A Comparison of Four-state Generating Unit Reliability Models for Peaking Units

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 2, MAY 2004 763

A Comparison of Four-State Generating UnitReliability Models for Peaking Units

Roy Billinton , Life Fellow, IEEE, and Jingdong Ge

Abstract—A peaking unit is different from a base load unit inthat it resides most of the time in the available but not operating(ABNO) state. The conventional unit unavailability index is theforced outage rate (FOR) and is based on a two-state model. Thismodel is not suitable for intermittent operating unit representationand results in an unreasonably high unavailability index estimatefor a peaking unit. Three four-state models, which recognize theintermittent operating characteristics of a peaking unit, are intro-duced and compared in this paper.

Index Terms—Generating units, peaking units, reliabilitymodels, unavailability indices.

I. INTRODUCTION

Agenerating unit is usually modeled by a series of states in

which the generating unit can reside. The unit can transit

from one state to another in accordance with certain actions.

These states and the possible transitions mimic the operating be-

havior of a generating unit. The resulting model is used to incor-

porate generating unit unavailability in power system reliability

evaluation. In North America, comprehensive generating unit

outage databases aremaintained by the Canadian Electricity As-

sociation (CEA) and the North American Electric Reliability

Council (NERC). The CEA Equipment Reliability Information

System (ERIS) [1] and the NERC Generating Availability Data

System (GADS) contain a wealth of important information. The

NERC-GADS is based on [2].The basic model for a generating unit is a two-state represen-

tation in which the unit resides either in the “Up” (operating)

state or in the “Down” (forced outage) state as shown in Fig. 1.

The “FOR” is defined as the ratio of the total forced outage time

to the total forced outage time plus the total operating time [1].

The two-state model is a reasonable representation for a base

load unit.

Peaking units normally operate for relatively short periods

of time. In order to recognize this behavior, the basic two-state

model was extended to a four-state representation and the IEEE

four-state model was developed in 1972 [3]. This model and

other two four-state models, which include some extra transi-

tions in the IEEE four-state model, are introduced and compared

in this paper. There are several indexes in use to describe the

unavailability of a peaking unit. These indexes are based on the

IEEE four-state model and include the utilization forced outage

Manuscript received April 30, 2003.R. Billinton is with the Power System Research Group, University of

Saskatchewan, Saskatoon, SK S7N 5A9, Canada (e-mail: [email protected]).

J. Ge is with the Grid Development Department, Saskatchewan Power Cor-poration, Regina, SK S4P 0S1, Canada (e-mail: [email protected]).

Digital Object Identifier 10.1109/TPWRS.2003.821613

Fig. 1. Two-state model.

probability (UFOP) [1] (ERIS), the derating adjusted utilization

forced outage probability (DAUFOP) [4] (Ontario Hydro) and

the equivalent forced outage rate when demanded (EFORd) [5]

(PJM Interconnection). The EFORd has also been included in

recent GADS reports [6]. The ERIS gas turbine database is uti-

lized to calculate the relevant unit unavailability indexes based

on the different models. This database includes all of the unit’s

state residence times and the transitions from state to state. Five

years of operation and outage data for 83 units are utilized in

the analysis.

II. DERATED OPERATION AND OPERATING FACTOR

These two concepts are directly related to unit unavailability

index evaluation. The definitions of these two concepts are in-

troduced in this section, and utilized in Section III for index

evaluations.

A. Derated Operation

Derating is a reduction in the capacity of a generating unit

due to equipment failure. In these conditions, a generating unit

cannot provide its maximum continuous rating (MCR) [1]. Par-

tial shortfalls in unit capacity arise due to equipment limitations

within the unit. These shortfalls can be modeled by a series of

derated states [7]. It is more usual, however, to aggregate theseinto the conventional two-state model.

In order to recognize the effect of derating on the generating

unit unavailability index, the operating time in the derated state

is adjusted to provide an energy equivalent time in the full forced

outage state. Table I gives the CEA state and time codes.

