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PERFORMANCE AND BEHAVIOR ANALYSIS OF WATER CIRCULATION SYSTEM OF A THERMAL
POWER PLANT
Seema Sharma1, Sushma2'*
Professor, Department of Mathematics and Statistics, Gurukul Kangri (Deemed to be University)
Haridwar, Uttarakhand, India-249404 2 Research Scholar, Department of Mathematics and Statistics, Gurukul Kangri (Deemed to be University) Haridwar, Uttarakhand, India-249404
*e-mail: [email protected] 2e-mail: [email protected] ^Corresponding Author
Abstract
This paper analyses the performance and behavior of water circulation system (WCS) of a thermal power plant in fuzzy environment. For this purpose, fuzzy A-t technique coupled with petrinet modelling has been used. To address the vagueness in data, trapezoidal fuzzy numbers have been employed in fuzzy A-t technique. Various reliability indicators of WCS viz. failure rate, repair time, expected number of failures, mean time between failures, reliability and availability have been computed at ±15%, ±25% and ±40% spreads using fuzzy A-t technique. Further, fuzzy values of reliability indicators have been defuzzified employing COA method and the failure dynamics of WCS have been studied on account of decreasing / increasing trends of reliability indicators. The outcomes of this study are of great importance for plant personnel / management to enhance the availability of WCS.
Keywords: thermal power plant, water circulation system, fuzzy A-t technique, trapezoidal fuzzy number
1. Introduction
Thermal power plant is a prominent source of electricity generation. It is a complex arrangement of various systems / subsystems / components. The highest availability of a thermal power plant depends upon reliability and maintainability of each of its systems / subsystems. Unfortunately, system failure cannot be avoided entirely, but it can be reduced to minimum possible level by proper planning and following a suitable maintenance strategy [1]. Therefore, the failure prediction of each system in a thermal power plant is necessary for its successful and perpetual operation. Further,
Water is an essential fluid used in a thermal power plant for ash removal, condenser cooling and steam generation etc. WCS of a thermal power plant regulates the flow of water and plays a vital role in its proper functioning. Therefore, it should remain operative with full capacity for longer duration.
Several techniques namely Markov technique, fault tree analysis and petrinet among others, are available in the literature for assessment of the performance / behavior of a system [2, 3]. The performance of many real-world industrial systems such as urea plants, sugar mills, paper mills and thermal power plants have been improved by using the probabilistic Markov technique, which considers a constant repair time and failure rate. Gupta et al. [4] calculated reliability indicators for plastic-pipe production plants, while, Garg et al. [5] analysed performance of a cattle feed plant employing Markov technique. Sikos and Klemes [6] optimised the availability, reliability and maintainability of a heat exchanger in a thermal power plant employing Markov technique. Modgil et al. [7] employed Markov technique to discuss the performance of a shoe upper manufacturing unit. Sharma and Vishwakarma [8] analysed performance of feeding system in a sugar industry employing Markov technique. Malik and Tewari [9] modeled the performance of water flow system in a thermal power plant using Markov technique.
To handle the uncertainty / imprecision of data due to system complexity as well as ambiguity in human verdicts, several academicians have employed fuzzy methodology (FM) for reliability analysis of systems in different sectors like healthcare, tunnel boring machines, power distribution systems and process industries. In fuzzy methodology, fuzzy numbers can be represented by triangular, trapezoidal, normal, gamma, gaussian types of membership functions. In literature, most of the studies using fuzzy methodology have been conducted using triangular membership functions due to their simplicity.
Fuzzy A-t technique using petrinet was proposed by Knezevic and Odoom [10] to analyse the behavior of a general production plant. Verma et al. [11] employed vague A-t technique with triangular fuzzy numbers and petrinet model to assess the reliability of combustion system of a gas turbine plant. The reliability of coal handling unit of a thermal power plant has been investigated by Kumar and Panchal [12] using fuzzy A-t technique with triangular fuzzy numbers. Srivastava et al. [13] analysed the reliability of a CNG dispensing unit using fuzzy A-t technique with triangular fuzzy numbers. Gopal and Panchal [14] evaluated the risk and reliability of milk process industry implementing fuzzy A-t technique with triangular fuzzy numbers. The performance of juice clarification unit has been analysed by Kushwaha et al. [15] employing triangular fuzzy numbers in intuitionistic fuzzy A-t technique.
