A PERFORMANCE MODELING AND DECISION SUPPORT SYSTEM FOR A FEED WATER UNIT OF A THERMAL POWER PLANT

The present paper discusses the performance modeling and decision support system for a feed water unit of a thermal power plant using the concept of performance analysis and modeling. A feed water unit ensures a proper supply of water for the sound functioning of a thermal power plant. The decision support system for a feed water unit has been developed with the help of performance modeling using a probabilistic approach. After drawing a transition diagram, differential equations are generated. After that, steady state probabilities are determined. Some decision matrices are also developed, which provide various performance levels for different combinations of failure and repair rates of all subsystems. Based upon various availability values obtained in decision matrices and plots of failure rates / repair rates of various subsystems, the performance of each subsystem is analyzed, and maintenance decisions are made for all subsystems.


NOTATIONS
Indicates the system is in a working state.
Indicates the system is in a failed state.
φ Failure rate λ Repair rate B, C, F Represent full working states of the boiler, condenser, and feed pump respectively.b, c, f Represent failed states of the boiler, condenser, and feed pump respectively.

INTRODUCTION
Reliability analysis is one of the main tools to ensure agreed delivery deadlines, which in turn maintain certain intangible factors such as customer goodwill and company reputation [1].Downtime often leads to both tangible and intangible losses.These losses may be due to some unreliable subsystems/components; so an effective strategy needs to be framed for the maintenance, replacement, and design changes related to those subsystems and components [2][3][4][5].A measure of how well a system performs or meets its design objectives is provided by the concept of system reliability.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 comprised of various units: coal handling, steam generation, cooling water, crushing, ash handling, power generation, and feed water [6].
For regular and economical generation of steam, it is necessary to maintain each subsystem of the feed water unit.The failure of each item of equipment or subsystem depends upon the operating conditions and maintenance policies used [6].From economic and operational points 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 operational conditions, making the feed water unit failure-free, by examining the behaviour of the system and making a top priority maintenance decision for the most critical subsystems.The maintenance aspects of a feed water unit -an important functional part of the steam generation unit of a thermal power plant -has been discussed [7].

FEED WATER UNIT DESCRIPTION
The feed water unit consists of three subsystems: (1) Boiler (B): This subsystem is without any standby unit, so its failure leads to a system failure.The transition diagram of the feed water unit is given in Figure 1, in which states 0 and 3 are working at full capacity and states 1,,2, 4, 5, and 6 have failed.

PERFORMANCE MODELING OF FEED WATER UNIT
Traditional binary reliability models allow only two functional states for a system and for each of its components: perfect functionality (UP) and complete failure (DOWN).Multi-state system (MSS) reliability analysis relates to systems for which one cannot formulate an 'all or nothing' failure criterion [8][9].
The mathematical modeling is done using probabilistic considerations and differential equations, using the Markov birth-death process.These equations are solved to determine the steady state availability of the feed water unit.Various probability considerations give the following differential equations associated with the feed water unit [10][11].
). ( ) ( Using the steady state equation, and by setting 0 , → ∞ → dt d t , the above equations reduce to:

DECISION SUPPORT SYSTEM
In the studies of reliability optimization, the number of components is usually taken as a decision variable [12][13].From the maintenance history sheet of the feed water unit of a thermal power plant, and from discussions with the plant personnel, appropriate failure and repair rates of all three subsystems are taken and decision matrices (availability values) are prepared by putting these failure and repair rates values in expression (8) for A 0 .The decision support system deals with the quantitative analysis of all the factors -the courses of action and states of naturewhich influence the maintenance decisions associated with the feed water unit of the thermal power plant.These decision models are developed in a real decision-making environment -i.e.decision-making under risk (probabilistic model) -and are used to implement the proper maintenance decisions for the feed water unit.Tables 1, 2, and 3 represent the decision matrices for various subsystems of the feed water unit.These matrices reveal the various availability levels for different combinations of failure and repair rates/priorities.These availability values, obtained in decision matrices for all three subsystems, are plotted.Figures 2, 3, and 4 represent the plots for various subsystems of the feed water unit, depicting the effect of the failure/repair rate of various subsystems on feed water unit availability.On the basis of the decision support system developed, one may select the best possible combinations ( φ , λ).

( 2 )
Condenser (C): This subsystem consists of a single condenser.(3) Feed Water Pump (F): This subsystem consists of two pumps; one works while the other remains on standby.System failure occurs only when both units fail simultaneously.

Figure 1 :
Figure 1: T ransition diagram of a feed water unit

∴
normalizing condition -i.e., the sum of all state probabilities = 1the availability of system (A 0 ) is given by the summation of probabilities of all working states -i.e.A

Figure 2 :
Figure 2: The effect of the failure and repair rate of the boiler subsystem on the feed water unit availability.Table1and Figure2reveal the effect of the failure and repair rates of the boiler subsystem on the availability of the feed water unit.It is observed that for some known values of failure / repair rates of condenser and feed water pump ( 2 φ