Nuclear Engmeenng and Design 110 (1988) 33-46 33 North-Holland, Amsterdam
APPLICATION OF A P O W E R PLANT SIMPLIFICATION M E T H O D O L O G Y : T H E E X A M P L E
O F T H E C O N D E N S A T E F E E D W A T E R S Y S T E M
P o o n g H. S E O N G 1, V i n c e n t P. M A N N O 2 and M i c h a e l W. G O L A Y 3.
J AT&T Bell Laboratomes, Middletown, NJ 07748, USA : Tufts Unwerslty, Medford, MA 02155, USA, also, Massachusetts Institute of Technology, Cambridge, MA 02139, USA s Massachusetts Instltute of Technology, Cambridge, MA 02139, USA
Received June 1988
A novel framework for the systemanc slmphflcatlon of power plant design is descnbed with a focus on the apphcation for the optimization of condensate feedwater system (CFWS) design. The evolution of design complexity of CFWS is rewewed with emphasis upon the underlying optirmzation process. A new evaluation methodology wtuch includes exphcit accounting of human as well as mechamcal effects upon system avaalablhty is described. The umfying figure of ment for an operating system is taken to be net electncity production cost The evaluation methodology is applied to the comparative analysis of three designs In the illustrative examples, the results illustrate how inclusion m the evaluanon of exphcit availability related costs leads to optimal configurations. These are different from those of current system design practices in that thermodynarmc efficiency and capital cost optimization are not overemphasized. Rather a more complete set of design-dependent variables is taken into account, and other important variables wluch remain neglected in current practices are identified A critique of the new optinuzanon approach and a discussion of future work areas including improved human performance modeling and different optimization constraints are prowded
1. Introduction
A popular prescription for the improvement of central power station performance is "design simplifica- tion". However, practical implementation of this advice is impossible without a more precise technical deflmtion of the concept. Further, it must be realized that the motivation to simplify originates from the deficient performance; which is a consequence of suboptimal design. Thus, the goal of simplification, i.e., improved plant performance through redesign, can be achieved only through a systematic consideration of the underly- ing performance goals of a plant, and the causes of inadequate performance. In general, the performance deficiencies which have led to dissatisfaction wxth the current generation of power stations have arisen from failure to take into account an adequate set of design- dependent variables in the optimization of designs. Complaints regarding the needless complexity of such
. i Member of Techmcal Staff 2 Assistant Professor of Mechamcal Engmeenng. 3 Professor of Nuclear Engineering
plants focus upon a symptom rather than a cause of poor performance.
The translation of the worthwhile vague goal of simplification to tangible engineering design methods with particular emphasis upon nuclear power plants has been a focal activity of the MIT Light Water Reactor (LWR) Innovat ion Project [1]. The definition of an overall conceptual base [2], the development of a method of design simphfication including use of probablhstlc performance models and econonuc analyses [3,4] as well as examination of the implications of this approach to design for new reactor plant [5] have been presented. The purpose of this paper is to descnbe this project 's first apphcation to the design optimization of a particu- lar plant system. This is perhaps the most important aspect of the project 's work to date since it provides a concrete test of the method 's utihty. The system chosen is the condensate feedwater system (CFWS) of a pres- surized water reactor (PWR).
The selection of the C F W S is motivated by a num- ber of observations. Histoncally, it has been an im- portant source of lost plant availability. Due to the nature of its constituent components of thermal-hydra-
( N o r t h - H o l l a n d Phys ics Pub l i sh ing D i v i s i o n )
34 P H Seong, V P Manno, M W Golay / Apph~atton of a power plant stmphfwatton
uhc, mechanical and control devices and its multlphclty of mission goals, Its refinement provides an adequate challenge to a method winch purports to have generic applicability. The current CFWS design configuration is the result of nearly a century of evolution and IS that of a mature technology The CFWS is not directly a safety related system These facts imply that it has a signifi- cant operational importance and is not over-designed due to external (e.g., safety, regulatory) constraints. The next section provides a synopsis of the evolution of the design complexity of tins system. Following that, an overview of the new method of design simplification is presented. Three representative CFWS designs are evaluated using the models of this method and the results are reviewed for both their design effects and implications regarding the value of the method
2. Evolution of design complexity
The CFWS represents one part of the overall, mod- ified Ranklne, thermal energy conversion cycle It has three primary missions
(i) to provide sufficient feedwater to the steam genera- tors,
(n) to heat feedwater in order to improve the thermo- dynanuc efficiency and prevent thermal shock, and
(ni) to maintain proper feedwater chemistry (e g., levels of dissolved 02, pH, metallic contamination).
