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Generating unit modeling in power system adequacy analysis
Reliability Engineering and System Safety 27 (1990) 155-165
Generating Unit Modeling in Power System Adequacy Analysis R. Billinton & K. D e b n a t h Power System Research Group, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 0W0 (Received 2 December 1988; accepted 8 March 1989)
ABSTRACT The selection of appropriate models which can be used to represent existing and proposed generating units is an important consideration in an electric power system capacity adequacy study. Base-load generating units are usually represented by a two state model (UP and DOWN). This simple model however, is not suitable for representing generating equipment such as peak load units which are only operated intermittently. These units usually residefor a considerable period of time in a reserve shutdown state and spend relatively short periods of time in the operating state. A four-state model which recognizes the peculiarities of peak-load units was developed by an IEEE subcommittee. This paper presents a modified version of the IEEE peak-load unit model. The paper illustrates the modified model using practical system data from the Canadian Electrical Association Equipment Reliability Information System.
1 INTRODUCTION The simplest reliability model o f a generating unit is the basic two-state representation. 1 This model is valid for base-load units, i.e. units which are placed in operation whenever they are available for operation. This simple but basic representation of a generating unit consisting o f an U P state and a D O W N state is shown in Fig. 1. This model is used extensively in power system reliability analysis. The basic parameters in this model are the forced outage rate (FOR), the failure rate (2) and the repair rate (#). 155 Reliability Engineering and System Safety 0951-8320/90/$03"50 © 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain
156
R. Billinton, K. Debnath
UP
I DOWN Fig. 1.
Basictwo-statemodel.
These parameters are sometimes difficult to estimate directly as there are many other states in which a unit can reside 2 and all transitions do not simply go from the UP to DOWN or the D O W N to UP states in actual application. The most basic statistic used in generating capacity assessment is the forced outage rate (FOR) which provides an estimate of the probability of finding the unit on outage at some distant time in the future. This statistic has been collected by Canadian utilities for many years. The F O R of a unit can be obtained using Eqn (1). FOR =
~ (DOWN time) (UP time) + ~ (DOWN time)
(1)
The unit failure rate (2) can be estimated using Eqn (2). Total number of transitions from 2 = operating state to forced outage state UP time
(2)
If the probability of being found in the D O W N state is estimated by the conventional FOR, then the 2 and # parameters in the two-state model must be consistent with this value. The unavailability or F O R can be expressed in terms of 2 and/~ by Eqn (3). 2 FOR (3) 2+// If the failure rate (2) is estimated from the raw data then the repair rate can be obtained using Eqn (4). u=
( 1 1 ) 2 FOR
(4)
Generating units can also reside in a range of partial output (i.e. derated) states. The most appropriate model therefore is one which recognizes the
Generating unit modeling in power system adequency analysis
157
significant derating states in addition to the full UP and D O W N states. The implications of derated state modeling are clearly illustrated in Ref. 1. Many utilities prefer to use a modified two state representation for a unit with derated states. In order to recognize the time spent in these derated states and still create a two-state model, the derated state residence times are apportioned between the UP and DOWN states. This adjustment of the derated times provides a derating-adjusted two-state model. The apportionment is done on the basis of 'proximity', which means that the closer a derated state is to the D O W N (or UP) state, the more contribution it makes to the residence time in the D O W N (or UP) state. Based on this principle, i f a generating unit operates in a derated state of 70 per cent of its maximum continuous rating (MCR) for 10 h, 7 h are apportioned to the UP state and the remaining 3 h are allocated to the D O W N state. In general, any residence time T(X) hours at a derating level of X per cent of M C R of the generating unit is converted into an 'equivalent' or adjusted outage time T(X)adj using Eqn (5).
