1. IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 2, JUNE 2004 435
Cost-Effective Wind Energy Utilization
for Reliable Power Supply
Rajesh Karki, Member, IEEE, and Roy Billinton, Life Fellow, IEEE
Abstract—Environmental concerns and fuel cost uncertainties Power utilities apply different reliability evaluation methods
associated with the use of conventional energy sources have re- depending on their system sizes, and their conventional prac-
sulted in rapid growth of wind energy applications in power gen- tice. Probabilistic risk indices, such as loss of load expectation
erating systems. It is important to assess the actual cost and ben-
efit of utilizing wind energy in a power system. Such assessments (LOLE) or loss of energy expectation (LOEE) [1], are used in
require realistic cost/reliability evaluation methods and quantita- many large power systems. Small isolated systems normally
tive indices. This paper presents a simulation technique that gener- apply deterministic techniques, such as the loss of the largest
ates probabilistic indices that can help determine appropriate wind unit (LLU) [2] to determine capacity requirements. These
power penetration in an existing power system from both the reli- techniques associate fixed capacity outputs to generating units
ability and economic aspects.
and cannot be extended to include wind energy sources that
Index Terms—Monte Carlo simulation, power generating have highly fluctuating capacity levels. On the other hand,
capacity, power system planning, power system reliability, wind although conventional probabilistic methods [1] recognize
energy, wind power.
random system behavior, they do not provide any information
on the available system capacity reserves, and have not been
I. INTRODUCTION readily accepted by small system planners who are used to
capacity planning based on physical and observable reserve
W IND energy sources have the potential to significantly
reduce fuel costs, greenhouse gas emissions, and natural
habitat disturbances associated with conventional energy gen-
margins.
This paper presents a well-being approach [3] that incorpo-
eration. Wind turbine generators (WTGs) are an ideal choice in rates a deterministic criterion in a probabilistic framework and
developing countries where the most urgent need is to supply provides probabilistic reliability indices useful to both the small
basic electricity in rural or isolated areas without any power in- and large system planners. This paper also introduces proba-
frastructure. Active public awareness of the need to save the en- bilistic indices that can be used to evaluate the energy costs and
vironment has encouraged many industrialized nations to pro- utilization efficiency of WTG. The applications of these indices
mote wind energy. Many large industrial companies have made in planning wind energy utilization in power systems are illus-
massive investments in the development of wind technology. As trated with practical examples. This paper also presents the eval-
a result, wind energy has become competitive with conventional uation model developed to obtain these indices.
forms of energy. Power system deregulation has opened oppor-
tunities for many private energy producers. Wind energy is a II. WIND ENERGY AND RELIABILITY INDEXES
potential choice for smaller energy producers due to relatively
In the well-being approach, a power system is considered to
short installation times, easy operating procedures, and different
reside in one of the three states shown in Fig. 1. A system op-
available incentives for investment in wind energy.
erates in the healthy state when it has enough capacity reserve
The environmental benefits of using renewable energy are
to meet a specified deterministic criterion such as the LLU. The
well perceived. Wind application also offsets fuel costs that can
degree of comfort associated with operating the system within
be relatively high in some generating plants. It is evident that
the accepted deterministic criterion is given by the probability of
limitations in the energy available in wind and its intermittent
residing within the healthy state or the healthy state probability
behavior degrade system reliability. A comprehensive evalua-
. The system violates the deterministic criterion without
tion of cost and reliability is required to analyze the actual ben-
causing any load curtailment in the marginal state. The load
efits of utilizing wind energy. The reliability aspects of utilizing
exceeds the available capacity in the at risk state. The
wind energy have largely been ignored in the past due the rela-
can be used as a useful reliability criterion in system adequacy
tively insignificant contribution of these sources in major power
evaluation.
systems, and consequently due to the lack of appropriate tech-
The expected wind energy supplied (EWES) is a useful en-
niques. Increasing application of wind energy can create signif-
ergy index for a power system containing wind power. It mea-
icant impacts on system cost and reliability.
sures the conventional fuel energy offset by wind application
and can be used to assess fuel cost and emission penalty cost
Manuscript received November 5, 2002. savings.