The physical boundaries of the system consist of the condenser hotwell, the various steam extraction ports on the main turbine and the steam generator feedwater inlet nozzle. The major components of the CFWS are feedwater pumps, high pressure heaters and associated piping. Minor components include flow control valves, dram pumps and noncondenslble gas removal devices
The first tasks of the simplification process are to define a reference design and to acquire detailed knowl- edge of the components and their operating modes. The CFWS designs of approximately 20 L W R plants [6-24] were reviewed with respect to the number and config- uration of major components This exercise advances the goal of reference destgn definition but does not provide the reqmred detailed knowledge. The latter was obtained through a component-level review of a particu- lar plant which was deemed to be representative of the group. The specific plant selected was Uni t 2 of the Beaver Valley Power Station (BVPS-2). A synopsis of the design variability review as welt as the particular BVPS-2 configuration is provided in table 1. Consider- ins the large number of plants surveyed, the degree of variation is surprisingly small. A typical system mcludes
Table 1 Current condensate feedwater system design variation
Component I tern Range of BVPS-2 number of components
Steam generator Number 2-4 3
Low pressure heater stnng Number 2 3 2
Low-pressure heater Number 3-5 (5) " 5
High pressure heater Number 1-2 (1) 1
Demlnerahzer Number 5-9
Condensate pump
Booster pump
Feedwater pump
Type Full flow Full flow
Number 2-3 (3) 3
Type Motor-driven Motor-dnven
Capacity 50% 50%
Number 0, 2 or 3 (3) 0
Type Motor-driven N / A
Capacity 50% N / A
Number 2-3 (2) 3
Type Turbine or Motor-dnven motor- driven
Capacity 50% 50, 50, 30%
a Content in ( ) indicates the mode of the distribution.
redundant feedwater heater trains, multiple partial flow condensate and feedwater pumps and full flow de- mmerahzers Some variation exists in number of levels of redundancy and feedwater pump type (motor- or turbine-driven) and utilization of booster pumps The lack of an open deaerating heater In all plants IS noted in contrast to both standard fossil-fueled plant practice and the design of certain European nuclear power plants
The BVPS-2 power conversion system is shown schematically in fig. 1. The rationale for the current form of the C F W S as shown in fig 1 is best understood through a stepwlse reconstruction of the design evolu- tion of the system. Fig 2a illustrates the simplest possi- ble power conversion system which consists of a feed- water pump, steam generator and turbine-generator set operated in an open configuration This system, while
P H Seong~ VP Manno, M W Golay / Apphcatlon ofapowerplant stmphflcatton
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r . . . . t . . . . , - - - , - - - 4 - - - - - - ' 1 . . . . . . . . . . . . . . . 7Li_ i . . . . . . p , 1 . . . . . . . .t .Y i / r . . . . . . b - - - i ' i I<<--, I II r - - l - r . . . . . . . . . " ~ . . . . . . . . , / , , . . . . . . . . . . . . . . . . -_i l_ ,_.
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! I I I I I I I I I i D l i u l l i , l l,tL I Z U
I I ~ l F . I l ' u ~ s I I I I
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u
Fig 1 Current BVPS-2 power conversion system design (in two trmns), also designated as System 2
35
admittedly "simple" (in terms of the number of compo- nents, for example), suffers from poor thermal effi- ciency (< 10%, susceptibility to thermal shock, poor water chemistry, and environmental effects due to the discharge of high temperature and potentially radioac- tive effluent. (Note that the reduction of environmental effects is not a primary system mission goal, but is an overall plant goal which is affected significantly by the system design.) Fig. 2b depicts a system which addres- ses some of these deficiencies through use of a closed configuration and through the addition of a low pres- sure condenser. These two alterations also require crea- tion of a second pump category (condensate pump) due to the increased value of the pressure loss around the coolant loop and to the provision for condenser pres- sure and for removal of noncondensible gases from the system (using vacuum pumps and air ejectors). The thermal efficiency is increased substantially to ap- proximately 28%, and the related environmental effects are reduced. The negative aspects of this design change extend beyond the problems of use of additional imper- fect components. They also include introduction of new failure mechamsms (e.g., turbine blade erosion due to use of low quality steam) and new system failure states (e.g., loss of condenser vacuum).
