskatchewan Power,Regina, SK, Canada. He was then a Professor in theDepartment of Electrical and Computer Engineering,University of Alberta, Edmonton, AB, Canada, untilhis death in 2011. He taught classes on reliabilityengineering, power quality, power system analysis,and “IEEE Gold Book.” He was the Editor of the In-

ternational Association of Science and Technology for Development (IASTED)International Proceedings on High Technology in the Power Industry in 1996.He authored or coauthored more than 300 technical publications in the fieldsof emergency and standby power systems, power system reliability, humanreliability, power system disturbances and outages, power quality, and computersystem performance.

Dr. Koval was a Registered Professional Engineer in the Provinces of Albertaand British Columbia, Canada, a Fellow of the American Biographical Institute,and a Life Fellow of the International Biographical Center, Cambridge, U.K.He served on the Board of Directors of several international societies, includ-ing IASTED and the International Institute for Advanced Studies in SystemResearch and Cybernetics (ICSRIC). He was listed in Marquis’s Who’s Whoin the West, Who’s Who in America, Who’s Who in the World, Personalities ofthe Americans, Who’s Who in Science and Engineering, 5000 Personalities ofthe World, and the International Biographical Center’s International Leadersof Achievement, International Who’s Who of Intellectuals, and Men of Achieve-ments. He was the Cochairman of the 1998 IEEE/Industry Applications Society(IAS) Industrial and Commercial Power Systems Technical Conference held inEdmonton. He was the Chairman of the IEEE Standard 493-1997 and 2007(IEEE Gold Book). He was elected as one of the six Distinguished Lecturers ofthe IEEE IAS in 2000–2001. He was appointed to the rank of Distinguished Vis-iting Professor and elected Fellow by the International Institute for AdvancedStudies in Systems Research and Cybernetics in Germany. He was also electeda Fellow of the Engineering Institute of Canada, and he was the recipient theIEEE Standards Medallion Award in 2008.

Documents

Probabilistic Wind Energy Modeling in Electric Generation System Reliability Assessment