In this paper, the performance of WCS in a thermal power plant has been analysed employing trapezoidal fuzzy numbers in fuzzy A-t technique coupled with petrinet modelling. The interval expressions for OR / AND transitions of petrinet model of WCS have been evaluated using trapezoidal fuzzy numbers. Here, trapezoidal fuzzy numbers have been chosen in the light of a comparison study presented by Princy and Dhenakaran [16]. They compared trapezoidal and triangular fuzzy membership functions and revealed the fact that "although trapezoidal membership functions make the procedure more complex but their performance is still better than the triangular membership functions". To counter the vagueness of input data, some reliability indicators of WCS have been evaluated at ±15%, ± 25% and ± 40% spreads. Then the obtained fuzzy values of reliability indicators have been defuzzified using COA method for quantitative analysis of performance of WCS.
2. Proposed Methodology
Fuzzy A-t technique [10] is a quantitative technique for analysing the performance of repairable systems in an ambiguous environment. In order to study the behavior of complex repairable systems, failure and repair rates are assumed to be constant in this technique. Moreover, this technique uses fuzzified values of repair time and failure rate data of each of its components / subsystems. This technique is more powerful than Markov technique since it takes care of ambiguity in repair time and failure rate data. Numerous researchers have implemented it in various areas like sugar mills, thermal power plants and chemical sector, among others. The various steps of methodology used in this paper are given below:
Step 1: Collect the information regarding various components and subsystems of WCS to construct its fault tree model and then its analogous petrinet model.
Step 2: Collect the data for failure rate and repair time of various components and subsystems of WCS.
Step 3: Fuzzify failure and repair data of each components and subsystems of WCS using trapezoidal membership function.
Step 4: Compute various reliability indicators of WCS at different spreads.
Step 5: Defuzzify the fuzzy values of reliability indicators employing COA method.
Step 6: Analyse the behavior of WCS.
3. Preliminaries
This section discusses some fuzzy set theory concepts to be used in this paper [17-19].
3.1. Fuzzy set
A fuzzy set A is defined as
A = {(x, M): * e X }
(1)
where, ^ : X ® [0,1] is the membership function.
3.2. Fuzzy number
A normal convex fuzzy set A on real line R is called fuzzy number if its support is bounded.
3.3. Trapezoidal fuzzy number A trapezoidal fuzzy number A = (l, l2, ux, u2 ) has its membership function x) given by
x) =
X -/
l2 — l1
/ < X < l2
l2 < x < u1
u1 < X < u2
otherwise
(2)
3.4. a-cut of a trapezoidal fuzzy number The a-cut of the trapezoidal fuzzy number A is given by
\la, ua~] = [ll + (l2 -)a, u2 -(u2 -U1 )a], where, a e [0,l]
and is shown in the figure 1.
Figure 1: Trapezoidal fuzzy number with a-cut
4. An application
Water circulation system has a significant role for proper functioning of a thermal power plant and therefore should remain operative for longer duration. The hot water collected from the condenser enters into the condensate extraction pump and then passes to low pressure (LP) heater where its temperature is further increased to improve the system efficiency. The hot water further passes through the deaerator where the dissolved gases are removed from the hot water. The ash content free water then enters into the high pressure (HP) heater with the help of the boiler feed pump and further enters into the economiser. In economiser, the hot flue gases exiting the boiler are used to
u2 x
u 2 u1
heat the feed water. This heated water enters the boiler drum, where super-heated steam is generated by super heaters of boiler. This steam is expanded in turbine to produce mechanical energy by the turbine shaft. Then the exhaust steam is condensed in condenser. Figure 2 depicts schematic flow diagram of WCS. It is made up of five subsystems as described below:
i. Subsystem 1 (SSi): It consists a condensate extraction pump (CEP) which is used to extract the condensate. The system will stop working if CEP fails.
ii. Subsystem 2 (SS2): It is made up of three LP heaters which are linked in a parallel arrangement and are used to raise the condensate's temperature. If one of them fails, the system will run at a lower efficiency.
iii. Subsystem 3 (SS3): It consists a deaerator to extract dissolved gases from hot water obtained from LP heater. The efficiency of the system reduces if deaerator fails.
iv. Subsystem 4 (SS4): Three boiler feed pumps (BFP) are connected in a parallel configuration in this subsystem. They are responsible for supplying hot water to the HP heater. The system efficiency is reduced if any of these pumps fails.
v. Subsystem 5 (SS5): It is made up of two HP heaters that are connected in a parallel manner. They are used to further heat the water received from the boiler feed pump. The efficiency of the system reduces if anyone HP heater fails.
Figure 2: Flow diagram of water circulation system
5. Reliability Analysis of WCS The reliability of WCS has been calculated using following steps:
Step 1. Fault tree and petrinet models construction: First a fault tree model of the complicated parallel and series arrangement of the WCS has been prepared (figure 3) and then its equivalent petrinet model has been developed (figure 4). The AND gate represents the parallel arrangement of components, while, the OR gate represents the series arrangement of components in these models.
Figure 3: Fault tree model of WCS
Figure 4: Petrinet model of WCS
Step 2. Data extraction: The failure and repair data of all ten components of WCS acquired from service logbook and validated by a maintenance specialist are given in Table 1 [20].
