International Journal of Technical Research (IJTR)
Vol. 2, Issue 2, Jul-Aug 2013
CAPACITY OUTAGE PROBABILITY TABLE
CALCULATION (COPT) OF HARYANA POWER
GENERATION CORPORATION LIMITED USING VBA
1,2,3
1
Ashish Kumar 1, Shivani Sehgal2, Deepika Arora 3, Aman Soni4
Doon Valley Institute of Engineering & Technology, Karnal, 4HPGCL, Hisar.
[email protected], [email protected], [email protected], [email protected]
Abstract--In this paper, a generation system Capacity Outage
Probability Table (COPT) calculation tool was developed using
MS Excel and the Visual Basic Editor. The tool was used to
evaluate the Capacity Outage Probability Table (COPT) of
IEEE Reliability Test System ’96 and HPGCL data.
I.
The most important input quantities required in generation
system reliability analysis are the capacity and the failure
probabilities of individual generating units. If a simple twostate model is assumed for the operation of a unit, its failure
probability is given by its unavailability U, which can be
expressed in terms of the unit failure rate λ and repair rate μ in
given equation.
INTRODUCTION
Electricity has been the driving force for economies of the
world and provides day-to-day necessity for the population in
the world. The generation, transmission and retailing of
electricity have existed hundreds of years in providing the
much needed electricity. Due to the nature of electricity
systems, the variable demand at every moment needs to be met
by consistent electricity supply to make sure the continuous
availability of the resources. Not meeting the demand in any
case will lead to a huge loss of income to the generators as well
as to the consumers.
Generation system reliability is an important aspect of planning
for the future capacity expansion to make sure that the total
installed capacity is sufficient to provide adequate electricity
when needed (2).
II. GENERATION SYSTEM RELIABILITY
Reliability has been and always is one of the major factors in
the planning, design, operation, and maintenance of electric
power system. Generation system reliability focuses on the
reliability of generators in the whole electric power system
where electric power is produced from the conversion process
of primary energy (fuel) to electricity before transmission. The
generation system is an important part of the electricity supply
chain and it is crucial that enough electricity is generated at
every moment to meet the demand. Generating units will
occasionally fail to operate and the system operator has to make
sure that enough reserve is available to be operated when this
situation happens.
In the analytical method, the generating system model used for
generation capacity adequacy assessment is a Capacity Outage
Probability Table (COPT) .
U =

+
... (1.1)
Where,
 = unit failure rate
µ = unit repair rate
U = unit unavailability
Unit unavailability is also known conventionally as “forced
outage rate” (FOR), although the value is not a rate. The FOR is
defined in Equation 1.2 below
... (1.2)
The FOR calculated for a long period of time (e.g. 365 days), is
the same index as the unavailability defined in Equation 3.1.
The FOR is a good approximation for the 2 state
approximations. The next step in building a generation model is
to combine the capacity and availability of the individual units
to estimate available generation in the system. The result of this
combination will be a capacity model, where each generating
unit is represented by its nominal capacity,
i
and its
unavailability,
i (or FOR). The capacity or the outage
capacity, X is considered to be a random variable in power
system reliability analysis. The capacity or outage capacity is
discrete and obeys an exponential distribution. The unit model
is the probability table of a generator unit’s capacity state.
The probability model of a two-state generator model has only
two states; in operation or on outage. There are 2n possible
different capacity states. The individual state probability can be
described in Equation 1.3
III. CONVENTIONAL GENERATING UNIT
RELIABILITY MODEL
... (1.3)
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International Journal of Technical Research (IJTR)
Vol. 2, Issue 2, Jul-Aug 2013
The cumulative state probability (the distribution function) can
be obtained by summing up the individual state probability for
all capacity less than xi. Equation 1.4 gives the cumulative state
probability.
equation (3.7)
Step 4 : Set O = 0
Step 5 : Set j = j + 1, calculate probability when 1st unit goes
on outage using
equation (3.7)
Step 6 : O = O + Cj
(1.4)
There will be a forced outage rate for every capacity
i, and
the individual state probability and cumulative state probability
are summarized in Equation 1.5 and 1.6 respectively.
P(X=xi)=P(xi) where i =0,1,2 ……(1.5)
From these equations, the Capacity Outage Probability Table
(COPT) that represents the probability of different capacity
outages of the system can be generated.
We can also use binomial distribution
calculation of probability of different outage states
for
... (1.6)
Where,
U-unit unavailability
A - unit availability
Step 7 : Repeat Step 5 & 6 for j ≤ N+ 1, otherwise go to Step 8
Step 8 : Print COPT table.
V. Generating Units Capacity Outage Probability Table
(COPT)
A power system normally consists of hundreds or thousands of
generating units of different types, capacity, and reliability in
parallel operations. With each units assumed to have dual
states, a system with n units has 2n capacity states. This will
prove too much for any manual calculations to be conducted.
