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AVAILABILITY ANALYSIS FOR IDENTIFICATION OF CRITICAL FACTOR OF A THERMAL POWER PLANT
Pardeep Kumar1, Vipin Kumar Sharma2, Dinesh Kumar3
iMaharishi Markandeshwar (Deemed to be University), Ambala, India, 2IIMT University, Meerut, U.P., India 3NIT Kurukshetra, Haryana, India ipardeepkambojSyahoo.com
2vipin2871985@gmail.com 3dinesh 61900120@nitkkr.ac.in
Abstract
In the present stimulated business environment, power sector is playing a major role in the economic growth of India. During the last 20 years, the country had been facing a poor supply of energy and this supply-demand gap is increasing continuously. So, it is important for power plants to improve its power generation capacity drastically by reducing the failure rate. In the present paper, to analyze the causes of poor availability, thermal power plant has divided into six different systems and a system comprising of waste gases heating system has been considered. With the help of transition diagram, mathematical equations have been used to find out the availability. After analyzing, it was found that the value of availability is very low and boiler tube failure is one of the most critical factors for this low availability of system. Economizer zone has identified having long existence time of failures and frequency of occurrence is very high. So, minimizing the failure rate with the help of a proper maintenance schedule will result in decreasing the shutdown period of the plant and increasing the system availability.
Keywords: Thermal Power Plant; Performance Evaluation; Availability, Boiler; Tube Failure; Economizer
I. Introduction
In today's competitive world, it becomes necessary that thermal power plant will be available for long run without any failure. In India, total installed capacity of electricity generation is 3,30,354 MW while total thermal installed capacity is 2,20,456 MW i.e. 66.8% of the total installed capacity (refer table 1). The major contribution almost 59% in thermal installed capacity is coal fired thermal power plant. For continuous power production, boiler becomes the backbone of a thermal power plant. Boiler tube failure is one of the critical problems which are facing the thermal power plant and influence the rate of power generation. This loss of generation increases the operating cost of plant and significant amount of water is being waste. Availability analysis gives the necessary information about various parameters of the system.
Table 1: Installed Capacity for Different Source of Fuel
Fuel Used Installed Capacity (MW) % of Total
Total Thermal 2,20,456 66.8 %
Coal 1,94,433 58.9 %
Gas 25,185 7.6 %
Oil 838 0.3 %
Hydro 44,614 13.5 %
Nuclear 6,780 2.1 %
Renewable Energy Sources 58,303 17.7 %
Total 3,30,354
II. Literature Review
From last decades, Complexity in the industries is increasing day by day, so many researchers using Markov Method for the performance evaluation of complex system in process industry. Tsarouhas [1] computed the parameters on which the reliability of the machine of the ice cream plant is dependent. Dai et al. [2] presented as a model for a system which is centralized heterogeneously widely used in distributed system design. With the help of this model the reliability of the distributed service is find out to provide a best service in a distributed environment. Gupta et al [3] studied the critical components on which the reliability of the plant is mainly dependent and on the basis of these components, a Decision Support system for for minimizing the failure rate of the industry has been decided. Gupta [4] discussed the DSS and performance modelling for a subsystem of feed water in a system of thermal power plant by using performance Modelling and analysis. With the help of a transition diagram, differential equations are generated and then study state probabilities are applied to find out the performance level for the combination of different failure and repair rate of all the sub-system. Using Markov process and probability theory, Gupta [5, 8] found the availability and reliability of a system of a thermal power plant. The author found that the reliability or availability decreases with increasing failure rate while the availability improves with increasing the repair rate for different sub-systems. On the basis of this, author made a maintenance policy for all the subsystems of a thermal power plant. To evaluate the reliability parameter, Gupta [6] expressed the mathematical formulation and expression for mission reliability and availability of a complex polymer powder production system with more realistic and practical assumption. Swiderski et al. [7] discussed the models of semi-Markov and Markov as best conventional tools to evaluate the availability and reliability of each subsystem of the full system. Kumar [9] developed a mathematical model based on the Markov birth-death process and developed differential equations based on probabilistic approach and solved these equations recursively. Khanduja et al. [10-11] developed a system for performance evaluation with the help of mathematical formulation and this performance evaluation deals with quantitative analysis of all critical factors which affects the maintenance decision support system of a paper plant. Lai et al. [12] designed a Markov based model and derived the equations to obtain the steady-state availability by considering both software and hardware failures. Kumar et al. [13-15] studied the behavior of a thermal power plant to improve the performance by minimizing the failure rate so that all the systems in thermal power plant can be function effectively. Sabouhi [16] proposed reliability oriented analysis to drive the
mathematical expression for the analysis of availability of the critical component of the plant so that an effective maintenance plan can be scheduled. Hassan et al. [17] purposed a stochastic model for liquefied natural gas plant using Markov analysis. Parkash and Tiwari [18-19] suggested a approach which can helps both engineers and managers to enhance the performability of the system by utilizing the best combination of failure and repair rates.