T(X)adj=
100-X
100
T(X) hours
(5)
In the derating-adjusted two-state representation, the portion T(X)adj hours is allocated to the D O W N state and the remaining time, i.e. T(X)-T(X)adj is retained in the UP state. 2 The derating-adjusted forced outage rate (DAFOR) statistic is then calculated using Eqn (6). Total forced outage time + ~ T(X)adj X
D A F O R - Total forced outage time + Total operating time
(6)
The D A F O R is known as equivalent forced outage rate (EFOR) in the United States. The equivalent repair rate in this case can be estimated using Eqn (4) but replacing F O R by DAFOR, The utilization of a deratingadjusted forced outage rate (DAFOR) rather than a multi-state model for a generating unit gives a pessimistic appraisal of overall system capacity adequacy. Peak-load units are, by definition, intended for operation during peak load periods which are usually short in duration. These units, therefore, spend more time in the reserve shutdown state than in the operating state. The difference between a base-load unit and a peak-load unit can be clearly seen from Fig. 2 which shows the state probabilities estimated from the state residence times of selected nuclear and combustion turbine units (CTUs). These data were obtained from the Canadian Electrical Association Equipment Reliability Information System (CEA-ERIS) data base. In Fig. 2, state code 11 represents operation at full capacity, state 12 operation
158
R. Billinton, K. Debnath 0'8' 0.7-
0"6" ~>" O & tg
~0.40"3-
0.20,1• State
Fig. 2.
Code
400-599MW nuclear units (ll) (El), 1980-84CEA-ERISdata.
State probabilities for
and
25-49MW CTU units
at a forced derated capacity and state 13 operation at a scheduled derated capacity. There can therefore, be many derated capacity levels contained in states 12 and 13 each with a probability of existence. Similarly, state codes 14, 15 and 16 represent the shutdown states at full capacity, forced derated capacity and scheduled derated capacity respectivity. It can be seen that the nuclear units resided most of the time in one of the operating states whereas the combustion turbine units resided most o f the time in one o f the shutdown (I - P O / T
RESERVE SHUTDOWN
IN
1/D
(2)
(o)
l
1/T
FORCED OUT I NOT NEEDED1 (z) Fig. 3.
SERVICE
]"
I/D
FORCED OUT i NEEDED
(3)
IEEE Four-state model for peak load units. 3
Generating unit modeling in power system adequency analysis
159
states. This important difference must therefore be recognized when modeling peak load generating units. 1.1 IEEE four-state model A Working Group of the IEEE Subcommittee on the Application of Probability Methods developed a four-state model a which recognizes the intermittent operation of peak load units. This model is shown in Fig. 3. The parameters used in this model are defined as follows: 2 = Failure rate = Repair rate P~ = Probability of starting failure resulting in inability to serve load during all or part of a demand period. Repeated attempts to start during one demand period should be interpreted as only one failure to start Total number of starting failures Total number of attempted starts D--Average in service time per occasion of demand Total operating time ( 1 - P~)(Total number of attempted starts) T = Average reserve shutdown time between periods of need Total operating time + Total reserve shutdown time Total number of attempted starts
D
In this model, States 1 and 3 together represent the forced outage state (i.e. D O W N state of Fig. 1). The Canadian Electrical Association Equipment Reliability Information System (CEA-ERIS) 2 does not recognize whether a forced outage state occurs during a period of need or during a period when the unit is not needed. There is, therefore, no direct method for dividing the total forced outage time into states 1 and 3. The state probabilities can, however, be estimated by solving the equations derived by considering the model in Fig. 3 as a Markov process. The state probabilities Po,/'1, P2 and P3 are as follows, 3 laT[O,~ + 1 + O(# + I/T)] po = A D2+P S PlA D/~{(1 -- P~) + O(l, + l/T)} A
R. Billinton, K. Debnath
160
and P3 =
D(p + 1/T)(D2 + e~) A