The authors are with the Power Systems Research Group, Department of Another useful index is the expected surplus wind energy
Electrical Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9
Canada (e-mail: Rajesh_Karki@engr.usask.ca; Roy_Billinton@engr.usask.ca). (ESWE), which is defined in this paper as the amount of en-
Digital Object Identifier 10.1109/TEC.2003.822293 ergy that was available but not utilized. A high value of this
0885-8969/04$20.00 © 2004 IEEE

2. 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 ESWE Fig. 2. Wind-conventional system model.
index also provides useful information in determining storage
capacity when considering energy storage options, and battery
charging and discharging patterns can be estimated using the
hourly distribution of this index.
The EWES and ESWE indices can be combined to create an
index designated as the wind utilization factor (WUF). This is
the 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- Fig. 3. Power curve of a WTG.
taining wind power is shown in Fig. 2. The overall generating
system is divided into subsystems of WTG and conventional
generators. The power output generated from the wind system where and are the
is combined with the capacity of the conventional system to autoregressive and moving average parameters of the model,
create the generation model for the entire power system. respectively.
The power output of a WTG depends on the stochastic na- An appropriate wind model should be selected to represent
ture and chronological variability of the wind velocity. Wind is the wind characteristics at a particular site [4]. A computer pro-
highly variable, site-specific, and terrain specific. There is also a gram has been developed to implement an ARMA [4, 3] model
nonlinear relationship between the available wind speed and the and utilize annual site-specific hourly data for mean wind speed
electric power generated by a WTG. The reliability evaluation and standard deviation and generate hourly wind speed data for
consists of three consecutive steps–wind data modeling, WTG a desired number of yearly samples.
power evaluation, and system adequacy assessment.
B. WTG Power Evaluation
A. Wind Data Modeling The second step involves the interaction of the hourly wind
The first step involves the modeling of the time-varying wind speed data generated in the first step with the WTG design pa-
speed that dictates the amount of energy that can be extracted rameters in order to evaluate the electrical power generated as a
from the wind at the system location. Historical wind speed data function of time.
are required for the specific site, from which hourly data can A power curve based on the WTG design is a plot of output
be predicted using a time series model [4]. The model parame- power against the average wind speed as shown in Fig. 3. Wind
ters are determined from actual wind data records at the site in turbines are designed to start generating at the cut-in wind speed
question. . Fig. 3 shows that the power output increases nonlinearly as
The simulated wind speed can be obtained from the the wind speed increases from to the rated wind speed .
mean wind speed and its standard deviation at time t The rated power is produced when the wind speed varies
using (1) from to the cut out wind speed at which the WTG will
be shut down for safety reasons. The electrical power generated
(1) hourly is calculated from the wind speed data using the power
curve of the WTG.
The data series is used to establish the wind speed time
series model in (2) C. System Adequacy Assessment
The hourly power generated by the WTG is combined with
the outputs of other existing conventional generating units in the
(2) system. Monte Carlo simulation is used to resolve the system

3. KARKI AND BILLINTON: COST-EFFECTIVE WIND ENERGY UTILIZATION FOR RELIABLE POWER SUPPLY 437
complexity by simulating the wind conditions and the corre- be calculated using (8) when the simulation is run for N sample
sponding system operation while recognizing the chronology of years with a W:G ratio of x
the actual events as they occur. Generating unit up and down res-
idence times are assumed to be exponentially distributed and can WLi
EWES (8)
be calculated using the unit mean times to failure and repair [1]. N
The outage histories of all the generating units are combined where
to create the generation model, which is compared with the
for and
hourly load and the accepted deterministic criterion to identify
the healthy, marginal, and the at risk states. The simulation pro- for and
ceeds chronologically from one hour to the next for repeated
and for load curtailment conditions
yearly samples until specified convergence criteria are satis-
fied. The number of healthy states , marginal states ,
and risk states , and their durations are for and
recorded for the entire N simulation years. The well-being in-
dices are evaluated using (5)–(7) [5]
for and
The ESWE, the energy harvested from wind which cannot be
Healthy State Probability
Year in hours supplied to the load, is calculated using (9)
(5)
Wi WLi
ESWE (9)
Marginal State Probability N
Year in hours
(6) The WUF is the ratio of the EWES to the total wind energy
harvested by WTG, and can be calculated using (10)
Loss of Load Probability
Year in hours EWES
(7) WUF % (10)
EWES ESWE
The simulation model described in this section assumes
The inclusion of WTG in a power system introduces ad- hourly events with WTG outputs dictated by hourly mean wind
ditional system stability problems. The power imbalances in speed variations. The model is, therefore, not intended for
supply and demand that are normally caused by load variations transient analyses of wind power fluctuations. The simulation
tend to accelerate or retard the rotating generators, causing model is appropriate for system planning studies which require
frequency and voltage fluctuations. Conventional units, such system performance analyses over an extended period of time
as diesel generators, respond to these stability problems by in the future.