III. Availability Analysis of Waste Gases System of a Thermal Power Plant
The flow diagram of thermal power plant consisting of waste gases system (refer figure 1) shows that flue or waste gases from furnace flow upward and this waste heat is utilized in superheater, economizer and air preheater to raise the temperature of some extent of steam, feed water and air.
Figure 1: Flow Diagram of Waste Gases Heating System
To find the availability, this system is divided further in four different subsystems.
Subsystem A: it consists of furnace, superheater, economizer and air preheater andarranged in
series to establish a single subsystem.
Subsystem B: It consists of two electrostatic precipitator (ESP) which makes a single subsystem. Subsystem C: Two forced draught fans working in parallel consists a subsystem. Subsystem D: Three induced draught fans (ID Fan) arranged in parallel, creating one subsystem. The table 2 shows some notation which are used to construct the transition diagram as shown in figure 2.
Table 2: Notation Used
Full capacity States (without standby) A2,A4,A5,A6
One unit of subsystem A1andA3 are in failed state and the system is working in full capacity with stand by unit. Aland A3*
Failed states ai a2 a3 a4, as, a6
Reduced capacity states A4
Failure rates ai' i=1to6
Repair rates p1; ;=1to6
System Working at Full Capacity O
System Working at Reduced Capacity c_
System in Failed State 1 1
I. Performance Modelling of Waste Gases System
The mathematical equations are derived using Chapman-Kolmogorov equation with the help of
transition diagram.
4
P0\t)+ZW))+A P6(t)+( )+( ) (1)
i=1 4
Pi'(t) + ^ (A, + (4 )Pi (t) = (P11 (t) + (2P7 (t) + (3P4 (t) + £4P2 (t) + £4Po (t) (2)
i=1 4
P2'(t) + ^ (A, + (4 )P2 (t) = (1P10 (t) + (2 Ps (t) + (3 P5 (t) + (4 P9 (t) + (4 P1 (t) (3)
,=1
4 3
P3'(t) + Z (a, + (3 )Ps (t) = Z('P-1s(t) + A3 Po (t) + (4 P4 (t) (4)
i=1 i=1 4 3
P4'(t) + Z (A + (3 + (4 )P4 (t) = Z (i P-15 (t) + A33P1 (t) + A4P3 (t) + (4P5 (t) (5)
i=1 i=1 44
P5'(t)+Z (a, + (4 + (3) P5 (t) = Z AP-12 (t)+A4 P4 (t)+A3 P2 (t) (6)
i=1 i=1
p '(t)+(mp (t) = amPj (t) (7) When
m = 1, ttewi = 12, j = 0;i = 11,j = 1,i = 10,j = 2;i = 13,j = 3;i = 16,j = 4;i = 19,j = 5;
m = 2, them = 6,j = 0;i = 7,j = 1;i = 8,j = 2;i = 14,j = 3;i = 17,j = 4;i = 20,j = 5 m = 3, theni = 15, j = 3;i = 18,j = 4,i = 21, j = 5 m = 4, theni = 9, j = 2;i = 22, j = 5
Figure 2: Transition Diagram of Waste Gases Heating System
IV. Steady State Availability of Waste Gases System
By putting derivatives = 0 as t^ro in equations 1 to 7 and solved by recursive method, the following values obtained of all 23 states probabilities (P0 to P22) in terms of full working state probability i.e. Po.