where A = (02 + Ps)(/t + 1/T)(D + T) + #DT{(1 - P~) + D(p + 1/T)(1/T+ l/D)} The parameters 2, p and Ps can be estimated from the unit operating data. The D and T parameters depend on the future role of the unit in the system. If these can be estimated then all the parameters required in the calculation of the state probabilities are available and the conditional FOR can be obtained using Eqn (7). In order for the state space diagram to represent a Markov process, all the transition rates must be constant. The residence time of the states characterized by D and T must therefore, be exponentially distributed. FOR =
P~ + P3 PI + P2 + P3
(7)
2 UTILIZATION F O R C E D OUTAGE PROBABILITY The IEEE peak load generating unit model recognizes the fact that a significant portion of the total forced outage time can occur in periods when the generating unit is not required by the system. The utilization of the total forced outage time in the calculation of the conventional FOR parameter results in a pessimistic appraisal of peak load generating unit performance. The IEEE subcommittee, therefore, proposed that a fraction of the total forced outage time be utilized in the calculation of forced outage probability associated with demand periods. The CEA Consultative Committee on Outage Statistics (CCOS decided to clearly recognize the conditional nature of the forced outage statistic by designating it as the utilization forced outage probability (UFOP). The UFOP is defined as the conditional probability that a generating unit is not available given that the unit is needed by the system. A weighting factor (f) can be derived from the state probabilities and used in the calculation of the UFOP parameter. The weighting factor and the UFOP are obtained using Eqns (8) and (9). 1'3 f=
UFOP =
P3 P3 + P1
-
-
p + lIT l,l + 1/T + 1/D
f(forced outage time) f(forced outage time) + operating time
(8)
(9)
The UFOP parameter is always smaller than the FOR except for purely
Generating unit modeling in power system adequency analysis
161
20-
15
E o_
\\
.~10
g 5-
o Z
Z
~
E
E
Z
•
Z
Z
a
~
~
o
a
o
o
O
Type a n d MCR Class of Generating Units
Fig. 4.
FOR (I-q) and UFOP (O) for fossil and hydraulic units, 1980-84 CEA-ERIS data base.
base load units in which case the two are identical. In the case of the nuclear units shown in Fig. 2, the F O R and the U F O P are identical because the residence time in state 1 is zero. This is not the case, however, with fossil and hydraulic units as can be seen in Fig. 4.
3 M O D I F I C A T I O N OF T H E IEEE F O U R - S T A T E M O D E L It was noted in Ref. 4 that a generating unit can experience failures while residing in the reserve shutdown state. This observation has been confirmed using the CEA-ERIS data base where it was found that there are a large number of transitions from State 0 to State 1. The modified model which includes this additional transition path is given in Fig. 5. The state probabilities associated with this model can be obtained using the following equations. Po
Bo
P1
Bl
B2
P3
B3
R. Billinton, K. Debnath
162
RESERVE SHUTDOWN
(1 -
&)/Ti
1/D
IN SERVICE
(o)
1/T F O R C E D OUT NOT NEEDED
1/D
(1) Fig. 5.
FORCED OUT NEEDED
(3)
Modified four-state model for peak load umts.
where Bo = #{(D2 + l) + D(/~ + l/T)} B, = (D2 + Ps)/T+ 2'{D/2 + (D2 + 1)} B z = #D{(/~ + 1/T)D/T+ (1 - P~)/T} + 2'I~DZ/T B 3 ----(D2 + P2)(/~ + 1/T)D/T+ 2'(D2 + 1)D/T and B = Bo + Bl + B2 + B3 The equation for the weighting factor (f') for this modified model is: (02 + Ps)(I.t + 1/T) + 2'(D2 + 1) f ' = (D2 + Ps)(/~ + l / T + l/D) + 2'T{la + (D2 + 1)(l/T+ l/D)} The modified weighting factor (f') has two important properties: (1) I f 2 ' = 0 , f ' reduces t o f (2) Unlike f f ' depends on 2 and Ps.
4 M O D I F I E D UTILIZATION FORCED OUTAGE PROBABILITY The modified UFOP (MUFOP), i.e. the UFOP resulting from the model of Fig. 5 can be obtained by using the basic equation for UFOP and replacing the weighting factor f by the modified value f'. The values of UFOP and M U F O P for the combustion turbine units (CTUs) and the diesel generating units (DGUs) in the 1980--84 CEA-ERIS data base are shown in Table 1.
