Performance evaluation model and decision support system for coal handling system of a typical thermal plant.

Gupta, Sorabh ; Tewari, P.C. ; Sharma, Avadhesh Kumar 等

Introduction

In a process plant the raw material is processed through various equipments to achieve the final product. The thermal industry is becoming quite complex with a huge capital investment being incurred on process automation to enhance the reliability of system. Invariably, the proper maintenance of such systems and the frequency of maintenance are some of the issues that are gaining importance in industry. The production suffers due to failure of any intermediate system even for small interval of time. The cause of failure may be due to poor design, system complexity, poor maintenance, lack of communication and coordination, defective planning, lack of expertise/experience and scarcity of inventories. Thus, to run a process plant highly skilled/ experienced maintenance personnel are required. The maintenance is not only performed on the process instruments but also on the equipment from utilities, which play a major role in the smooth running of the process. For efficient functioning, it is essential that various systems of the plant remain in upstate as far as possible. However, during operation they are liable to fail in a random fashion. The failed subsystem can however be inducted back into service after repairs/replacements. The rate of failure of the subsystems in the particular system depends upon the operating conditions and repair policies used [1]. A measure of how well a system performs or meets its design objectives is provided by the concept of system reliability. According to Barabady et al. [2], the most important performance measures for repairable system designers and operators are system reliability and availability. Improvement of system availability has been the subject of a large volume of research and articles in the area of reliability. Availability and reliability are good evaluations of a system's performance. Their values depend on the system structure as well as the component availability and reliability. These values decrease as the component ages increase; i.e. their serving times are influenced by their interactions with each other, the applied maintenance policy and their environments [3].

During the past decade a lot of study has been done on analysis tools [4-7] for reliability, availability, performance and performability modeling. The considerable efforts have been made by the researchers providing general methods for prediction of system reliability [8, 9], designing equipments with specified reliability figures, demonstration of reliability values [10], issues of maintenance, inspection, repair and replacement and notion of maintainability as design parameter [9]. For the prediction of availability, several mathematical models have been discussed in literature, which handle wide degree of complexities [11, 12]. Most of these models are based on the Markovian approach, wherein the failure and the repair rates are assumed to be constant. In other words, the times to failure and the times to repair follow exponential distribution. The steady state availability continues to be applicable as long as the components of the system are statistically independent [13, 14]. For regular and economical generation of steam, it is necessary to maintain each subsystem of coal handling system. From economic and operational point of view, it is desirable to ensure an optimum level of system availability. The goal of maximum steam generation may be achieved under the given operative conditions, making the coal handling system failure free, by examining the behavior of the system and making the maintenance decision on a top priority for most critical subsystem. . In this direction, the work presents a 'performance evaluation model' for steam thermal power plant, which will help in decision making.

Coal Handling System

In most of the complex systems encountered in practice, it has been observed that they consist of components and subsystems connected in series, parallel or standby, or a combination of these. A thermal power plant is a complex engineering system comprising of various systems: Coal handling, Steam Generation, Cooling Water, Crushing, Ash handling, Power Generation and Feed water system. In the thermal power plants maximum requirement of fuel is a coal. The handling of this fuel is a great job. To handle the fuel i.e. coal, each power station is equipped with a coal handling plant. Maintenance of critical equipments for coal handling plants (CHP) of thermal power stations is typical job. Any production system should be kept failure free (as far as possible) under the given operative conditions to achieve the set goals of economical production and long run performance. A highly reliable system tends of increase the efficiency of production. To maintain an efficiently operating subsystem and avoid failure of critical equipment, it is necessary to maintain the critical parts of that equipment. There are varieties of critical equipment components in coal handling system. These components require routine inspection to ensure their integrity.

System Description

The Coal handling system consists of five subsystems, which are as follows:

(1) The wagon tippler 'A' is having two units. Failure of any one forces to start with stand-by unit. Complete failure of the system occurs when stand-by system of the wagon tippler also fails.

(2) The Screener 'B' subsystem is single unit, failure of which leads to system failure.