changing the supply power to match the demand through A software tool named SIPSREL has been developed by
excitation and governor controls, respectively. The WTG units, the authors which implements the evaluation model described
however, cannot provide the proper power balance since their in this section, and can be used to generate the mean values and
power supply fluctuates randomly and often at a higher rate the distribution of the indices discussed above. The software was
relative to the load variations. On the contrary, the rapid fluc- used to obtain the results of the studies in Section V.
tuations in the WTG supply become the root cause for power
imbalance rather than the load variations in a conventional IV. CAPACITY FACTOR VERSUS WIND UTILIZATION FACTOR
system. A common practice to solve this problem is to impose Capacity factor (CF) is a familiar term in wind power tech-
an operating constraint which limits the wind system to a nology, and is the WTG’s actual energy output for the year di-
specified fraction of the total demand. vided by the energy output if the machine operated at its rated
The wind system generation model, therefore, depends on the power output for the entire year. Although a large CF is gener-
load due to the operating constraint applied. A wind energy to ally preferred, it may not always be an economical advantage.
conventional energy dispatch ratio (W:G ratio) has been used For example, it may be of advantage to use a larger generator
as an operating constraint in building the generation model for with the same rotor diameter in a very windy location. This
the wind system. The load is shared jointly by the wind and would lower the CF, but it may substantially increase annual
conventional systems in the specified ratio, always dispatching energy production [6].
wind energy to allow a maximum of its share. In this way, the CF depends on the intermittent nature of the wind regime,
useful capacity of the wind system is calculated and added to the and on the relative turbine rotor and generator capacities. On
available capacity of the conventional generating units in order the other hand, the WUF introduced in this paper depends on
to create the generation model. the system operating policies, and on how well the system load
The saving in fuel energy is the total expected energy sup- variations follow the wind variation pattern.
plied by all of the WTG units in a power system. If and WTG capacity decisions based merely on CF, lack informa-
are the total available wind and conventional generating ca- tion on the actual wind utilization that is important for relia-
pacity, respectively, and the load in hour i, the EWES can bility/cost assessment. The CF and WUF can be combined to

4. 438 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 2, JUNE 2004
Fig. 5. Wind utilization with increasing wind capacity.
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 in Fig. 6. Cost comparison with increasing wind capacity.
WTG, and therefore, provides useful information on deciding an
appropriate level of wind energy penetration in a power system.
Fig. 4 shows the increase in system reliability when an in-
The lower the value of WUE for a power system, the lower will
creasing number of 720-kW-rated WTGs are added to the base
be the benefits of utilizing wind energy in that system.
system. It is not necessary to expand the system capacity as far
as system adequacy is concerned since it is assumed that the
V. WIND ENERGY UTILIZATION STUDIES AND RESULTS
base system reliability is acceptable. However, the addition of
Case study results on a typical small power generating system wind energy offsets conventional fuel consumption which not
are presented in order to illustrate how an appropriate level of only reduces environmentally harmful emissions but also lowers
wind energy utilization can be determined. Such studies and operating costs. Fig. 4 also shows the amount of fuel energy
techniques can also be applied to larger systems where a sig- offset by the wind. It may be economically advantageous to in-
nificant proportion of wind power is anticipated. stall wind power at a time when the system adequacy may be
The example system has three diesel generating units with well above the acceptable level. This can be determined by com-
5% FOR (MTTF h, MTTR h) that are rated at 720, paring the cost savings resulting from fuel offset against the in-
1000, and 1400 kW, respectively. The geographic location of the stallation and operating costs of WTGs.
system has wind conditions that can be represented by the Swift There is normally a linear increase in investment cost with
Current, Saskatchewan, Canada, data. The system peak load is an increasing number of WTGs; whereas the increase in relia-
1540 kW with hourly chronological load shape of the IEEE-RTS bility tends to saturate as seen in Fig. 4. It is important to assess
[7]. A typical operating constraint of limiting the wind energy both the reliability benefit and the costs associated with adding
to 40% of the system load (W:G ratio of 0.67) is considered. WTGs in determining appropriate wind capacity expansion in a
The healthy state probability with a LLU criterion is 0.901 power system. The relative amount of wind energy that can be
and is taken as the accepted adequacy criterion in this example. actually utilized by the system load decreases with increasing
This criterion should, however, be determined from a reliability wind capacity installation as shown in Fig. 5. This figure also
cost and worth analysis, or from planning experience, as is the gives an indication of how the return in wind investment de-
case with most conventional probabilistic risk criteria accepted clines with increasing investment.