163
Generating unit modeling in power system adequency analysis TABLE 1
Comparison between UFOP and MUFOP for CTU and DGU Units, 1980-84 ERIS Data Base MCR Class
f
f'
FOR(%)
UFOP(%)
MUFOP(%)
0-064 8 0"231 9 0"3208 0"211 1
58-62 30.49 38'50 68"93
10-53 13.05 19.42 37"63
8.41 9.24 16"73 31'90
0.443 0 0"8604
15'88 33"88
7'85 3ff71
7-72 30'60
Combustion Turbine Units
1-9 MW 10-24 MW 25--49 MW 50+ MW
0"083 1 0"342 1 0'384 9 0"271 9
Diesel Generating Units
1--4MW 5 + MW
0"451 4 0"8648
It can clearly be seen from Table 1 that the modified U F O P is slightly lower than the original U F O P obtained without recognizing the additional transition path shown in Fig. 5. The modified values given in Table 1 are based on transition rate parameters determined from actual utility operating data and therefore the M U F O P is a more realistic parameter.
5 DERATING-ADJUSTED UTILIZATION FORCED OUTAGE PROBABILITY A further observation from the peak load generating unit data in the ERIS data base is that these units, and particularly the larger ones, experience significant deratings. This can be included in the model by adjusting the time spent under forced deratings in a similar m a n n e r to the adjustment made in the development of the derating-adjusted two-state model, creating a derating-adjusted U F O P (DAUFOP). This parameter is greater than the corresponding U F O P whenever forced deratings exist.
6 MODIFIED DERATING-ADJUSTED UTILIZATION FORCED OUTAGE PROBABILITY If the modified four-state model shown in Fig. 5 is used to calculate the derating-adjusted UFOP, a modified D A U F O P ( M D A U F O P ) will result. Figure 6 shows the six generating unit parameters (i.e. FOR, D A F O R , U F O P , M U F O P , D A U F O P and M D A U F O P ) for the 1980-84 Canadian fossil, hydraulic, nuclear, C T U and D G U units data. It can be seen from Fig. 6 that for the D G U and larger C T U units, D A U F O P is considerably
R. Billinton, K. Debnath
164
80
•
7o
"~ it
~ 6o. ESO
I\
I
fl_
.,o.
,
,i.ili!
.-~ 30-
I~ //~,l.l!../~
7
° I, J ~,2o
::t7'/
:E )
Fig. 6.
:E :E :E E E :E E '
o
~
u
÷
'.
Type and MCR Class of Generating Units FOR ([]), DAFOR ( i ) , UFOP (©), MUFOP (O), DAUFOP ( i ) and MDAUFOP ( 0 ) of all types of generating units, ]980-84 CEA-ERIS data base.
larger than the UFOP. The modified values ( M D A U F O P and MUFOP) are lower than the corresponding unmodified quantities.
7 CONCLUSIONS Figure 6 clearly illustrates that the conventional two-state representation of a generating unit provided by the F O R and D A F O R statistics may not be appropriate for a wide range of units. It may be more appropriate to consider all generating equipment as intermittent operating units and derive a U F O P parameter. The conventional F O R for a base load unit therefore becomes a special case of the general four state model. The unique nature of the CEA-ERIS data base 2 in the form of continuous state monitoring of generating unit states has made it possible to clearly recognize the additional transition path shown in Fig. 5. The modified four state model shown in Fig. 5, therefore, provides a more realistic representation than the original
Generating unit modeling in power system adequency analysis
165
IEEE model given in Fig. 3. As can be seen from Table 1, the modified conditional probabilities are lower than the unmodified values which enhances the utilization of intermittent operating units in overall system generating capacity adequacy assessment.
REFERENCES 1. Billinton, R. & Allan, R. N., Reliability Evaluation of Power Systems. Longman, London (England)/Plenum Publishers, New York, 1984. 2. The Consultative Committee on Outage Statistics, Canadian Electrical Association. Instruction Manual for Reporting Generation Equipment Outage Data. Canadian Electrical Association, Montreal, 1976. 3. IEEE Task Group on Models for Peaking Service Units, A Four-state Model for Estimation of Outage Risk for Units in Peaking Service. IEEE Transactions on Power Apparatus and Systems, Vol. PAs-91, No. 2, 1972, pp. 618-623. 4. Wang, L., Ramani, N. & Davies, T. C., Reliability modeling of thermal units for peaking and cycling operations. IEEE PES Winter Meeting, January 30February 4, 1980.