p = cp p = cp p = cp p = cp
1 C12P0 2 C13P0 P3 C14J0 4 C11J0
1 13
c p C15p 0 Pe = ^P 11 P7 = a c P « C12p 0 Ps = c p ~ C13p 0
A c p ~ C13p0 À4 PP° = A C P ~ C13p° P11 = A C P * c12p 0 P2 =a p àp
A C P r, C14p 0 p14 = a c p ~ C14p 0 À2 P5 = a c p ~ C14p 0 à p6 =A C p r, C11P0
c p ~ C11p0 À2 Ps = A C P r, C11p 0 p9 = A C P r, C15p0 p p 20 = A c p ~ C15P 0 À2
a c p r, C15P 0 à p p 22 = A c p * C15p0 À4
The probability of full working capacity, namely, P0 determined by using normalizing condition: i.e (sum of the probabilities of all working states, reduced capacity and failed states is equal to 1)
22
Z p=1
, therefore
p = 1
1 n
(1 + C11 + C12 + C13 + Ci4 + Ci5 )
( (
1 +
V v
A
+ X3 (C11 + C14 + C15 (C14 + C15 )
H4
A A J A
À
9
Where
C = À + A4
C4 = à4 + a3 À4A3
c7 =
C3C6 -^3A3
r __
C10 =
C2 A4C8
C = C C + C
C12 C9C11 + C1
1°
(-1 _ C\3À + C11À4 Ci
"15
Hence
C2 = à +À4 + A4 C2 = \ +A3 +A4
C8 =
À4C6
C3C6 ^3^3
C3 = à + A4 C6 = A3+ A
c9 =
À + C7 a4
C3 — A 4C8
Q _ C3C4 AA3 C1°C4 A4
11 = A3A4 - C9CA4
C13 = C7C11 + CSC12
C =
C14
C11&4 + À
C
Av = p + p + p + p + p + p
Av = p°(1 + C11 + C12 + C13 + C14 + C15)
Table 3 shows the variation of system availability with different possible combination of failure and repair rates for waste gases heating system. System availability decreases (0.9402 - 0.7985) appreciably by 14.2 % with increasing the failure rate from 0.005 (once in 200 hrs) to 0.040 (once in 25 hrs). Similarly other values show the decreasing trend of availability. Correspondingly, repair rate also effect the value of availability, as repair rate increases from 0.10 (once in 10 hrs) to 0.50
(once in 2 hrs), the system availability increases (0.9784-0.9402) drastically by 3.82 %.
Table 3: Availability Matrix for Waste Gases Heating System
Ai ßi 1 - 0.1 0.2 0.3 0.4 0.5 Constant values
0.005 0.9402 0.9596 0.9676 0.9712 0.9784 A2 = 0.010, A3 = 0.0033, A4 = 0.005, ß2 - 0.20, ß3 - 0.25, ß4 - 0.20
0.0066 0.9298 0.9424 0.9639 0.9701 0.9731
0.100 0.9192 0.9322 0.9412 0.9565 0.9698
0.020 0.9085 0.9408 0.9533 0.9599 0.9653
0.040 0.7985 0.9164 0.9398 0.9492 0.9619
This table also shows that the failure rate influences the availability of the system. System availability can be improved by decreasing the failure rate. Maintenance data shows that boiler tube failure is one of the most critical reasons for low availability of waste gases heating system.
V. Results
The performance evaluation of waste gases heating system has been done with the help of simulation modeling. Table 3 showed the variation in the system performance with the variation in failure and repair rates of its different components. The various availability levels (Av.) for different combinations of failure and repair rates were also calculated and found that availability of system decreases appreciably as failure rate increases. To improve the availability of the system it becomes essential that reduces the significant causes of failure.
References
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