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Multistate Wind Energy Conversion System Models

for Adequacy Assessment of Generating Systems

Incorporating Wind Energy

Roy Billinton and Yi Gao

Abstract—Wind energy is considered to be a very promising al-

ternative for power generation because of its tremendous environ-

mental, social, and economic beneﬁts. Electrical power generation

from wind energy behaves quite differently from that of conven-

tional sources. The fundamentally different operating characteris-

tics of those facilities, therefore, affect the power system reliability

in a manner different from that of the conventional systems. This

paper is focused on the development of suitable models for wind

energy conversion systems, in adequacy assessments of generating

systems, using wind energy. These analytical models can be used

in the conventional generating system adequacy assessment uti-

lizing analytical or Monte Carlo state-sampling techniques. This

paper shows that a ﬁve-state wind energy conversion system model

can be used to provide a reasonable assessment of the practical

power system adequacy studies, using an analytical method, or a

state-sampling simulation approach.

Index Terms—Generation adequacy assessment, reliability eval-

uation, wind system models.

I. INTRODUCTION

T

HE development and utilization of wind energy to satisfy

the electrical demand has received considerable attention

in recent years, owing to the concerns regarding the dwindling

energy resources and enhanced public awareness of the potential

impact of the conventional energy systems on the environment.

Improvements in wind generation technologies will continue to

encourage the use of wind energy in both the grid-connected and

stand-alone systems. Owing to the random nature of the wind,

the wind generators behave quite differently from the conven-

tional generators. Therefore, it is important for the power system

planners and engineers to carefully consider the reliability is-

sues [1] associated with the wind energy sources.

A wind energy conversion system (WECS) converts the natu-

ral energy available at the system location into electrical energy.

Developing an adequacy model for a wind turbine generator

(WTG) requires the consideration of three factors that directly

affect the generator output. The ﬁrst factor is the random nature

of the site resource, which must be included in an appropri-

ate model to reﬂect the variable characteristics of the wind at

that particular site. The second factor is the relationship be-

tween the power output and the site resource. This relationship

can be determined using the WTG operational parameters and

speciﬁcations. The third factor is the unavailability of the WTG

expressed by the unit forced outage rate (FOR) [2].

Manuscript received February 16, 2006; revised June 2, 2006. Paper no. TEC-

00053-2006.

The authors are with the Power System Research Group, University of

Saskatchewan, Saskatoon, SK S7N 5A5, Canada.

Digital Object Identiﬁer 10.1109/TEC.2006.882415

In this paper, time series models are utilized to simulate hourly

wind speeds. The power output of a WTG unit is then obtained

using the relationship between the power output and the wind

speed. An apportioning method [2] is introduced and used to

create multistate models for a WTG unit, and for a WECS con-

taining multiple WTGs. An analytical procedure that incorpo-

rates the WTG FOR is used to build a multistate WECS model.

Attention is focused on the development and examination of

appropriate multistate WECS models for generating system ad-

equacy evaluation.

The analytical method [2] and the state-sampling simulation

technique [2] are applied to two test systems designated as the

Roy–Billinton test system (RBTS) [3] and the IEEE reliability

test system (IEEE-RTS) [4]. The total installed capacity and

system peak load of the RBTS are 240 and 185 MW, respec-

tively. The IEEE-RTS installed capacity and system peak load

are 3405 and 2850 MW, respectively. The wind site used in the

studies is located in Saskatchewan, Canada.

II. E

VALUATION TECHNIQUES

Considerable work has been done on the development and ap-

plication of models and techniques for generating capacity relia-

bility evaluation, and is documented in [5]–[8]. Certain speciﬁc

examples of wind related documentations, are presented in [1]

and [9]–[14]. The most comprehensive approach to incorporate

wind energy in a generating capacity evaluation is to use Monte

Carlo sequential simulation. This can be accomplished using

time series wind models [9], [12]. There is, however, a need to

develop suitable WECS models that can be easily incorporated

in more conventional approaches to generating capacity ade-

quacy assessment, such as analytical methods and the Monte

Carlo state-sampling technique. The detailed chronological na-

ture of the wind energy, modeled in the sequential simulation

approach, is not recognized in these techniques and the wind

variability is represented by a probability distribution.