Generating Unit Modeling in Power System Adequacy Analysis R. Billinton & K. D e b n a t h Power System Research Group, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 0W0 (Received 2 December 1988; accepted 8 March 1989)
ABSTRACT The selection of appropriate models which can be used to represent existing and proposed generating units is an important consideration in an electric power system capacity adequacy study. Base-load generating units are usually represented by a two state model (UP and DOWN). This simple model however, is not suitable for representing generating equipment such as peak load units which are only operated intermittently. These units usually residefor a considerable period of time in a reserve shutdown state and spend relatively short periods of time in the operating state. A four-state model which recognizes the peculiarities of peak-load units was developed by an IEEE subcommittee. This paper presents a modified version of the IEEE peak-load unit model. The paper illustrates the modified model using practical system data from the Canadian Electrical Association Equipment Reliability Information System.
1 INTRODUCTION The simplest reliability model o f a generating unit is the basic two-state representation. 1 This model is valid for base-load units, i.e. units which are placed in operation whenever they are available for operation. This simple but basic representation of a generating unit consisting o f an U P state and a D O W N state is shown in Fig. 1. This model is used extensively in power system reliability analysis. The basic parameters in this model are the forced outage rate (FOR), the failure rate (2) and the repair rate (#). 155 Reliability Engineering and System Safety 0951-8320/90/$03"50 © 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain
156
R. Billinton, K. Debnath
UP
I DOWN Fig. 1.
Basictwo-statemodel.
These parameters are sometimes difficult to estimate directly as there are many other states in which a unit can reside 2 and all transitions do not simply go from the UP to DOWN or the D O W N to UP states in actual application. The most basic statistic used in generating capacity assessment is the forced outage rate (FOR) which provides an estimate of the probability of finding the unit on outage at some distant time in the future. This statistic has been collected by Canadian utilities for many years. The F O R of a unit can be obtained using Eqn (1). FOR =
~ (DOWN time) (UP time) + ~ (DOWN time)
(1)
The unit failure rate (2) can be estimated using Eqn (2). Total number of transitions from 2 = operating state to forced outage state UP time
(2)
If the probability of being found in the D O W N state is estimated by the conventional FOR, then the 2 and # parameters in the two-state model must be consistent with this value. The unavailability or F O R can be expressed in terms of 2 and/~ by Eqn (3). 2 FOR (3) 2+// If the failure rate (2) is estimated from the raw data then the repair rate can be obtained using Eqn (4). u=
( 1 1 ) 2 FOR
(4)
Generating units can also reside in a range of partial output (i.e. derated) states. The most appropriate model therefore is one which recognizes the
Generating unit modeling in power system adequency analysis
157
significant derating states in addition to the full UP and D O W N states. The implications of derated state modeling are clearly illustrated in Ref. 1. Many utilities prefer to use a modified two state representation for a unit with derated states. In order to recognize the time spent in these derated states and still create a two-state model, the derated state residence times are apportioned between the UP and DOWN states. This adjustment of the derated times provides a derating-adjusted two-state model. The apportionment is done on the basis of 'proximity', which means that the closer a derated state is to the D O W N (or UP) state, the more contribution it makes to the residence time in the D O W N (or UP) state. Based on this principle, i f a generating unit operates in a derated state of 70 per cent of its maximum continuous rating (MCR) for 10 h, 7 h are apportioned to the UP state and the remaining 3 h are allocated to the D O W N state. In general, any residence time T(X) hours at a derating level of X per cent of M C R of the generating unit is converted into an 'equivalent' or adjusted outage time T(X)adj using Eqn (5).