Consider a unit operating for a time at a derated level

of its MCR. The adjusted outage time adj is calcu-

lated as in (1)

adj (1)

0885-8950/04$20.00 © 2004 IEEE



764 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 2, MAY 2004

In the CEA ERIS, the modified forced outage time is denoted

by the “adj” subscript. adj representstheadjusted forced

derated operating time. adj is determined in the

same manner.

B. Operating Factor

Generating units are traditionally divided into groups based

on their capacities for unit unavailability study. In the case of a

peaking unit, the operating factor is a more important character-

istic than the unit capacity. The operating factor is defined

[1] as

Total Operating Time

Unit Hours(2)

where Total Operating Time

Unit Hours ABNO ABNO

ABNO

Significant differences in the operating factors of the 83 units

were found on reviewing the CEA ERIS database. The unit op-

erating factors ranged from 0.1% to 33.5%. The 83 units were

divided into four subgroups using the operating factors. Each

group contains an approximately equal number of units. The

group information is given in Table II.

III. MODEL INTRODUCTIONS

Three four-state models are illustrated in this section and the

related indexes are calculated using the CEA ERIS database.

A. IEEE Four-State Model and Indexes

As noted earlier, an IEEE Task Force developed a four-state

model in 1972 in order to recognize the peaking unit character-

istics [3]. This model is shown in Fig. 2. The parameters used

in Fig. 2 are

D average in-service time per occasion of demand;

T average reserve shutdown time between periods of

need;

r average repair time per forced outage occurrence;

m average in-servicetime between occasions of forced

outage when needed;

probability of a starting failure resulting in inability

to serve load during all or part of a demand period.

The reserve shutdown state in the four-state model corre-

sponds to the ABNO condition in the CEA ERIS. The in-service

state represents the operating condition. The forced out state is

divided into two segments. One is a state in which the unit is

forced out but not needed by the system and the other is a state

in which the unit is forced out and needed by the system.

One problem that exists with the four-state model is that

in most data reporting systems, such as the CEA ERIS, the

“DOWN” time (forced out time) cannot be readily separated

into the two required segments because it is very difficult to

record when the unit is “Needed” and “Not Needed.” The

TABLE IGENERATING UNIT STATE AND TIME CODES

TABLE IIGROUP INFORMATION FOR THE 83 UNITS

Fig. 2. IEEE four-state model.

demand factor given by (3) was introduced to facilitate this

[3]

(3)

where is the probability of being in state 1 and is the

probabilityof being in state 3. Theforced outneeded time canbe

obtained by multiplying the total “DOWN” time by the demand

factor .

The Markov approach is used to evaluate the demand factor.

In order to use the Markov approach, the unit behavior should

have two characteristics, lack of memory, and be stationary [8].

These conditions are normally assumed to apply to generating

units. A detailed discussion of the Markov approach is given



B ILLI NTON AND GE: A C OMPARI SON OF FOUR- STAT E GENERAT ING UNI T R ELI ABI LI TY MODELS F OR PE AKING UNI TS 7 65

in [8]. The frequency balance equations [8] for the four-state

model shown in Fig. 1 are as follows:

(4)

The objective in solving these equations is to find the demandfactor using the operating parameters r, m, T, D, and in

Fig. 2. The first step is to estimate these parameters from the raw

data. This can be done using the equations given in Table III.

All of the data on the right-hand side of the equations in

Table III can be obtained from the available CEA ERIS data-

base directly. The probabilities for state 1 and state 3

can be obtained by solving (4) as shown in (5) and (6)

(5)

(6)

where M is a function of , , , , , and it is given by the

following equation:

The demand factor is given by (7) using and from

(5) and (6)

(7)

A new unit unavailability index was developed based on the

four-state model [3]. In the CEA protocol, this index is desig-nated as the utilization forced outage probability (UFOP). The

UFOP is the probability of a generating unit not being available

when needed, and it is given by (8)

forced outage time

forced outage time total operating time(8)

Using the CEA ERIS state duration codes, the UFOP is given

by (9)

(9)

Derated states can be incorporated into the unit unavailabilityindex using the concept of adjusted time. The modified unavail-

TABLE IIIPARAMETER ESTIMATION

ability index in this case is known as the derating adjusted uti-

lization forced outage probability (DAUFOP). The development

of DAUFOP is shown in an Ontario Hydro research report [4].