Analytical techniques represent the system by analytical mod-

els and evaluate the system risk indices from these models using

mathematical solutions [2]. The loss of load expectation (LOLE)

approach is the most common method in use and is also used to

this paper. In this approach, the generating system represented

by the capacity outage probability table (COPT), and the load

represented by the load duration curve (LDC), are convolved to

calculate the LOLE index [2].

In the state-sampling Monte Carlo simulation approach, the

system state is obtained by sampling all the component states.

0885-8969/$25.00 © 2008 IEEE

The basic sampling procedure is conducted by assuming that the

behavior of each component can be categorized by a uniform

distribution under [0, 1]. The component can be represented by

a two-state or a multistate model. One of the advantages of the

system state-sampling method is that the multistate components

can be incorporated in the analysis without a signiﬁcant increase

in the computing time.

A commercial software designated as Monte Carlo

Evaluation of COmposite system REliability(MECORE) [15],

which utilizes the state-sampling Monte Carlo simulation tech-

nique, was used in part of the studies described in this paper. The

MECORE software was developed to analyze composite gen-

eration and transmission systems. The transmission elements in

the test system are assumed to be 100% reliable, when MECORE

is used in a generating system study. The basic LOLE index used

in the analytical method [2] is the same, as the expected duration

of load curtailment (EDLC) used in MECORE [15].

III. W

IND TURBINE GENERATOR UNIT MODELS

A. Modeling and Simulating Wind Speeds

The wind speed model and data for the Swift Current site

located in the Province of Saskatchewan, Canada, have been

used in this paper. The mean and standard deviation of the

wind speed at the Swift Current site are 19.46 and 9.7 km/h,

respectively. The hourly mean and standard deviation of wind

speeds from a 20-year database (Jan. 1, 1984 to Dec. 31, 2003)

for this location were obtained from Environment Canada. These

data were used to build the auto-regressive and moving average

model (ARMA) time series model [9]. The ARMA(4, 3) model

is the optimal time series model for the Swift Current site, for

which the parameters are shown as

y

t

=1.1772y

t−1

+0.1001y

t−2

− 0.3572y

t−3

+0.0379y

t−4

+ α

t

− 0.5030α

t−1

− 0.2924α

t−2

+0.1317α

t−3

α

t

∈ NID

0, 0.524760

2

. (1)

where {α

t

} is a normal white noise process with zero mean and

variance 0.524760

2

.

Once the wind speed time series model is established, the

simulated wind speed SW

t

can be calculated as

SW

t

= µ

t

+ σ

t

y

t

(2)

where σ

t

is the standard deviation of the observed wind speed

at hour t and µ

t

is the observed mean wind speed at hour t.

Fig. 1 shows a comparison of the observed wind speed prob-

ability distribution for the original 20 years of data, and the

simulated wind speed probability distribution obtained using

the ARMA(4, 3) model and a large number (8000) of simulated

years. The observed average wind speed is 19.46 km/h, and the

simulated value is 19.53 km/h. The observed wind speed prob-

ability distribution is not as continuous as the simulated distri-

bution, as it is based on only 20 years of data.

Fig. 1 shows that the ARMA(4, 3) model provides a reason-

able representation of the actual wind regime. Simulation results

are used to generate the wind speed probability distributions in

the system adequacy studies described later in this paper.

Fig. 1 Observed and simulated wind speed distributions for the Swift Current

site.

B. Modeling Wind Turbine Generators

The power-output characteristics of a WTG are quite differ-

ent from those of a conventional generating unit. The output

of a WTG depends strongly on the wind regime as well the

performance characteristics of the generator.