(3) The Feeder 'C' subsystem is single unit, failure of which leads to system failure.

(4) The Hopper 'D' subsystem is single unit, failure of which leads to system failure.

(5) The conveyor 'E' consists of two units, failure of first force the stand-by unit to run. Complete failure of the system occurs when the stand-by system of conveyor also fails.

Assumptions for Performance Evaluation Model

The assumptions used in developing the probabilistic model are

1. Failure/repair rates are constant over time and statistically independent [15]

2. A repaired system as good as new, performance wise, for a specified duration.

3. Sufficient repair facilities are provided. [16]

4. Standby systems are of the same nature as that of active systems. [17]

5. System failure/repair follows the exponential distribution.

6. Service includes repair and/or replacement. [17]

7. There are no simultaneous failures. [18, 19]

The transition diagram [20] (figure 1) of Coal handling system shows the various possible states, the system can acquire. Based on the transition diagram, a performance-evaluating model has been developed. The failures and repairs for this purpose have been modeled as birth and death process.

[FIGURE 1 OMITTED]

Performance Evaluation Model

The performance modeling is an activity in which the performance of a system is characterized by a set of performance parameters (repair and failure rates) whose quantitative values are used to assess the system's availability. The failure and repair rates are statistically independent and these can be obtained with the help of history cards and maintenance sheets of various subsystems of Coal handling system available with maintenance personnel of the thermal plant. The mathematical modeling is done using simple probabilistic considerations and differential equations are developed using birth-death process. Various probability considerations give the following differential equations associated with the Coal handling system. [21]

(d/dt + [5.summation over (i=1)] [[phi].sub.i]) [P.sub.1] (t) = [P.sub.2] (t). [[lambda].sub.1] + [P.sub.3](t). [[lambda].sub.5] + [P.sub.4](t). [[lambda].sub.3] + [P.sub.6](t). [[lambda].sub.4] + [P.sub.5](t). [[lambda].sub.2] (1)

(d/dt + [5.summation over (i=1)] [[phi].sub.i] + [[lambda].sub.1]) [P.sub.2](t) = [P.sub.10](t) [[lambda].sub.1] + [P.sub.15](t) [[lambda].sub.5] + [P.sub.9](t) [[lambda].sub.4] + [P.sub.8](t) [[lambda].sub.3] + [P.sub.11](t) [[PHI].sub.1] + [P.sub.7](t) [[lambda].sub.2] (2)

(d/dt + [5.summation over (i=1)] [[phi].sub.i] + [[lambda].sub.5]) [P.sub.3](t) = [P.sub.1](t)[[PHI].sub.t] + [P.sub.11](t). [[lambda].sub.2] + [P.sub.12](t). [[lambda].sub.3] + [P.sub.13](t). [[lambda].sub.4] + [P.sub.14](t). [[lambda].sub.5] + [P.sub.15](t). [[lambda].sub.1] (3)

(d/dt + [5.summation over (i=1)] [[phi].sub.i] + [[lambda].sub.1] + [[lambda].sub.5]) [P.sub.15](t) = [P.sub.2](t) [[PHI].sub.5] + [P.sub.3](t) [[PHI].sub.1] + [P.sub.16](t) [[lambda].sub.1] + [P.sub.17](t) [[lambda].sub.2] + [P.sub.18](t) [[lambda].sub.3] + [P.sub.19](t) [[lambda].sub.4] + [P.sub.2] 0(t)[[lambda].sub.5] (4)

[P.sub.4](t)[d/dt] + [[lambda].sub.3] = [P.sub.1](t). [[PHI].sub.3] (5)

[P.sub.5](t)[d/dt] + [[lambda].sub.2] = [P.sub.1](t). [[PHI].sub.2] (6)

[P.sub.6](t)[d/dt] + [[lambda].sub.4] = [P.sub.1](t). [[PHI].sub.4] (7)

[P.sub.7](t)[d/dt] + [[lambda].sub.2] = [P.sub.2](t). [[PHI].sub.2] (8)

[P.sub.8](t)[d/dt] + [[lambda].sub.3] = [P.sub.2](t). [[PHI].sub.3] (9)