Table 1: Failure and repair data of different components of WCS
Components Failure rate 1k (failures / h) Repair time tk (h)
Condensate extraction pump 5.78x10-5 11
(SSi) (k = 1)
Low pressure heater (SS2) 3.85*10-s 16
(k = 2, 3, 4)
Deaerator (SS3) (k = 5) 1.15*10-4 9
Boiler feed pump (SS4) 1.15*10-4 11
(k = 6, 7, 8)
High pressure heater (SS5) (k = 9, 3.85*10-5 11
10)
Step 3. Fuzzification of crisp data: The acquired crisp data for repair time and failure rate has been fuzzified into trapezoidal fuzzy numbers using trapezoidal membership functions to reduce ambiguity in the collected data. The values of 1k ,1k3
acquired crisp data whereas the values of 1kl, 1k 4 and ± 40% spreads for each component of the system. Figure 5 depicts trapezoidal fuzzy numbers for failure rate (lk ) and repair time {rk ) for kth component.
tk2 and tk3 have been fixed at ±10% of
Tkl and tk4 have been changed at ±15%, ± 25%
Figure 5: Trapezoidal fuzzy numbers for failure rate (l) and repair time (t ) for k'h component
Step 4. Computation of fuzzy reliability indicators: After fuzzifying the failure rate and repair time of all the components of WCS shown in petrinet model (figure 4) as trapezoidal fuzzy numbers, the fuzzy failure rate and repair time of the top most position of petrinet model of WCS are evaluated using interval expressions for OR / AND transitions presented in equations (3-6). These interval expressions are obtained utilising the extension principle and a-cut along with interval arithmetic operations on the basic A-t expressions for OR / AND gates given in Table 2.
Table 2: Basic expressions for A-t technique
Gate
l
OR
'OR
l
'AND
'AND
Expressions (n-inputs)
Zi El
k=1
k=1
k=1
ni
i=i
in
1=1 1=1 k
Interval expressions for OR transition
ta =
n n
E [{lk1 + (lk2 - 1 №>1 + 2 - t )»}] E [{l4 - 4 - 13 M{tk4 - 4 - t3 )»}]
k=1
k=1
Z {1 k4 k4 -1k 3)a}
n
Z {lk1 2 -1k1 M
k=1
k=1
(3)
=
n n
Z {lk1 + 2 -Àk1 M , Z {lk 4 - (A 4 - \ 3 M
k=1
k=1
(4)
Interval expressions for AND transition
t =
n {tk1 + (tk2 - tk1 M n {tk4 - (tk4 - t3 M
n {tk4 - (tk4 -tk3 )a}
k=1 k
n .{tk1 + (tk2 -tk1 M
k=1 k
l =
n L1R1+(lk 2 - ll RI [n lu «l {tkl +{tk 2 -tki )«}] ,
l=1
nLR4 - (l4 -1k3 )a}I [nn=1,k«l {tk4 - (t4 -tk3 )a}]
l=l
(5)
(6)
k=1
k=1
To analyse the performance of WCS quantitatively the reliability indicators viz., failure rate, repair time, expected number of failures, mean time to failure, mean time to repair, mean time between
failures, reliability and availability are calculated using expressions given in Table 3 at ±15%, ±25% and ± 40% spreads for a = 0.0 (0.1) 1.0.
Table 3: Expressions for reliability indicators
Reliability indicator Expression
Expected number of failures ENOF = ' + [l ^ +1 »] g + 1 (g +1)2 L J
Mean time to failure MTTF = — A
Mean time to repair MTTR = — = t g
Mean time between failures MTBF = MTTF + MTTR
Reliability R = eXt
Availability A = 7 + 1 > ' 7 +1 7 + 1
The left and right spread fuzzy values of the reliability indicators of WCS at 15% spread are presented in Table 4 and Table 5, respectively. The fuzzy reliability indicators at ±15%, ± 25% and ± 40% spreads for a = 0.0 (0.1) 1.0 are depicted in figure 6.