After the hourly wind speed is obtained, the next step is to

determine the power output of the WTG as a function of the wind

speed. This function is described by the operational parameters

of the WTG. The parameters commonly used are the cut-in

wind speed (at which the WTG starts to generate power), the

rated wind speed (at which the WTG generates its rated power),

and the cut-out wind speed (at which the WTG is shut down

for safety reasons). The hourly power output of a WTG can be

obtained from the simulated hourly wind speed using

PP(SW

t

)

=

0, 0 ≤ SW

t

<V

ci

(A + B × SW

t

+ C × SW

2

t

) × P

r

,V

ci

≤ SW

t

<V

r

P

r

,V

r

≤ SW

t

<V

co

0,SW

t

≥ V

co

(3)

where P

r

,V

ci

,V

r

and V

co

are the rated power output, the cut-in

wind speed, the rated wind speed, and the cut-out wind speed of

the WTG, respectively. The constants A, B, and C depending

on V

ci

,V

r

, and V

co

are presented in [16].

C. The Capacity Outage Probability Table of the WTG

The hourly mean wind speeds and output power for the WTG

unit, without considering its FOR, are generated based on the

ARMA time series model and the power curve, respectively.

The capacity outage probability table (COPT) of a WTG unit

can be created by applying the hourly wind speed to the power

curve. The procedure is brieﬂy described as follows.

1) Deﬁne the output states for a WTG unit as segments of

the rated power.

2) Determine the total number of times that the wind speed

results in a power output, falling within one of the output

states.

3) Divide the total number of occurrences for each output

state by the total number of data points to estimate the

probability of each state.

Fig. 2 Capacity outage probability proﬁle for the WTG unit.

Fig. 3 Comparison of capacity outage probability proﬁles for the WTG unit.

The WTG COPT is formed using this approach. Two cases

are illustrated in this section. The ﬁrst case utilizes the actual

observed 20 years of Swift Current site data. The second case

uses the simulated 8000-year data. Fig. 2 shows the two capac-

ity outage probability distributions. The class interval width is

5% in this ﬁgure and the indicated capacity-outage level is the

midpoint of the class.

Fig. 2 illustrates that the observed probability proﬁle is dis-

continuous, owing to the limited wind data collection. The sim-

ulated wind data provides a reasonable representation for ade-

quacy assessment. The power-output characteristics of a WTG

are very different from those of the conventional generating

units. The WTG can be considered as a generating unit with

many derated states [2]. Fig. 2 shows that the probability of

having a full WTG output (0% capacity outage), is relatively

low for this wind regime.

As noted earlier, the power output of a WTG unit depends

strongly on the wind resource at the speciﬁc location. In order

to illustrate the effect of site resources on the WTG unit, the

average wind speed used in the ARMA model was changed

from 19.46 to 38.92 km/h, using a simple multiplication factor

of 2.0. The results are illustrated graphically in Fig. 3, which

shows that the power output of a WTG is completely dependent

on the wind regime, and will increase if the facilities are located

at a site, where a higher wind velocity is available. Fig. 3 shows

the change in the capacity outage proﬁle, when the mean wind

speed is signiﬁcantly increased.

D. Building a Multistate WECS Model Using the Apportioning

Method

There are many derated states in which the output of a

WTG can reside in the course of its operating history. One

of the requirements of the adequacy assessment is to repre-

sent the WTG by an acceptable reduced number of derated

states.

The apportioning method [17] has been used in this paper to

create the selected multistate models for a WTG and the WECS.

An analytical procedure that incorporates the WTG FOR is

presented and used to build a multistate WECS model. The

probability of a unit, residing in the full down state in a two-state

representation, is known as the derating adjusted forced outage

rate (DAFOR) [8]. The term DAFOR is used by the Canadian

electric power utilities. In the United States, the designation for

this statistic is the “equivalent forced outage rate” (EFOR). The

EFOR or DAFOR is obtained using the apportioning method

in which the residence times of the actual derated states are

apportioned between the up (normal) and down (outage) states,

and there are no assigned derated states.