At present, the recurrent algorithm based upon discrete
distribution is used by all (7).
The process of using the recurrent algorithm starts off with
creation of a capacity table for a single generating unit as of
Table 1.1
Outage
capacity,
MW
Exact
probability,
Pi
Cumulative
probability, P
j - outage state
Available
capacity,
MW
P(j) - probability of outage state j
c
0
1-q
1
0
c
q
q
N - no: of units
The total cost of operation includes the fuel cost, cost of labour,
supplies and maintenance. Generally, costs of labour, supplies
and maintenance are fixed percentages of incoming fuel costs.
The power output of fossil plants is increased sequentially by
opening a set of valves to its steam turbine at the inlet. The
throttling losses are large when a valve is just opened and small
when it is fully opened.
IV. ALGORITHIM FOR COPT
Following steps present the method of calculating COPT
(capacity outage probability table) for evaluating reliability of
generation system:
Step 1 : Input N, λ, μ, and capacity of units (Cj) for j = 1,2…,N
Step 2 : For N units calculate no: of states & Calculate U & A
from equation (3.1)
Step 3 : Set j = 0, calculate probability when no generating unit
is on outage using
ISSN 2278-5787
Table 1.1 Probability model for a single generating unit
Where
c is the generating unit’s effective capacity
q is the forced outage rate (FOR)
Then, the table is revised as units are added one after another
until the last generating unit and the capacity outage probability
table for the whole generating system is completed. To add on
generating units into the table, the recurrent formula provides a
means to do that using a computer algorithm. First of all,
suppose the capacity outage table for n – 1 generating units has
been formed as in Table 4.1 and the outage capacity X is a
random variable with a discrete distribution and an exact
probability of pn-1 (X). When the nth new unit is added with
effective capacity Cn and forced outage rate qn, the exact
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International Journal of Technical Research (IJTR)
Vol. 2, Issue 2, Jul-Aug 2013
probability of the system outage capacity pn (X) can be directly
obtained by using the convolution formula in Equation 1.7
pn (X) = pn -1 (X) . p (0) + pn-1 (X - Cn) . p (Cn)…… (1.7)
U50
Hydro
6
50
0.01
U76
Coal/Steam
4
76
0.02
According to the two states generation model, the exact
probability of no outage is p(0) = 1-q and the exact probability
of full outage is p(Cn) = qn . When substituted into Equation
1.8, the recurrence formula is obtained:
U100
Oil/Steam
3
100
0.04
pn (X) = pn -1 (X) . (1 – q) + pn-1 (X - Cn) . qn ……(1.8)
U155
Coal/Steam
4
155
0.04
U197
Oil/Steam
3
197
0.05
U350
Coal/Steam
1
350
0.08
U400
Nuclear
2
400
0.12
Equation 4.2 can be used for iterative calculations of both the
exact state probability and the cumulative state probability
Pn(X), changing only pn - 1 (X) and pn -1 (X - Cn) to the
corresponding cumulative state probabilities. However, the
initial conditions are different. When X ≤ Cn, it can be
stipulated that pn - 1 (X - Cn) = 0 for the exact probability and
Pn - 1 (X - Cn) = 1 for the cumulative probability.
It is important to note that when using the recurrence formula to
calculate the cumulative probability and cumulative frequency
of a generating system, a certain increment of the outage
capacity is used as the step, not the unit capacity. The size of
the step increment can be determined by the largest common
divisor of the various types of assembly capacity, the scale of
the system and the needed calculation accuracy. The discussion
of the addition of individual units can be found in (7).
Table 1.2 IEEE RTS 96 Data
For the purpose of this study, a computer code is written for the
calculation of the outage table using the recursive formula in
Equation 1.8 for the IEEE RTS generating system.
The generation system reliability and modeling is conducted in
the “RTSCOPT” and “HPGCLCOPT” worksheet. By
simulating the computer code “RTSCOPT COPT( )” and
“HPGCLCOPT” each generating units will be added unit by
unit into the worksheet based on the recursive formula to obtain
the exact and cumulative probability for each outage capacity
level. The summarized Capacity Outage Probability Table for
the IEEE RTS is shown in Figure1.3.