T(X)adj=
100-X
100
T(X) hours
(5)
In the derating-adjusted two-state representation, the portion T(X)adj hours is allocated to the D O W N state and the remaining time, i.e. T(X)-T(X)adj is retained in the UP state. 2 The derating-adjusted forced outage rate (DAFOR) statistic is then calculated using Eqn (6). Total forced outage time + ~ T(X)adj X
D A F O R - Total forced outage time + Total operating time
(6)
The D A F O R is known as equivalent forced outage rate (EFOR) in the United States. The equivalent repair rate in this case can be estimated using Eqn (4) but replacing F O R by DAFOR, The utilization of a deratingadjusted forced outage rate (DAFOR) rather than a multi-state model for a generating unit gives a pessimistic appraisal of overall system capacity adequacy. Peak-load units are, by definition, intended for operation during peak load periods which are usually short in duration. These units, therefore, spend more time in the reserve shutdown state than in the operating state. The difference between a base-load unit and a peak-load unit can be clearly seen from Fig. 2 which shows the state probabilities estimated from the state residence times of selected nuclear and combustion turbine units (CTUs). These data were obtained from the Canadian Electrical Association Equipment Reliability Information System (CEA-ERIS) data base. In Fig. 2, state code 11 represents operation at full capacity, state 12 operation
158
R. Billinton, K. Debnath 0'8' 0.7-
0"6" ~>" O & tg
~0.40"3-
0.20,1• State
Fig. 2.
Code
400-599MW nuclear units (ll) (El), 1980-84CEA-ERISdata.
State probabilities for
and
25-49MW CTU units
at a forced derated capacity and state 13 operation at a scheduled derated capacity. There can therefore, be many derated capacity levels contained in states 12 and 13 each with a probability of existence. Similarly, state codes 14, 15 and 16 represent the shutdown states at full capacity, forced derated capacity and scheduled derated capacity respectivity. It can be seen that the nuclear units resided most of the time in one of the operating states whereas the combustion turbine units resided most o f the time in one o f the shutdown (I - P O / T
RESERVE SHUTDOWN
IN
1/D
(2)
(o)
l
1/T
FORCED OUT I NOT NEEDED1 (z) Fig. 3.
SERVICE
]"
I/D
FORCED OUT i NEEDED
(3)
IEEE Four-state model for peak load units. 3
Generating unit modeling in power system adequency analysis
159
states. This important difference must therefore be recognized when modeling peak load generating units. 1.1 IEEE four-state model A Working Group of the IEEE Subcommittee on the Application of Probability Methods developed a four-state model a which recognizes the intermittent operation of peak load units. This model is shown in Fig. 3. The parameters used in this model are defined as follows: 2 = Failure rate = Repair rate P~ = Probability of starting failure resulting in inability to serve load during all or part of a demand period. Repeated attempts to start during one demand period should be interpreted as only one failure to start Total number of starting failures Total number of attempted starts D--Average in service time per occasion of demand Total operating time ( 1 - P~)(Total number of attempted starts) T = Average reserve shutdown time between periods of need Total operating time + Total reserve shutdown time Total number of attempted starts
D
In this model, States 1 and 3 together represent the forced outage state (i.e. D O W N state of Fig. 1). The Canadian Electrical Association Equipment Reliability Information System (CEA-ERIS) 2 does not recognize whether a forced outage state occurs during a period of need or during a period when the unit is not needed. There is, therefore, no direct method for dividing the total forced outage time into states 1 and 3. The state probabilities can, however, be estimated by solving the equations derived by considering the model in Fig. 3 as a Markov process. The state probabilities Po,/'1, P2 and P3 are as follows, 3 laT[O,~ + 1 + O(# + I/T)] po = A D2+P S PlA D/~{(1 -- P~) + O(l, + l/T)} A
R. Billinton, K. Debnath
160
and P3 =
D(p + 1/T)(D2 + e~) A