The DAUFOP is the probability of a generating unit (including

derated states) not being available when needed. It is the ratio

of the equivalent forced outage time, when the unit is needed, to

the equivalent operating time, when the unit is needed, plus the

equivalent forced outage time, when the unit is needed.

Using the CEA ERIS state duration codes, the DAUFOP is

given by (10) shown at the bottom of the page.

The demand factor in (9) and (10) has the same definition

as in (3). It should be noted that the difference between UFOP

and DAUFOP is significant if the forced derating time is large.

The NERC GADS has recently introduced a similar statistic

EFORd based on an approach used by the PJM Interconnection

[5]. It is expressed by (11) as shown at the bottom of the page.

The GADS follows IEEE Standard 762 [2]. Utilizing standard

762 duration codes, (11) becomes (12)

EFORdFOH EFDH

FOH SH(12)

where SH is service hours, FOH is forced outage hours, and

EFDH is the equivalent forced derating hours. A detailed

comparison between the definitions and indexes used in the

CEA-ERIS and the NERC-GADS data reporting systems is

given in [9].

In the GADS reporting system, the EFDH is not recorded sep-

arately as equivalent forced derating service hours (EFDSH) and

equivalent reserve shutdown forced derating hours (ERSFDH).

A partial outage factor is introduced [10] in order to divide

EFDH into EFDSH and ERSFDH and is defined as

EFDSH

EFDH

EFDSH

EFDSH ERSFDH(13)

(10)

EFORdforced outage hours equivalent forced derated hours

service hours forced outage hours(11)




The factor cannot be obtained directly from the GADS data-

base and is estimated using (14)

Service Hours

Service Hours+Reserve Shutdown Hours(14)

The ratio of service hours to service hours plus reserve shut-

down hours is an approximation for . The EFORd using

obtained from (14) is therefore also an approximation of the

original definition. The EFDSH and ERSFDH values could be

calculated if GADS received information on all of the reserve

shutdown (RS) events. GADS and PJM have traditionally not

required this information and, therefore, the estimate is re-

quired.

Table IV shows the basic indexes for each of the four unit

groups in Table II and for the total unit set.

B. Modified Four-State Model

There are two inherent assumptions in the IEEE four-state

model. These are as follows.

• The duty cycles are the same for the available states (be-

tween the in-service state and the reserve shutdown state)

and the unavailable states (between the forced out needed

state and the forced out but not needed state).

• There is no failure rate from the reserve shutdown state to

the forced out but not needed state.

The first assumption is straightforward because the load re-

quirement rather than the generating unit itself determines the

duty cycles. For the second assumption, in the review of the

data from the ERIS database, it was found that there is a large

number of transitions from the ABNO state (reserve shutdown

state) to the forced outage state, in addition to start failures. This

transition is neglected in the IEEE four-state model. A modified

four-state model was developed by adding this transition to the

original model. The modified model shown in Fig. 3 is a more

realistic representation of actual peaking unit operation.

The parameters in Fig. 3 are the same as those in Fig. 2 with

the addition of

ABNO ABNO ABNO

Number of Forced Outages from the ABNO State

The demand factor is different from that determined for

the basic IEEE four-state model when the failure rate from the

reserve shutdown state to the forced outage but not needed state

is included. The frequency balance equations in this case are

given in (15). The basic equation for the new demand factor

is shown in (16) together with a modified form using a ratio

factor . The formula to obtain is given by (17)

(15)

(16)

(17)

TABLE IVBASIC INDEXES AND PARAMETERS

Fig. 3. Modified four-state model.

Equations (9) and (10) can still be used to calculate the UFOP

and DAUFOP, respectively, for the modified model. The de-

mand factor now is given by (16).

The unavailability indexes calculated using the modified

four-state model are shown in Table V.

C. Extended Four-State Model

It can be seen by comparing Tables IV and V that significant

differences exist for the same unit unavailability index due to the

different models. These differences are caused by the assump-

tions inherent in the models. It is therefore important to review

all of the assumptions in the previous models. The modified

four-state model is an extension of the IEEE four-state model

in which the failure rate from the reserve shutdown state to the

forced out but not needed state is included. There is a further

assumption that should be examined.