Unit
Group
Unit Type
No. of
Unit
Forced
Size, C
Outage
(MW)
Rate, U
Units
U12
Oil/Steam
5
12
0.02
U20
Oil/ Steam
4
20
0.1
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International Journal of Technical Research (IJTR)
Vol. 2, Issue 2, Jul-Aug 2013
HPGCL DATA
Inde
x
1
2
3
4
5
6
7
Total no. of groups
9
Total System Capacity
3232.1
Unit Group
PTPS
U1
PTPS
U2,U3,U4
PTPS U5,U6
PTPS
U6,U7
DBCRTPP
U1,U2
RGTPP
U1,U3
WYCHES
U1,U2,U3,U
4,U5,U6
9
WYCHES
U7,U8
KMHP
10
Others
8
Forc
ed
Outa
ge
Rate,
U
0.259
5
0.259
5
0.259
5
0.259
5
Unit
Type
No. of
Units
Uni
t
Siz
e, C
Thermal
1
117
.8
Thermal
3
110
Thermal
2
210
Thermal
2
250
Thermal
2
300
0.2
Thermal
2
600
0.2
Hydro
6
8
0.5
Hydro
2
8
0.5
Hydro
1
0.5
Others
1
0.3
500
0
0.1
32
PTPS - Panipat Thermal Power Station, Panipat
DBCRTPP - Deen Bandhu Chhotu Ram Thermal
Power Project, Yamuna Nagar
RGTPP - Rajiv Gandhi Thermal Power Project,
Khedar, Hisar
WYCHES - WYC Hydro Electric Station, Yamuna
Nagar
KMHP-Kakroi Micro Hydel Project
Table 1.3 HPGCL Generation Data
ISSN 2278-5787
Figure 1.1 COPT of IEEE RTS 96 Data
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International Journal of Technical Research (IJTR)
Vol. 2, Issue 2, Jul-Aug 2013
Figure 1.3 IEEE RTS 96 Data COPT Results
ISSN 2278-5787
Figure 1.4 COPT of IEEE RTS 96 Data
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International Journal of Technical Research (IJTR)
Vol. 2, Issue 2, Jul-Aug 2013
CONCLUSION
Generation system reliability is an important aspect of planning
for the future capacity expansion to make sure that the total
installed capacity is sufficient to provide adequate electricity
when needed.
In this project, a generation system reliability model and
calculation tool was developed using VBA in MS Excel.. The
tool was used to evaluate the Capacity Outage Probability
Table (COPT) of conventional generation systems based on the
analytical method and was referred to as COPT calculator.
Data from the IEEE Reliability Test System ’96 and Haryana
Power Generation Corporation Limited was used in the system
modelling so that evaluation of the COPT calculator could be
carried out.
The COPT of IEEE Reliability Test System ’96 was evaluated
and the results obtained were compared with IEEE Reliability
Test System ’96 results. The results are found same. Hence this
software can be used to evaluate Capacity outage Probability
table for any generation system by providing the required Input
data. Further this tool was used to evaluate the COPT of
HPGCL system.
FUTURE SCOPE OF WORK
The presented work can be extended in following area:
•
Development of program for calculation of LOLP,
LOLE and other reliability indices.
•
Security analysis of generation system.
•
Reliability evaluation of power system for transient
conditions.
•
Reliability of complete system which includes
generation, transmission and distribution.
[4] Allan, R.N., Billinton, R., and Lee, S.H., “Bibliography
on the Application of Probability Methods in Power
System Reliability Evaluation, 1977-1982”, IEEE
Transactions on Power Apparatus and Systems, Vol.
PAS-103, No.2, pp. 275-282, February 1984.
[5] IEEE subcommittee on Application of Probability
Methods of Power System Engineering Committee,
“Bibliography on Application of Probability Methods in
Power System Reliability Evaluation, 1971-1977”, IEEE
Transactions on power Apparatus and systems, Vol. PAS97, pp. 2235-2242, November/December 1978.
[6]
IEEE RTS Task Force of APM Subcommittee (1999) The
IEEE Reliability Test System –1996. IEEE Transactions
on Power Systems, Vol. 14, NO. 3.
[7] Wang, X. and McDonald, J. R. “Modern Power System
Planning”, McGraw-Hill (1994) International (UK) Ltd
[8] Kueck, J.D. et al. “Measurement Practices for Reliability
and Power Quality – A Tool kit of Reliability
Measurement Practices”. Oak Ridge National Laboratory,
U.S. Department of Energy. Report No. ORNL/TM2004/91, 2004.
[9] "Reliability Indices for Use in Bulk Power Supply
Adequacy Evaluation", Committee Report, IEEE
Transactions, PAS-99, pp. 1097-1103, 1978.
[10] HPGCL Tariff Petition for the FY 2013-14.
REFERENCES
[1]
Billinton, R. and Allan, R.N., “Reliability Evaluation of
Power Systems” 1st Edition, Plenum Press, New York,
1984.
[2]
Billinton, R. and Allan, R.N, “Reliability Evaluation of
Power Systems”2nd Edition Plenum Press, New York,
1996.
[3]
Endrenyi, J. (1978) “Three-State Models In Power System
Reliability Evaluations” Power Apparatus and Systems,
IEEE Transactions on Volume: PAS-90, Issue: 4 John
Wiley & Sons.
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