[P.sub.9](t)[d/dt] + [[lambda].sub.4] = [P.sub.2](t). [[PHI].sub.4] (10)

[P.sub.10](t)[d/dt] + [[lambda].sub.1] = [P.sub.2](t). [[PHI].sub.1] (11)

[P.sub.11](t)[d/dt] + [[lambda].sub.2] = [P.sub.3](t). [[PHI].sub.2] (12)

[P.sub.12](t)[d/dt] + [[lambda].sub.3] = [P.sub.3](t). [[PHI].sub.3] (13)

[P.sub.13](t)[d/dt] + [[lambda].sub.4] = [P.sub.3](t). [[PHI].sub.4] (14)

[P.sub.14](t)[d/dt] + [[lambda].sub.5] = [P.sub.3](t). [[PHI].sub.5] (15)

[P.sub.16](t)[d/dt] + [[lambda].sub.1] = [P.sub.15](t). [[PHI].sub.1] (16)

[P.sub.17](t)[d/dt] + [[lambda].sub.2] = [P.sub.15](t). [[PHI].sub.2] (17)

[P.sub.18](t)[d/dt] + [[lambda].sub.3] = [P.sub.15](t). [[PHI].sub.3] (18)

[P.sub.19](t)[d/dt] + [[lambda].sub.4] = [P.sub.15](t). [[PHI].sub.4] (19)

[P.sub.20](t)[d/dt] + [[lambda].sub.5] = [P.sub.15](t). [[PHI].sub.5] (20)

These equations are solved for determining the steady state availability of Coal handling system. The steady state behaviour of the system can be analysed by setting t [right arrow] 0, d/dt [right arrow] [infinity] [22] and Solving these equations recursively, we get all value of P in terms of [P.sub.1].

[P.sub.2] = h [P.sub.1]

[P.sub.3] = g [P.sub.1]

[P.sub.15] = (i) [P.sub.1]

[P.sub.4] = ([[PHI].sub.3]/[[lambda].sub.3])[P.sub.1]

[P.sub.5] = ([[PHI].sub.2]/[[lambda].sub.2])[P.sub.1]

[P.sub.6] = ([[PHI].sub.4]/[[lambda].sub.4])[P.sub.1]

[P.sub.7] = ([[PHI].sub.2]/[[lambda].sub.2])h[P.sub.1]

[P.sub.8] = ([[PHI].sub.3]/[[lambda].sub.3])h[P.sub.1]

[P.sub.9] = ([[PHI].sub.4]/[[lambda].sub.4])h[P.sub.1]

[P.sub.10] = ([[PHI].sub.1]/[[lambda].sub.1])h[P.sub.1]

[P.sub.11] = ([[PHI].sub.2]/[[lambda].sub.2])g[P.sub.1]

[P.sub.12] = ([[PHI].sub.3]/[[lambda].sub.3])g[P.sub.1]

[P.sub.13] = ([[PHI].sub.4]/[[lambda].sub.4])g[P.sub.1]

[P.sub.14] = ([[PHI].sub.5]/[[lambda].sub.5])g[P.sub.1]

[P.sub.16] = ([[PHI].sub.1]/[[lambda].sub.1])i[P.sub.1]

[P.sub.17] = ([[PHI].sub.2]/[[lambda].sub.2])i[P.sub.1]

[P.sub.18] = ([[PHI].sub.3]/[[lambda].sub.3])i[P.sub.1]

[P.sub.19] = ([[PHI].sub.4]/[[lambda].sub.4])i[P.sub.1]

[P.sub.20] = ([[PHI].sub.5]/[[lambda].sub.5])i[P.sub.1]

Normalizing Condition

The probability of full working capacity, namely, [P.sub.1] determined by using normalizing condition: (i.e sum of the probabilities of all working states and failed states is equal to 1). [23]

i.e [t=20.summation over (i=1)] [P.sub.i] = 1,

Hence [P.sub.1] = 1/[((1+h+g+i).(1+(([[PHI].sub.3]/[[lambda].sub.3]) + ([[PHI].sub.2]/[[lambda].sub.2]) + ([[PHI}.sub.4]/[[lambda].sub.4]))) + (([[PHI].sub.1]/[[lambda].sub.1]).(h+i) + ([[PHI].sub.5]/[[lambda].sub.5]). (g+i))]