• The repair rates from the forced out needed state to the

in-service state and from the forced out but not needed

state to the reserve shutdown state are identical in the twointroduced four-state models.

This assumption should be reconsidered as there is no evi-

dence in the CEA ERIS database to support this assumption.

The generating unit repair time will be influenced by the load

requirements, the available capacity in the system, and the na-

ture of the repairs. If the system is short of capacity, the repair

time may be reduced. If the system reserve capacity is large,

the repair time may be lengthened. It is obvious that the unit is

needed more by the system when it is in the forced out needed

state than in the forced out but not needed state. It is therefore

morelikely that the repair time for a unitin the forcedout needed

state will be shorter than that in the forced out but not needed



B ILLI NTON AND GE: A C OMPARI SON OF FOUR- STAT E GENERAT ING UNI T R ELI ABI LI TY MODELS F OR PE AKING UNI TS 7 67

TABLE VMODIFIED MODEL INDEXES AND PARAMETERS

state. An extended four-state model was developed considering

different repair rates from the different forced outage states.

Fig. 4 shows an extended four-state model in which the repair

rates are different.

The frequency balance equations for the extended four-state

model are as follows:

(18)

where is the average repair time per forced outage but not

needed occurrence and the repair time is the average repair

time per forced outage needed occurrence. The parameters ,

, , and can be estimated using the equations in Table III

and n is the same as that in the modified four-state model. Pa-

rameters and can be estimated using the CEA ERIS data-

base directly.

Equation (18) contains four unknown parameters— , , ,

and . These parameters can be obtained as functions of , ,

, , , , and .

The ratio factor can be therefore determined as

(19)

Based on this , the demand factor can be obtained using

(16).

The UFOP and DAUFOP indexes can be obtained using this

demand factor based on (9) and (10). The UFOP and DAUFOP

indexes based on the extended four-state model using the unit

groups are shown in Table VI.

IV. MODELS AND INDEXES COMPARISON

Three different four-state models are presented to represent

peaking units. They are designated as the IEEE four-statemodel, the modified four-state model, and the extended

four-state model. A simple breakdown of the basic difference

in these models is as follows.

• The duty cycles for the available states and the unavailable

states are identical for all three models.

• The failure rate from the reserve shutdown state is ne-

glected in the IEEE four-state model but considered in the

other two models.

• The repair rates from the forced out needed state and the

forced out not needed state are different in the extended

four-state model but are assumed to be identical in the

other two models.

Fig. 4. Extended four-state model.

TABLE VIEXTENDED MODEL INDEXES AND PARAMETERS

TABLE VIIINDEX COMPARISONS OF THE THREE FOUR-STATE MODELS

The peaking unit unavailability indexes UFOP and DAUFOP

for the unit groups are compared in Table VII based on the dif-

ferent models. Where A denotes the IEEE four-state model, B

denotes the modified four-state model, and C denotes the ex-

tended four-state model.

It can be seen that the UFOP or DAUFOP index values for

the IEEE four-state model are the highest for all of the groups

compared to those from the other two models. The indexes ob-

tained using the extended four-state model are the smallest. The

indexes from the modified four-state model lie between these

two values. The reasons for this can be explained as follows.

The modified four-state model is a basic extension of the

IEEE four-state model. The difference between these twomodels is the inclusion in the modified model of the transition

(failure) rate from the reserve shutdown state. The introduction

of this failure rate increases the forced out but not needed time

and decreases the forced out needed time. Unit unavailability

indexes such as UFOP and DAUFOP decrease. This model is

therefore closer to actual peaking unit operation than the IEEE

four-state model. The indexes based on the modified four-state

model are therefore more meaningful than those based on the

IEEE four-state model.