where A = (02 + Ps)(/t + 1/T)(D + T) + #DT{(1 - P~) + D(p + 1/T)(1/T+ l/D)} The parameters 2, p and Ps can be estimated from the unit operating data. The D and T parameters depend on the future role of the unit in the system. If these can be estimated then all the parameters required in the calculation of the state probabilities are available and the conditional FOR can be obtained using Eqn (7). In order for the state space diagram to represent a Markov process, all the transition rates must be constant. The residence time of the states characterized by D and T must therefore, be exponentially distributed. FOR =
P~ + P3 PI + P2 + P3
(7)
2 UTILIZATION F O R C E D OUTAGE PROBABILITY The IEEE peak load generating unit model recognizes the fact that a significant portion of the total forced outage time can occur in periods when the generating unit is not required by the system. The utilization of the total forced outage time in the calculation of the conventional FOR parameter results in a pessimistic appraisal of peak load generating unit performance. The IEEE subcommittee, therefore, proposed that a fraction of the total forced outage time be utilized in the calculation of forced outage probability associated with demand periods. The CEA Consultative Committee on Outage Statistics (CCOS decided to clearly recognize the conditional nature of the forced outage statistic by designating it as the utilization forced outage probability (UFOP). The UFOP is defined as the conditional probability that a generating unit is not available given that the unit is needed by the system. A weighting factor (f) can be derived from the state probabilities and used in the calculation of the UFOP parameter. The weighting factor and the UFOP are obtained using Eqns (8) and (9). 1'3 f=
UFOP =
P3 P3 + P1
-
-
p + lIT l,l + 1/T + 1/D
f(forced outage time) f(forced outage time) + operating time
(8)
(9)
The UFOP parameter is always smaller than the FOR except for purely
Generating unit modeling in power system adequency analysis
161
20-
15
E o_
\\
.~10
g 5-
o Z
Z
~
E
E
Z
•
Z
Z
a
~
~
o
a
o
o
O
Type a n d MCR Class of Generating Units
Fig. 4.
FOR (I-q) and UFOP (O) for fossil and hydraulic units, 1980-84 CEA-ERIS data base.
base load units in which case the two are identical. In the case of the nuclear units shown in Fig. 2, the F O R and the U F O P are identical because the residence time in state 1 is zero. This is not the case, however, with fossil and hydraulic units as can be seen in Fig. 4.
3 M O D I F I C A T I O N OF T H E IEEE F O U R - S T A T E M O D E L It was noted in Ref. 4 that a generating unit can experience failures while residing in the reserve shutdown state. This observation has been confirmed using the CEA-ERIS data base where it was found that there are a large number of transitions from State 0 to State 1. The modified model which includes this additional transition path is given in Fig. 5. The state probabilities associated with this model can be obtained using the following equations. Po
Bo
P1
Bl
B2
P3
B3
R. Billinton, K. Debnath
162
RESERVE SHUTDOWN
(1 -
&)/Ti
1/D
IN SERVICE
(o)
1/T F O R C E D OUT NOT NEEDED
1/D
(1) Fig. 5.
FORCED OUT NEEDED
(3)
Modified four-state model for peak load umts.
where Bo = #{(D2 + l) + D(/~ + l/T)} B, = (D2 + Ps)/T+ 2'{D/2 + (D2 + 1)} B z = #D{(/~ + 1/T)D/T+ (1 - P~)/T} + 2'I~DZ/T B 3 ----(D2 + P2)(/~ + 1/T)D/T+ 2'(D2 + 1)D/T and B = Bo + Bl + B2 + B3 The equation for the weighting factor (f') for this modified model is: (02 + Ps)(I.t + 1/T) + 2'(D2 + 1) f ' = (D2 + Ps)(/~ + l / T + l/D) + 2'T{la + (D2 + 1)(l/T+ l/D)} The modified weighting factor (f') has two important properties: (1) I f 2 ' = 0 , f ' reduces t o f (2) Unlike f f ' depends on 2 and Ps.
4 M O D I F I E D UTILIZATION FORCED OUTAGE PROBABILITY The modified UFOP (MUFOP), i.e. the UFOP resulting from the model of Fig. 5 can be obtained by using the basic equation for UFOP and replacing the weighting factor f by the modified value f'. The values of UFOP and M U F O P for the combustion turbine units (CTUs) and the diesel generating units (DGUs) in the 1980--84 CEA-ERIS data base are shown in Table 1.