Where d = ([[lambda].sub.1] + [[PHI].sub.5]) - (([[PHI].sub.5] [[lambda].sub.5])/ ([[lambda].sub.1] + [[lambda].sub.5]))

e = ([[lambda].sub.5] + [[PHI].sub.1]) - (([[PHI].sub.1] [[lambda].sub.1])/ ([[lambda].sub.1] + [[lambda].sub.5]))

f = e - (([[lambda].sub.5].[[PHI].sub.5].[[PHI].sub.1].[[lambda].sub.1])/ [([[lambda].sub.1] + [[lambda].sub.5]).sup.2].d))

g = [[PHI].sub.t] + (([[lambda].sub.1].[[PHI].sub.1].[[PHI].sub.5])/ (([[lambda].sub.1] + [[lambda].sub.5]).d))

h = [[PHI].sub.1](([[lambda].sub.1] + [[[lambda].sub.5].g/ ([[lambda].sub.1] + [[lambda].sub.5])])/d

i = ([[PHI].sub.5].h + [[PHI].sub.1].g)/([[lambda].sub.1] + [[lambda].sub.5])

Steady State availability

Now, steady state availability of the system may be obtained as summation of all working state probabilities.

Hence [A.sub.v.] = [P.sub.1] + [P.sub.2] + [P.sub.3] + [P.sub.15]

= [P.sub.1] + h[P.sub.1] + [g.sub.1] + i[P.sub.1] or [A.sub.v] = [P.sub.1] (1 + h + g + i) (21)

Decision Support System

From maintenance history sheet of Coal handling system of thermal power plant and through the discussions with the plant personnel, appropriate failure and repair rates of all five subsystems are taken and decision matrix (availability values) are prepared accordingly by putting these failure and repair rates values in expression for availability [A.sub.v] (eq. 21). The decision support system deals with the quantitative analysis of all the factors viz. courses of action and states of nature, which influence the maintenance decisions associated with the Coal handling system of thermal plant. This decision model is developed under the real decision making environment i.e. decision making under risk (probabilistic model) and used to implement the proper maintenance decisions for the Coal handling system. Table 1 represents the decision matrix for all five subsystems of the Coal handling system. This matrix simply reveals the various availability levels for different combinations of failure and repair rates. These availability values obtained in decision matrix for all five subsystems depict the effect of failure /repair rate of various subsystems on Coal handling system availability. On the basis of decision support system developed, we may select the best possible combinations ([PHI], [lambda]).

Results and Discussion

The following observations are made from table 1, which reveals the effect of failure and repair rates of various subsystems on the availability of coal handling system.

1. It is observed that for some known constant values of failure / repair rates of other four subsystems, as failure rate of wagon tippler ([[PHI].sub.1]) increases from 0.005 (once in 200 hrs) to 0.04(once in 25 hrs), the system availability decreases by almost 2 %. Similarly as repair rate of wagon tippler ([[lambda].sub.1]) increases from 0.1 (once in 10 hrs) to 0.6 (once in 1.67 hrs), the system availability increases slightly.

2. It is observed that for some known constant values of failure / repair rates of other four subsystems, as failure rate of screener ([[PHI].sub.2]) increases from 0.001 (once in 1000 hrs) to 0.005(once in 200 hrs) the system availability decreases by almost 1 %. Similarly as repair rate of screener ([[lambda].sub.2]) increases from 0.30 (once in 3.33 hrs) to 0.50 (once in 2 hrs) there is slight change in system availability.

3. It is observed that for some known constant values of failure / repair rates of other four subsystems as failure rate of feeder ([[PHI].sub.3]) increases from 0.002 (once in 500 hrs) to 0.005(once in 200 hrs) the system availability decreases by almost 1 %. Similarly as the repair rate of feeder ([[lambda].sub.3]) increases from 0.2 (once in 5 hrs) to 0.40 (once in 2.5 hrs), system availability increases by 1%.