Table 4: The left spread fuzzy values of WCS at 15% spread
a Failure Repair ENOF MTBF Reliability Availability
Rate Time (h) x 10 -2 x 103 (h)
x 10-4 (/h)
1.0 1.555441 7.118736 2.610373 5.266834 0.968564 0.997535
0.9 1.546797 7.007978 2.595923 5.242912 0.968423 0.997487
0.8 1.538153 6.898654 2.581470 5.219206 0.968282 0.997438
0.7 1.529509 6.790745 2.567017 5.195713 0.968142 0.997389
0.6 1.520865 6.684231 2.552621 5.172431 0.968001 0.997339
0.5 1.512222 6.579095 2.538106 5.149355 0.967861 0.997288
0.4 1.503578 6.475318 2.523648 5.126484 0.967720 0.997236
0.3 1.494934 6.372881 2.509189 5.103816 0.967579 0.997183
0.2 1.486290 6.271767 2.494729 5.081346 0.967439 0.997129
0.1 1.477647 6.171960 2.480267 5.059073 0.967298 0.997074
0 1.469003 6.073441 2.465804 5.036994 0.967158 0.997019
Seema Sharma, Sushma
PERFORMANCE AND BEHAVIOR ANALYSIS RT&A, No 1 (72) OF WATER CIRCULATION SYSTEM_Volume 18, March 2023
Table 5: The right spread fuzzy values of WCS at 15% spread
a Failure Repair Time ENOF
Rate (h) x 10-2
X10 -4 (/h)
1.0 1.901244 12.999494
0.9 1.909890 13.191290
0.8 1.918536 13.385785
0.7 1.927182 13.583026
0.6 1.935829 13.783060
0.5 1.944475 13.985935
0.4 1.953122 14.191699
0.3 1.961768 14.400403
0.2 1.970415 14.612099
0.1 1.979061 14.826838
0 1.987708 15.044674
MTBF Reliability Availability x 103 (h)
6.442043 0.974207 0.998894
6.478163 0.974349 0.998917
6.514689 0.974490 0.998940
6.551628 0.974632 0.998962
6.588987 0.974773 0.998984
6.626774 0.974915 0.999006
6.664995 0.975056 0.999027
6.703659 0.975198 0.999048
6.742773 0.975339 0.999069
6.782345 0.975481 0.999089
6.822383 0.975623 0.999109
3.186822 3.201183 3.215540 3.229894 3.244246 3.258594 3.272938 3.287279 3.301617 3.315951 3.330282
1.5 2
Failure rate
10 15 20
Repair time
0.025 0.03
ENOF
Figure 6: Graph representation of fuzzy reliability indicators
0.97 0.975 0.S
Reliability
0.992 0.993 0.994 0.995 0.996 0.997 0.998 0.9 Availability
Figure 6: Graph representation of fuzzy reliability indicators (continued)
Step 5. Defuzzification of fuzzy reliability indicators: The fuzzy results of reliability indicators are defuzzified by employing COA method for defuzzification. The reliability indicators have been defuzzified for ±15%, ±25% and ±40% spreads using equation (7) and are presented in Table 6 together with their crisp values.
ix2
x.ßj (x)dx
— •'x1
x = —-
ix2
( x)dx
x
(7)
Table 6: Values of reliability indicators of WCS
Reliability Indicator Crisp Value Defuzzified Values
Spreads
± 15 % ± 25 % ± 40 %
Failure rate x 10-4 (/h) 1.728332 1.730000 1.730000 1.731031
Repair time (h) 9.668175 10.327083 11.320939 14.323654
ENOF x 10-2 2.898757 2.898380 2.897209 2.894103
MTBF x 103 (h) 5.795593 5.894658 6.043965 6.493699
Reliability 0.971382 0.971388 0.971397 0.971421
Availability 0.998332 0.998134 0.997831 0.996912
6. Results and Discussion
It is observed from the behavioral graphs given in figure 6 that the membership curves of many reliability indicators are deformed trapezoids, whose non-parallel sides are parabolic. Further, it is demonstrated that the defuzzified values vary with changes in spread. For instance, for the spread expansion from ±15% to ±25%, the failure rate does not change, the reliability increases marginally, the repair time and MTBF increase by 9.62% and 2.53%, respectively, the ENOF and availability decrease by 0.04% and 0.03%, respectively. Further, for spread expansion from ±25% to ±40%, failure rate, repair time, MTBF and reliability increase by 0.06%, 26.52%, 7.44% and 0.002%, respectively,
while, ENOF and availability decrease by 0.10% and 0.09%, respectively. The effect of spread change is most significant on repair time in comparison to other reliability indicators, resulting in system availability loss. These findings will assist plant managers in planning and adapting best maintenance policy to improve performance of WCS and minimise operational and maintenance expenses.
7. Conclusion
In this study, the performance of WCS of a thermal power plant has been analysed using fuzzy A-t technique. Trapezoidal fuzzy numbers have been employed to remove ambiguity in acquired data. To eliminate unexpected failure of the plant, the trend of different reliability indicators viz. repair time, failure rate, reliability, availability, ENOF and MTBF with respect to spread changes has been analysed. The maintenance personnels of the considered system should focus at system's availability because it diminishes by increasing spread, which is unfavorable. The reason behind this is that repair time varies more rapidly in comparison to other reliability indicators. A structured framework has been established in this research to assist maintenance engineers for improving availability of the considered plant.
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