1) Multistate WTG Models: The WTG COPT, shown graph-

ically in Fig. 2, based on the simulated wind speeds, can be

reduced to form different multistate capacity outage probability

tables using the apportioning method. A state capacity outage

probability table is designated as a SCOPT. A 5 SCOPTW is a

ﬁve-state WTG capacity outage probability table. Table I shows

the effects of reducing the COPT in Fig. 2 to a series of different

SCOPTW. These results do not include the WTG FOR. The ef-

fects of wind variability can be aggregated to produce a DAFOR

statistic, similar in form to that used for conventional generat-

ing units. This statistic is designated as DAFORW, which in this

case is 0.76564. The DAFORW is the same for each SCOPTW

shown in Table I.

2) Wind Energy Conversion System Model: A WECS can

contain one or more WTG. A WECS has two basic parts: One

is the wind resource and the other is the actual WTG units. If

the WECS consists of identical WTG units with zero FOR, the

WECS multistate models are the same as those of the single

WTG unit shown in Table I. If the FOR of the WTG units is

not zero, the WECS derated state capacity outage probability

tables are not the same as those of a single WTG unit. An an-

alytical procedure has been used to create WECS multistate

models, including WTG FOR. The designation MSCOPTW is

used to indicate a SCOPTW, modiﬁed to include the WTG

FOR. A 2 MSCOPTW is a two-state WECS model, in-

cluding the WTG FOR. The following cases illustrate the

procedure.

Consider a WECS containing one 2-MW WTG unit with a

4% FOR. The wind condition is represented by the two-state

model (2 SCOPTW) shown in Table I. The wind condition and

the actual WTG unit form a simple series system as shown

in Fig. 4. The availability (A) of the WTG unit is 0.96 and

unavailability (U ) or FOR is 0.04.

A 20-MW WECS, containing ten identical 2-MW WTG units,

is represented in Fig. 5. The WTG units are considered to have

either a zero FOR, or a FOR of 4%. The procedure used to

TABLE I

M

ULTISTATE WTG COPT (SCOPTW)

Fig. 4 Single unit model.

Fig. 5 Multiple WTG unit model.

TABLE II

WTG U

NIT COPT WITH DIFFERENT FOR

develop the WECS COPT is similar to the previous two cases

and is brieﬂy described in the following.

Step 1) The wind condition models are represented by the

SCOPTW shown in Table I.

Step 2) The identical WTG units (0% and 4% FOR) are com-

bined to create the COPT shown in Table II.

Step 3) The wind condition and the WTG unit COPT are

combined to create the multistate WECS COPT. The

COPT for 2 SCOPTW and 5 SCOPTW are shown in

Table III as examples.

Step 4) The WECS COPT obtained in Step 3 can be reduced,

if desired, using the apportioning method. When the

FOR is equal to 0, the MSCOPTW is the same as

the SCOPTW shown in Table I. Table IV shows the

MSCOPTW, when the WTG FOR is 4%. The modi-

ﬁed derating adjusted forced outage rate of the WECS

(MDAFORW) is 0.77501. The MDAFORW is the

same for each MSCOPTW as shown in Table IV.

A procedure similar to that used to model a 20-MW WECS

containing ten identical 2-MW WTG units, can be used to model

large wind farms. The binomial distribution can be used if the

WTG units are identical. The WTG COPT can be created us-

ing the conventional COPT algorithm [2], if the WTG units are

not identical. The multistate models of a 400-MW WECS con-

taining 200 WTG units of 2 MW with 4% FOR are shown in

Table V. These multistate models are very similar to the 20-MW

WECS multistate models shown in Table IV. The MSCOPTW

models are dominated by the SCOPTW models created for this

wind regime.

The FOR effect is minimal for reasonable FOR values at this

mean wind speed. The FOR effect will increase as the mean

TABLE III

WECS COPT M

ODELS FOR DIFFERENT WIND CONDITION MODELS

wind speed increases. The effect of varying the WTG unit FOR

on the generating system adequacy is analyzed on the RBTS and

the IEEE-RTS systems, using the WECS 5 MSCOPTW models

shown in Tables IV and V, respectively. Fig. 6 shows the annual

system LOLE, with varying WTG FOR for the RBTS and the

RTS using the analytical method and MECORE. The RBTS and

the RTS system peak loads are 185 and 2850 MW, respectively.