4. It is observed that for some known constant values of failure / repair rates of other four subsystems as failure rate of hopper ([[PHI].sub.4]) increases from 0.005 (once in 200 hrs) to 0.02(once in 50 hrs) the system availability decreases by almost 6 %. Similarly as repair rate of hopper ([[lambda].sub.4]) increases from 0.2 (once in 5 hrs) to 0.5 (once in 2 hrs) there is about 2% increase in system availability.

5. It is observed that for some known values of failure / repair rates of other four subsystems as failure rate of conveyor ([[PHI].sub.5]) increases from 0.02 (once in 50 hrs) to 0.1(once in 10 hrs), the system availability decreases by about 8%. Similarly as repair rate of conveyor ([[lambda].sub.5]) increases from 0.10 (once in 10 hrs) to 0.50 (once in 2 hrs), the system availability increases by about 0.5%.

Conclusions

The expression for Av. (eqn. 21) is the performance evaluation model for Coal handling system. Similarly decision support system has been developed with the help of mathematical modeling using probabilistic approach. The decision matrix is also developed. This matrix facilitates the maintenance decisions to be made at critical points where repair priority should be given to some particular subsystem of Coal handling system. Decision matrix as given in table 1 clearly indicates that the conveyor subsystem is most critical as far as maintenance aspect is concerned. So, Conveyor subsystem should be given top priority as the effect of its failure/repair rates on the system availability is much higher than that of other all four subsystems. Further, after conveyor, most critical subsystem is hopper, as the effect of its failure/repair rates on the system availability is much higher than that of other all subsystems, except conveyor. Similarly after conveyor and hopper, most critical subsystem is wagon tippler, as the effect of its failure/repair rates on the system availability is much higher than screener and feeder.

The effect of failure/repair rates of screener and feeder subsystems respectively on the system availability is equal but less than other three subsystems. Therefore Screener and Feeder subsystems should be given equal priority immediately after the conveyor, hopper and wagon tippler subsystems.

Therefore, on the basis of failure/repair rates, the maintenance priority should be given as per following table:

S.No. Name of subsystem Maintenance
 Priority

 1 Conveyor First
 2 Hopper Second
 3 Wagon tippler Third
 4 Screener or Feeder Fourth

References

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* Sorabh Gupta (1), P.C. Tewari (2) and Avadhesh Kumar Sharma (3)

(1) Assistant Professor, Mechanical Engineering, HCTM, Kaithal (Haryana), India E-mail: [email protected]

(2) Assistant Professor, Mechanical Engineering, NIT, Kurukshetra (Haryana), India E-mail: [email protected]

(3) Department of Mechanical Engineering, D.C.R. University of Sc. & Technology, Murthal (Sonepat)-131039, INDIA, E-mail: [email protected]

Table 1: Decision matrix of various subsystems of Coal handling system
[right arrow] Availability (Av) [right arrow] [A.sub.0]

 Subsytem 1 : Wagon Tippler

[[lambda].sub.1] .1 .225 .35 .475 .6
[[PHI].sub.1]

 0.005 0.9373 0.9376 0.9377 0.9377 0.9378
 0.0138 0.9346 0.9365 0.9369 0.9372 0.9373
 0.0225 0.9300 0.9347 0.9358 0.9364 0.9367
 0.0313 0.9236 0.9322 0.9343 0.9353 0.9358
 0.04 0.9155 0.9291 0.9324 0.9339 0.9347

 Subsytem 1 : Wagon Tippler

[[lambda].sub.1] Constant Values
[[PHI].sub.1]

 0.005 [[PHI].sub.2] = .003, [[lambda].sub.2] = .4
 0.0138 [[PHI].sub.3] = .0035, [[lambda].sub.3] = .3
 0.0225 [[PHI].sub.4] = .0125, [[lambda].sub.4] = .35
 0.0313 [[PHI].sub.5] = .06, [[lambda].sub.5] = .3
 0.04

