Effect Of Switch-Over Devices on Availability of a Steam Generating System in A Thermal Power Plant

: Purpose: Suggests a method to compute availability of the main part i.e

Markov Process in which transition from one state to another is governed by the transition probabilities of a Markov process but the time spent in each state, before a transition occurs , is a random variable depending upon the last transition made. Thus, at transition instants, the semi Markov process behaves just like a Markov process. Singh (1980) considered the Semi-Markov process generated by the system with imperfect switch over devices. Gupta et al.(2005 ) studied the numerical analysis of reliability and availability of the serial processes in butter-oil processing plant. Sarhan (2006) studied the reliability equivalences of a series system consisting of n Independent and Non-identical components. . Bansal and Goel (2016) studied the availability analysis of poultry , cattle and fish feed plant by taking various probability considerations. Ram and Nagiya (2017) discussed the gas turbine power plant performance evaluation under key failures by assuming the different types of component failure by using supplementary variable techniques, Laplace transformation and Markov process. Bala (2018) gave an idea about patents. Ghamry et al (2022) availability and reliability analysis of a k-Out-of-n Warm Standby System with common-cause failure and fuzzy failure and repair rates by assuming that the failure time of each operating unit or warm standby unit follows Weibull distribution with two fuzzy parameters and the repair time of any failed unit follows exponential distribution with one fuzzy parameter. Each fuzzy parameter is represented by triangular membership function estimated from statistical data taken from random samples of each unit. Bala K. (2022) discussed about impact of covid-19. Saini et al. (2023) studied the availability and performance analysis of primary treatment unit of sewage plant by introducing the concept of redundancy and constant failure rates. It has been observed that reliability and availability of a system in different industries have been discussed so far. This has motivated me to consider the case of thermal power plant. In this paper, a method to compute availability of Steam-generation part of a Thermal Power Planti is proposed by assuming constant failure and repair rates. Transition diagram of the system is drawn and problem is formulated using Markov Method. The governing differential equations are solved recursively for a steady state. System is analyzed for long run availability followed by illustration, table and graph. This paper is organized in five sections. The present is introductory section . Section 2 consists of brief description about system and assumptions and notations. Mathematical formulation is done in section 3. Section 4. gives numerical illustrations. In last section results are analyzed.

System, Notations and assumptions
The steam generating system in a thermal power plant consists of three subsystems A, B, D and two switch over devices S1, S2.Subsystem A (Gas Classifier) provides air to furnace. It consists of components in series. Failure of any component in it causes the complete failure of A and hence the complete failure of the plant. Subsystem B ( Crushing Mills) from where powdered form of the coil is sent to boiler furnace with the help of compressed air consisting of two units in operating state and one in cold standby mode each composed of several components in series. The subsystem B is further supported by a fuel subsystem BF . If two units of subsystem B fail, then fuel system runs the system. It is assumed that fuel subsystem BF never fails because it is used only when both the main units fail. As soon as the unit of B are repaired it is switched in and the full subsystem BF is switched out. Steam is generated in Subsystem D (Boilers). It is composed of several components in parallel. Failure of a unit(s) in D reduces the working capacity of D and hence the efficiency of the plant. It is assumed that subsystem D never fails completely.
Switch-over device S1 is imperfect. Whenever the unit of subsystem B fails, it is switched out and standby unit if available is switched in by S1 successfully with probability u. Failure of S1, when online unit has already failed causes the complete failure of the system. Switch-over device S2 is imperfect. Whenever two units fail in subsystem B, the fuel subsystem BF is switched in by Switch-over device S2 successfully with probability v. Failure of S2 when on line unit(s) as in subsystem B has already failed causes complete failure of the system. Most of researchers have work in the field of reliability for different techniques.

Assumptions and Notations:
1.Failures and repairs are S-independent. 2. Separate repair facilities are available for each subsystem and switch over devices. 3.Upon failure, if all repair facilities are busy, the failed unit joins the end of the queue of respective non-operating units. 4. A repaired unit is as good as new and after repair it is immediately reconnected to the system. 5. Nothing can fail when the system is in failed state. 6. System comes in field state if the switch(es) cannot detect and disconnect a failed unit. 7.Switchover is instantaneous. 8. The repair of a failed unit starts at once. 9. The failure and repair rates of all units are constant. A, B, D denote that subsystems are in full operating state. BS denotes that subsystem B is working on standby unit. BF denotes that subsystem B is working on fuel system when all units in system B have failed. BF' denotes that subsystem B is working on fuel system when one unit in subsystem B is still in good state. ̅ denotes that subsystem D is working in reduced-state. a denotes that system is in failed state. b1, b2, b3 denote that one, two and three units in subsystem B are in failed state. 1 denotes the failure rate of sub-system A from good to failed state. 2 denotes the transition rate of the one unit as a system be from good to failed state. 3 denotes the transition rate of two units of subsystem B from good to failed state. 4 denotes the failure rate of subsystem D from good to reduce state D. 1 denotes the constant transition rate of the subsystem A from failed state to good state. 2 denotes the constant transitions rate of subsystem B from failed state b1 to good state. 3 denotes the constant transition rate of subsystem B from their failed state to good state. 4 denotes the constant transition rate of subsystem D from reduced state to good state. 5 , 6 denotes the respective mean constant repair rates of switch-over devices S1, S2 from failed states to good states. u, v denotes the respective probabilities of successful working of switches S1, S2 for each failure event.
Pn is the probability that the system is in n th state at the time t, (1≤ n ≤ 22) Pn = lim →∞ Pn (t) dash (ꞌ ) denotes the derivative with respect to time t.
Following the above assumptions and notations , the block diagram and transition diagram of the system as shown in the figure 1 and 2respectively.

Fig. 2. Transition diagram of the System
With initial conditions P1 (0)=1 and 0 otherwise. Since management is generally interested in long run availability of the system, the system is required to run satisfactorily for a long time.

Numerical illustrations:
To study the effect of switch -over device over the availability, we evaluate availability of the system by taking u = v = 0.9, 1 = 2= 0.02, 4  Perfect Switch-over Devices: When the switch-over device is perfect, the results are obtained by taking u = v = 1 in the forgoing analysis. By taking 1 = 2= 0.02, 4 = 0.01, 3 =0.001, 2 = 4= 0.2, 1 = 0.3, 3 = 0.15 Availability of the system is evaluated to be 0.938493205.

5.Analysis of results:
Study of above Availability table and graph reveals that 5 increases the availability of the system more effectively than 6. Although we should try to keep the switches good, availability for perfect switchover devices can be calculated by taking u=v=1. Athough, the repair of the switch S1 , requires more care than the switch S2 . Similar comparative tables and graphs can be prepared by taking repair/failure rates for various components. As controlling the failure of subsystems/units is more difficult than controlling the repair. Table for repair rates provides good information about the effectiveness of the system components.