It can be seen from Fig. 6 that the changes in the FOR of the

WTG units do not have a signiﬁcant impact on the calculated

system reliability indices. The WTG FOR can be neglected in

many practical situations without creating unreasonable errors

in the calculated LOLE. The results will, of course, be slightly

optimistic and favor the installation of WTG units. The WECS

models shown in Tables IV and V are used in the following

studies on the RBTS and the IEEE-RTS.

IV. A

PPLICATION OF WECS MULTISTATE MODELS IN

GENERATING CAPACITY ADEQUACY ASSESSMENT

The 20- and 400-MW WECS multistate models shown in

Tables IV and V are used in the RBTS and RTS analyses, re-

spectively. The analytical technique and the state-sampling ap-

proach used in MECORE provide similar results, when the same

load model is used. The MECORE software [15] uses a hybrid

simulation and enumeration procedure to incorporate the vari-

ous load levels in the assigned time period, and therefore, uses

a multistep load model in the analysis. The MECORE software,

as noted earlier, was designed to conduct adequacy evaluation in

composite generation and transmission systems, and to provide

TABLE IV

M

ULTISTATE MODELS FOR A 20-MW WECS WITH 4% WTG FOR

individual load point and system adequacy indices. Composite

system studies have also been conducted using multistate WECS

models in MECORE. The following results are restricted to the

basic generating capacity adequacy assessment.

V. RBTS S

YSTEM ANALYSIS

The WECS multistate models, shown in Table IV, were used

to investigate the impact of different WECS models on the RBTS

generating system adequacy. Both the analytical method and

MECORE were used in this study. The annual system LOLE

TABLE V

M

ULTISTATE MODELS FOR A 400-MW WECS WITH 4% WTG FOR

for a peak load of 185 MW, are presented in Fig. 7. This ﬁgure

shows that the LOLE ﬂuctuates slightly owing to the different

number of states used in the analysis, and that the use of a

two-state representation provides a pessimistic appraisal of the

system adequacy. This is consistent with the use of the DAFOR

to represent large conventional generating units. The original

RBTS at a peak load of 185 MW has a LOLE of 1.15 h/year,

and therefore, has a reasonable level of generating adequacy.

The addition of a 20-MW WECS produces a recognizable but

relatively small decrease in the LOLE. The results show that

Fig. 6 Test systems’ HL-I annual system LOLE as a function of the WTG

FOR.

Fig. 7 RBT Sannual system LOLE for a peak load of 185 MW using different

WECS state models.

Fig. 8 HL-I annual system EDLC (LOLE) with WECS multistate models.

the LOLE does not change considerably, when the WECS is

modeled with at least three states. The effect of varying the

peak load on this conclusion is illustrated in Fig. 8.

Fig. 8 shows the effects of adding different WECS models to

the RBTS at various system peak loads. It also shows that the

beneﬁt associated with adding the 20-MW WECS to the RBTS

increases as the peak load increases. This beneﬁt is relatively

small at the system design peak of 185 MW.

Fig. 9 RTS annual system EDLC for a peak load of 2850 MW with different

WECS multistate models using MECORE.

Fig. 10 HL-I annual system EDLC with different WECS models versus peak

load.

Figs. 7 and 8 show that the annual system indices are relatively

close, using a model with three or more states to represent

the WECS when the peak load is 185 MW. Fig. 8 shows that

additional states are required in the WECS model, when the

peak load increases signiﬁcantly. The system EDLC in these

situations may be unacceptably high.

VI. IEEE-RTS S

YSTEM ANALYSIS

The IEEE-RTS annual system LOLE (EDLC), obtained us-

ing MECORE and the WECS multistate models, represented in

Table V is shown graphically in Fig. 9. The IEEE-RTS, in its

original form, is considered to be relatively weak from a gen-

eration point of view at the designed peak load of 2850 MW.