 Subsytem 2 : Screener

[[lambda].sub.2] .3 .35 .4 .45 .5
[[PHI].sub.2]

 0.001 0.9395 0.9399 0.9402 0.9405 0.9407
 0.002 0.9365 0.9374 0.938 0.9385 0.9389
 0.003 0.9336 0.9349 0.9358 0.9365 0.9371
 0.004 0.9307 0.9324 0.9336 0.9346 0.9354
 0.005 0.9279 0.9299 0.9315 0.9327 0.9336

 Subsytem 2 : Screener

[[lambda].sub.2] Constant Values
[[PHI].sub.2]

 0.001 [[PHI].sub.1] = .0225, [[lambda].sub.1] = .35
 0.002 [[PHI].sub.3] = .0035, [[lambda].sub.3] = .3
 0.003 [[PHI].sub.4] = .0125, [[lambda].sub.4] =.35
 0.004 [[PHI].sub.5] = .06, [[lambda].sub.5] = .3
 0.005

 Subsytem 3 : Feeder

[[lambda].sub.3] .2 .25 .30 .35 .40
[[PHI].sub.3]

 0.002 0.9373 0.9390 0.9402 0.9411 0.9417
 0.00275 0.9340 0.9364 0.9380 0.9392 0.9400
 0.0035 0.9307 0.9338 0.9358 0.9373 0.9384
 0.00425 0.9275 0.9312 0.9336 0.9354 0.9367
 0.005 0.9243 0.9286 0.9315 0.9335 0.9351

 Subsytem 3 : Feeder

[[lambda].sub.3] Constant Values
[[PHI].sub.3]

 0.002 [[PHI].sub.1] = .0225, [[lambda].sub.1] = .35
 0.00275 [[PHI].sub.2] = .003, [[lambda].sub.2] = .4
 0.0035 [[PHI].sub.4] = .0125, [[lambda].sub.4] = .35
 0.00425 [[PHI].sub.5] = .06, [[lambda].sub.5] =.3
 0.005

 Subsytem 4: Hopper

[[lambda].sub.4] .2 .275 .350 .425 .5
[[PHI].sub.4]

 0.005 0.9453 0.9514 0.9550 0.9573 0.9589
 0.00875 0.9288 0.9392 0.9453 0.9492 0.9520
 0.0125 0.9129 0.9274 0.9358 0.9414 0.9453
 0.01625 0.8976 0.9158 0.9265 0.9336 0.9386
 0.02 0.8827 0.9045 0.9174 0.9260 0.9321

 Subsytem 4: Hopper

[[lambda].sub.4] Constant Values
[[PHI].sub.4]

 0.005 [[PHI].sub.1] = .0225, [[lambda].sub.1] = .35
 0.00875 [[PHI].sub.2] = .003, [[lambda].sub.2] = .4
 0.0125 [[PHI].sub.3] = .0035, [[lambda].sub.4] = .3
 0.01625 [[PHI].sub.5] = .06, [[lambda].sub.5] = .3
 0.02

 Subsytem 4: Conveyor

[[lambda].sub.5] .1 .2 .3 .4 .5
[[PHI].sub.5]

 0.02 0.9427 0.9447 0.9454 0.9457 0.9459
 0.04 0.9315 0.9391 0.9417 0.943 0.9437
 0.06 0.9139 0.9303 0.9358 0.9386 0.9402
 0.08 0.8912 0.9186 0.9280 0.9327 0.9355
 0.1 0.8644 0.9043 0.9183 0.9254 0.9297

 Subsytem 4: Conveyor

[[lambda].sub.5] Constant Values
[[PHI].sub.5]

 0.02 [[PHI].sub.1] = .0225, [[lambda].sub.1] = .35
 0.04 [[PHI].sub.2] = .003, [[lambda].sub.2] = .4
 0.06 [[PHI].sub.3] = .0035, [[lambda].sub.3] = .3
 0.08 [[PHI].sub.4] = .0125, [[lambda].sub.4] = .35
 0.1