by major power utilities. The expected fuel energy consumption Fig. 6 compares the investment cost and the fuel cost savings
for this system is 8258 MWh/yr. The resulting emissions will with increasing WTG installation. All monetary values are in
consist of about 7510 tons of CO , 180 tons of No , 9 tons of Canadian dollars. A WTG unit, installation, and maintenance
SO , including other gases and hazardous waste oils. A heat rate cost of $120/kW/yr is assumed in calculating the investment
of 3.2 kWh/l for diesel fuel is assumed in these calculations. cost. Fuel cost of $0.55/l is assumed for the diesel units in cal-
This study considers the addition of different amounts of wind culating the fuel cost savings. Additional installations of up to
capacity to determine a reasonable wind penetration level. A 4% three WTG units are justified by the cost comparison analysis
FOR (MTTF h, MTTR h) is assumed for the in Fig. 6. In practice, the cost analysis should also include any
WTGs, with 5, 18, and 25 m/s as the cut-in, rated, and cut-out subsidies received for wind installations, penalty costs for emis-
wind speeds, respectively. sions, and other conventional unit operation cost offset, etc.

5. KARKI AND BILLINTON: COST-EFFECTIVE WIND ENERGY UTILIZATION FOR RELIABLE POWER SUPPLY 439
Fig. 7. WTG capacity required to maintain reliability. Fig. 8. WTG capacity requirement criteria.
VI. DISCUSSION OF RESULTS
The vertical line in Fig. 6 indicates the amount of wind ca-
pacity installation for which the investment cost and savings are This section highlights some interesting findings from the re-
equal. Further increase in wind capacity is not economically jus- sults of the studies illustrated in the previous section.
tified. This vertical line corresponds to 8% WUE in Fig. 5. This New units are usually brought into service just before the
paper recommends the use of a WUE criterion in conjunction system adequacy level falls below the accepted criterion in con-
with a reliability criterion to help determine the appropriate level ventional capacity expansion. The study results show that ca-
of wind penetration in a system. pacity expansion dates should not be determined by the relia-
Consider a situation where capacity expansion is being con- bility criterion alone when considering WTG. There may be a
sidered in order to meet increasing demand. The rising curve significant economic advantage in adding WTG at a time when
in Fig. 7 shows the amount of wind capacity required to main- the system adequacy is relatively high.
tain the specified system reliability criterion for different peak A specified reliability criterion can always be obtained by
load levels. The falling curve shows the WUE at those capacity adding appropriate conventional generating capacity. Since the
additions. power supply reliability of WTG is dictated by the intermittent
It can be seen from the capacity curve in Fig. 7 that the de- nature of wind availability, addition of any amount of wind ca-
sired reliability cannot be achieved by adding any amount of pacity in a power system may not provide the specified system
wind capacity if the peak load exceeds 2060 kW. The vertical adequacy. Capacity expansion should then be considered by
line L2 shows the maximum load growth that can be met at the adding conventional generating units.
acceptable reliability level by adding wind power. The vertical The WUE is the ratio of the actual energy utilized to the total
line L1 indicates the maximum load that can be supplied with an energy based on rated WTG capacity. This index, therefore, re-
economic advantage by installing wind power. A WUE of 8% flects the ratio of the cost savings from fuel offset to the total
is taken as the acceptable criterion in this case. The acceptable investment on WTG. The WUE criteria can be significantly dif-
WUE criterion is a managerial decision based on cost analyses ferent for different systems depending on various factors such
that should foresee anticipated variations in cost parameters up as wind regime, system composition, fuel costs, and operating
to the planning horizon. Capacity expansion strategy should policies. A wind penetration level that falls below the specified
consider conventional generating units if the anticipated peak WUE criterion is not justified from cost considerations. Con-
load exceeds this limit. For a lower load, say 1700 kW, the re- ventional generating units should be considered during capacity
quired WTG capacity should be at least 900 kW to meet the expansion if WTG does not meet the WUE criterion.
required reliability criterion, and should not exceed 2500 kW Turbine design characteristics should be selected to match
for the WUE criterion, as shown in Fig. 8. An appropriate pene- the available wind data at the installation site for optimum CF.
tration level can be determined by comparing the costs and ben- This will usually increase the WUF and provide better system
efits represented by the two curves within the two vertical lines availability. Any increased investment costs for custom design
in Fig. 8. should, however, be included in the analysis.