The transition (repair) rates from the two different down

states are assumed to be the same in both the IEEE four-state

model and the modified four-state model. These rates are




different in the extended four-state model. It was found that the

repair time in the forced out needed state is much shorter than

that in the forced out but not needed state. The shorter repair

time in the forced out needed state leads to a reduced residence

time (state 3) probability. The UFOP and DAUFOP indexes

decrease due to the decrease in in the extended four-state

model.

V. CONCLUSION

The basic two-state model, the IEEE four-state model, the

modified four-state model, and the extended four-state model

are discussed in this paper. The two-state model is normally

used for a base load unit and it is not a good representation for

a peaking unit operation. The FOR for a peaking unit based on

the two-state model is usually unreasonably high and is not a

practical unavailability index.

The generating unit reliability models presented are based on

the existing data reporting system. The detailed examination of

the gas turbine unit operating and outage data provided by the

CEA indicates a large number of transitions from the reserveshutdown state to the forced out but not needed state and that

the transition (repair) rates from the two different forced outage

states have quite different values. The first observation leads

to the development of the modified four-state model. The ex-

tended four-state model was developed in order to recognize

both observations.

The extended four-state model is a straightforward modifi-

cation of the IEEE four-state model. The unit unavailability

indexes can be estimated using the extended four-state model

without any change in the existing CEA ERIS generating unit

operating and outage data reporting system. The peaking unit

unavailability indexes of UFOP and DAUFOP obtained using

the extended four-state model involve fewer data assumptionsand provide practical and realistic unit reliability indicators.

ACKNOWLEDGMENT

The authors would like to thank the Canadian Electricity As-

sociation for providing the required data.

REFERENCES

[1] Canadian Electricity Association Equipment Reliability InformationSystem, “2000 Generation Equipment Status Annual Report,” Rep.,Montreal, QC, Canada, 2001.

[2] IEEE Standard Definitions for Use in Reporting Electrical GeneratingUnit Reliability, Availability, and Productivity, May 20, 1987.

[3] IEEE Task Group on Peaking Service Units, “A four-state model for es-timation of outage risk for units in peaking service,” IEEE Trans. Power

App. Syst., vol. PAS-91, pp. 618–627, Mar./Apr. 1972.[4] N. Ramani, “Modeling of Thermal Units for Peaking and Cycling Oper-

ation,” Reliability and Statistics Section, Operations Research Depart-ment, Rep. B1-469-K, Jan. 1982.

[5] PJM Interconnection, L.L.C., Reliability Assurance Agreement AmongLoad Serving Entities in the PJM Control Area, Sept. 19, 2000.

[6] Generating Availability Data System, Generating Unit StatisticalBrochure 1995–1999, Oct. 2000.

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

[8] , Reliability Evaluation of Engineering Systems: Concepts and Techniques, 2nd ed. New York: Plenum, 1992.

[9] R. Billinton and J. Ge, “A comparison of North American generatingunit outage parameters and unavailability indices,” in Proc. IEEE Can.Conf. Elect. Comput. Eng., May 2002, pp. 66–71.

[10] M. P. Bhavaraju, J. A. Hynds, and G. A. Nunan, “A method for esti-mating equivalent forced outage ratesof multistate peaking units,” IEEE Trans. Power App. Syst., vol. PAS-97, pp. 2067–2075, Nov./Dec. 1978.

Roy Billinton (SM’73–F’78–LF’01) received the B.Sc. andM.Sc.degreesfromthe University of Manitoba, Winnipeg, MB, Canada, and Ph.D and D.Sc. de-grees from the University of Saskatchewan, Saskatoon, SK, Canada.

He is the author of papers on power systgem analysis, stability, economicsystem operation and reliability.

Dr. Billinton is a Fellow of EIC, Canadian Academy of Engineering, and theRoyal Society of Canada.

Jingdong Ge, received the B.Sc. degree in electrical engineering from XianJiaotang University in 1991. He received the M.Sc. degree in electrical engi-neering in 2002.

After graduation, he was an Electrical Engineer with the China State PowerSouth Company before joining the University of Saskatchewan, Saskatoon,SK, Canada, as a graduate student in September 2002. He was also with theSaskatchewan Power Corporation in the Grid Development Department.

A Comparison of Four-state Generating Unit Reliability Models for Peaking Units

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