The LOLE (EDLC) under this condition is 13.005 h/year. The

addition of a 400-MW WECS, using a two-state representation,

provides a signiﬁcant beneﬁt under this condition. The beneﬁt

of adding the WECS increases as the number of states in the

multistate WECS model increases. Fig. 9 illustrates that the sys-

tem EDLC at a peak load of 2850 MW is relatively constant,

when the WECS is represented by models containing ﬁve or

more states.

Fig. 10 shows the annual system EDLC with different WECS

multistate models as a function of the system peak load level.

It also indicates that the WECS ﬁve-state model can be used

to represent a WECS in a practical adequacy assessment of the

RTS.

The conclusion can be drawn based on the analyses of the

RBTS and the RTS that using a ﬁve-state WECS model can

provide a reasonable adequacy assessment of similar power

systems containing a WECS. This model can be applied in

practical studies using an analytical method or a state-sampling

procedure, such as that used in MECORE. If the wind regime

varies considerably over the course of a year, a series of multi-

state WECS models can be created, using the relative data for

each time period. The annual LOLE is then determined by sum-

ming up the period values. This procedure is used to incorporate

scheduled maintenance of generating units.

VII. C

ONCLUSION

A comparison of the observed wind speed probability dis-

tribution and the simulated wind speed probability distribution

created by the ARMA model, illustrates that ARMA models

provide a useful representation of the actual wind regimes. A

comparison between the COPT for the observed wind data and

the simulated wind data shows that simulated wind data can

be used to provide a reasonable representation for adequacy

assessment. The effect of wind speed on the WTG power output

shows that the power output of a WTG is totally dependent on

the wind regime, and will increase if the facilities are located at

a site, where higher wind velocities are experienced. Increased

wind speeds will also result in different multistate WTG or

WECS models.

The apportioning method can be used to create selected WTG

multistate models. A WECS multistate model is the same as that

of a single WTG unit, when the FOR of the WTG units is zero.

The DAFOR of the WECS and the single WTG unit are also

the same. An analytical procedure is introduced and used to

create WECS multistate models, when the WTG FOR is in-

corporated. This procedure is applicable to large wind farms,

which are composed of a number of identical or nonidentical

WTG. The studies on the RBTS and the IEEE-RTS LOLE, with

different WTG FOR, indicate that the changes in WTG FOR

do not have a signiﬁcant impact on the calculated reliability

indices. Using zero FOR will not signiﬁcantly impact the cal-

culated indices, and can greatly simplify the WECS modeling

procedure.

The analyses of the generating systems, including WECS,

indicate that a ﬁve-state WECS model can be used to provide

a reasonable assessment in practical studies, using the analyti-

cal method or a state-sampling procedure such as that used in

MECORE. This is an important observation as it permits WECS

to be incorporated in large practical system studies without re-

quiring a signiﬁcant increase in computer solution time. This

representation can also be used in composite generation and

transmission system reliability studies.

R

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Roy Billinton (S’59–M’64–SM’73–F’78) received the B.Sc. and M.Sc. degrees

from the University of Manitoba, Winnipeg, MB, Canada, in 1960 and 1963,

respectively. He received the Ph.D. and D.Sc. degrees, both in electrical engi-

neering, from the University of Saskatchewan, Saskatoon, SK, Canada, in 1967

and 1975, respectively.

He was with the System Planning and Production Divisions of Manitoba Hy-

dro, MB, Canada. Since 1964, he has been with the University of Saskatchewan.

He is the author or coauthor of eight books on reliability evaluation and over

850 papers on power system reliability evaluation, economic system operation,

and power system analysis.

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

a Registered Professional Engineer in the Province of Saskatchewan, Canada.

Yi Gao received the B.Sc. and M.Sc. degrees from the Zhengzhou University,

Henan, China, in 1996 and 2006, respectively. She is currently working toward

the Ph.D. degree at the University of Saskatchewan Saskatoon, SK, Canada.

She was an Instructor at the Zhengzhou Electric Power College, Henan.

Since January 2004, she has been with the Power System Research Group at the

University of Saskatchewan.