It should be noted that the WTG used in the example has typ- The reliability and cost criteria indicated above can be used
ical rotor design parameters suitable for a more windy location jointly to obtain an acceptable range of wind penetration levels,
than swift current which has a mean wind speed of 6.2 m/s. Op- as shown in Fig. 8, when considering wind energy application
timum wind utilization requires proper matching of wind tur- in a power system. Analyses as shown in this figure can help
bine characteristics with installation site wind data. Studies as the system planner compare the costs and benefits at different
illustrated above can be done to compare different turbine char- wind capacities within the acceptable range to determine an ap-
acteristics to obtain the appropriate wind penetration level. propriate penetration level.

6. 440 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 2, JUNE 2004
VII. CONCLUSION [4] R. Billinton, H. Chen, and R. Ghajar, “Time-series models for reliability
evaluation of power systems including wind energy,” Microelectron. Re-
Determining the right amount of wind penetration in a power liab., vol. 36, no. 9, pp. 1253–1261, 1996.
system is becoming increasingly important, as the application [5] R. Billinton and R. Karki, “Application of Monte Carlo simulation to
generating system well-being analysis,” IEEE Trans. Power Syst., vol.
of this relatively new form of energy is expected to grow much 14, pp. 1172–1177, Aug. 1999.
faster than other existing forms. The main difficulty arises due [6] The Danish Wind Industry Association website, “Wind Energy Refer-
to the highly fluctuating power output capacity of WTGs in con- ence Manual” [Online]. Available: www.windpowr.org
[7] Reliability Test System Task Force of the Application of Probability
trast to the stable power capacity of conventional generating Methods Subcommittee, “IEEE Reliability Test System,” IEEE Trans.
units. Some planners use capacity factors to estimate the equiv- Power App. Syst., vol. PAS-98, pp. 2047–2054, Nov./Dec. 1979.
alent power rating of WTG. A realistic method to determine
an appropriate wind penetration level should, however, include
both cost and reliability analyses based on actual utilization of
wind energy in a power system. Rajesh Karki (M’02) received the B.E. degree from Burdwan University,
This paper presents a reliability/cost evaluation model using Durgapur, India, and the M.Sc. and Ph.D. degrees from the University of
Saskatchewan, Saskatoon, SK, Canada.
Monte Carlo simulation to obtain probabilistic quantitative in- Currently, he is an Assistant Professor in the Department of Electrical
dices that recognize the random nature of wind, load variation, Engineering at the University of Saskatchewan. He was a Lecturer for
unit failures and repairs, and system operation. The healthy state Tribhuvan University, Kathmandu, Nepal. He was also an Electrical Engineer
with Nepal Hydro & Electric, Butwal, Nepal; Udayapur Cement Industries,
probability measures system adequacy based on specified deter- Udayapur, Nepal; Nepal Telecommunications Corporation, Kathmandu, Nepal;
ministic criteria. Wind utilization efficiency indicates how much and General Electric Canada, Peterborough, ON.
of the total investment in WTG is actually being utilized. This
paper illustrates the use of these two indices in specifying reli-
ability and cost criteria to help determine an appropriate wind
penetration level in a power system. Roy Billinton (LF’01) received the B.Sc. and M.Sc. degrees from the University
of Manitoba, Winnipeg, MB, Canada, and the Ph.D. and D.Sc. degrees from the
University of Saskatchewan, Saskatoon, SK, Canada.
REFERENCES Currently, he is a Professor Emeritus in the Department of Electrical
[1] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems, Engineering at the University of Saskatchewan. He joined the University of
2nd ed. New York: Plenum, 1996. Saskatchewan in 1964. He was also with Manitoba Hydro, Winnipeg, MB,
[2] Isolated Systems Generating Planning Practices; A Survey of Canadian Canada, in the System Planning and Production Divisions. He is Formerly
Utilities, Nov. 1995. Acting Dean of Graduate Studies, Research and Extension of the College of
[3] R. Billinton and R. Karki, “Capacity reserve assessment using system Engineering at the University of Saskatchewan. He is also an author of power
well-being analysis,” IEEE Trans. Power Syst., vol. 14, pp. 433–438, system analysis, stability, economic system operation, and reliability papers.
May 1999. Dr. Billinton is a Fellow of the EIC and the Royal Society of Canada.