163
Generating unit modeling in power system adequency analysis TABLE 1
Comparison between UFOP and MUFOP for CTU and DGU Units, 1980-84 ERIS Data Base MCR Class
f
f'
FOR(%)
UFOP(%)
MUFOP(%)
0-064 8 0"231 9 0"3208 0"211 1
58-62 30.49 38'50 68"93
10-53 13.05 19.42 37"63
8.41 9.24 16"73 31'90
0.443 0 0"8604
15'88 33"88
7'85 3ff71
7-72 30'60
Combustion Turbine Units
1-9 MW 10-24 MW 25--49 MW 50+ MW
0"083 1 0"342 1 0'384 9 0"271 9
Diesel Generating Units
1--4MW 5 + MW
0"451 4 0"8648
It can clearly be seen from Table 1 that the modified U F O P is slightly lower than the original U F O P obtained without recognizing the additional transition path shown in Fig. 5. The modified values given in Table 1 are based on transition rate parameters determined from actual utility operating data and therefore the M U F O P is a more realistic parameter.
5 DERATING-ADJUSTED UTILIZATION FORCED OUTAGE PROBABILITY A further observation from the peak load generating unit data in the ERIS data base is that these units, and particularly the larger ones, experience significant deratings. This can be included in the model by adjusting the time spent under forced deratings in a similar m a n n e r to the adjustment made in the development of the derating-adjusted two-state model, creating a derating-adjusted U F O P (DAUFOP). This parameter is greater than the corresponding U F O P whenever forced deratings exist.
6 MODIFIED DERATING-ADJUSTED UTILIZATION FORCED OUTAGE PROBABILITY If the modified four-state model shown in Fig. 5 is used to calculate the derating-adjusted UFOP, a modified D A U F O P ( M D A U F O P ) will result. Figure 6 shows the six generating unit parameters (i.e. FOR, D A F O R , U F O P , M U F O P , D A U F O P and M D A U F O P ) for the 1980-84 Canadian fossil, hydraulic, nuclear, C T U and D G U units data. It can be seen from Fig. 6 that for the D G U and larger C T U units, D A U F O P is considerably
R. Billinton, K. Debnath
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larger than the UFOP. The modified values ( M D A U F O P and MUFOP) are lower than the corresponding unmodified quantities.
7 CONCLUSIONS Figure 6 clearly illustrates that the conventional two-state representation of a generating unit provided by the F O R and D A F O R statistics may not be appropriate for a wide range of units. It may be more appropriate to consider all generating equipment as intermittent operating units and derive a U F O P parameter. The conventional F O R for a base load unit therefore becomes a special case of the general four state model. The unique nature of the CEA-ERIS data base 2 in the form of continuous state monitoring of generating unit states has made it possible to clearly recognize the additional transition path shown in Fig. 5. The modified four state model shown in Fig. 5, therefore, provides a more realistic representation than the original
Generating unit modeling in power system adequency analysis
165
IEEE model given in Fig. 3. As can be seen from Table 1, the modified conditional probabilities are lower than the unmodified values which enhances the utilization of intermittent operating units in overall system generating capacity adequacy assessment.
REFERENCES 1. Billinton, R. & Allan, R. N., Reliability Evaluation of Power Systems. Longman, London (England)/Plenum Publishers, New York, 1984. 2. The Consultative Committee on Outage Statistics, Canadian Electrical Association. Instruction Manual for Reporting Generation Equipment Outage Data. Canadian Electrical Association, Montreal, 1976. 3. IEEE Task Group on Models for Peaking Service Units, A Four-state Model for Estimation of Outage Risk for Units in Peaking Service. IEEE Transactions on Power Apparatus and Systems, Vol. PAs-91, No. 2, 1972, pp. 618-623. 4. Wang, L., Ramani, N. & Davies, T. C., Reliability modeling of thermal units for peaking and cycling operations. IEEE PES Winter Meeting, January 30February 4, 1980.