Reduction of water chemistry problems can be ad- dressed through the introduction of a dlminerahzatlon (condensate polishing) system while turbine blade ero- sion can be reduced through the introduction of rind- stage moisture removal (as embodied in the current Moisture Separator Reheaters (MSRs)) Such a system is depicted in fig. 2c. Note again that the introduction of a new failure mechanism (blade erosion) causes the introduction of equipment (MSR) which is not focused primarily upon accomplishment of the original mission goals of the systems. Thermal eficiency and shock con- siderations lead to the introduction of regenerative heat- lng as embodied in closed (usually tube-in-shell heat exchangers) feedwater heaters. A typical system using five heaters with cascaded drains is shown in fig. 2d. The large number of heaters is noteworthy in that the addition of one stage of regenerative heating can im- prove cycle efficiency by 2-3% while the addition of a fifth level of heating provides a marginal efficiency improvement of much less than 0.5%. The evolution to maximize the thermal efficiency is evident from the addition of other regenerative devices including turbine-driven (vs. motor-driven) feedwater pumps, steam jet air ejector condensers (SJAEC), turbine gland steam seal condensers (GSSC) and heater drain pumps
36 P H Seong, V P Manno, M W Golay / Apphcatlon of a po~er plant stmphhcatlon
Figure 2~. The Power Conversion System of Step ! ~ Cycle System wttb a Steam Generator
wate r Pumps, Turbines with a Genera to r )
F e e d v a c e r p t t t ~
Steam I Genereco r
Ftgure 2b Tile P o ~ e r Convers ion Sys tem of Step 2 cStep One System with & Condenser and ondet)sat~ Pump)
Geusrscor r u r b t n e l
/ 1 .....
Condetmsca P m t p
Feedw&t e r Pump
Figure 2c The Po~er Con~erslon System of Step 4 (_Step Three System with a Condensate Polnsl~ng System)
g£gh Pressur@ Low P r e s s u r e Turb~ .~ Turb:tne C, e n e r a t o ,
HLgh P r e s s u r e
Fngure 2d The Power Convers ton Sys tem 6f Step S (Step Four Sys tem w t t h m a n y F e e d w a m r Heaters)
High P r e s | u r l Lov P r e s s u r e Tu rb ine MS/R T u r b i n e G e n e r a t o r
I~w P r e a o u r e Turb£mt H R T u r b i n e C n e r a t : o r
I " " " T - " - C o n d e n s e r | r . . . . . . . .
i : t n t i
1 1 t 0
1 : i ~ Steam J e t
I s~ I ' I I 1 I ' - r a C o ' ' . . . .
1 CZand Seal t . . . . . . J I S toma Condenser
C o n d e n s a t e P o l i s h i n 8
Dra in Puntps
Condenser a Po liel~c41c S y s t e m
F,gure 2e The Power Convers ion Sys tem of S tep 6 Step Fzve Sys t em wsth o the r Mnnor Heat x e h ~ g e r s and D r m n P u m p s )
Fig 2 Schemauc illustration of the design evolution of condensate feedwater systems
P H Seon~ VP Manno, M. W Golay / Apphcatton ofa powerplant stmphficatton 37
(winch have smaller thermodynanuc availabxhty effects than the practice of cascading drams). The addition of the last three device categories increases a typical plant electrical output by approximately 0.4%. Such a system is shown in fig. 2e.
When the design evolutton of the CFWS is reviewed m this stepwlse exercise, it becomes apparent that al- though the three mission goals are all taken mto account the primary mfluence in the evolving optmuzaUon ts mtnnslcally economic. In particular, the modern CFWS design has been determined from the predominant con- cern for mlmmizang the sum of capital and fuel costs and less from concern for operating costs. Such costs mclude those of lost plant availability and component maintenance. This is exemphfied as follows. - in the type and levels of component redundancy
employed in current CFWS designs (e.g., heater trams are redundant but feedwater pumps usually are not),
- in the choice of eqmpment used (no deaerators are used even though water chemistry, e.g, dissolved 0 2, would be improved), and
- in the number of heaters used (where the tmphed mcrease in unavailabthty due to an increase in the number of components is not constdered to be as important as the thermal gain in efficiency which ts achieved). It ~s ~mportant to note that these observations do not
tmply a natve design evolution. Rather they illustrate that the underlying opttmizatlon criteria which gutded past system development are not adequate for current plant economics. It is notable that availability-related economic performance is more difficult to evaluate quantitatwely than are those of fuel and capttal. This is because the required analysis methods and data bases are the least developed of the entire design process. In order to measure the achievement of system (and plant) mission goals, a unified, implicitly economic evaluation framework xs required. The optimizatton criteria must be stated and understood exphcxtly from the beginning of the design process. System avaflabthty is not a per- formance charactenstic winch can be improved easily m completed plants This fact leads to the need for a design evaluatton method so that Ingh rehabihty can be made mherent m a destgn.
These statements are also valid concerning plant operation and maintenance costs. Such costs have not been treated traditmnally as dependent variables m the economic opttrmzatton of power station destgns. A com- prehensive design method should take them mto account in addttion to availability-related costs. Operatmn and maintenance costs are not dxscussed further m this paper. However, tins omission is not intended to imply
that they should be neglected tn formulatton of a com- prehensive design approach.
3 . D e s i g n s i m p l i f i c a t i o n e v a l u a t i o n m e t h o d
The term "simphficatlon" is included deliberately m the identification of the desxgn refinement method described here. Its use imphes that the design opttmiza- tton exerctse ~s to be a refinement of an existing entity. Two benchmark elements of an evaluation method are a unffymg figure of merit and a computational framework for its estimation. For an operational system, the figure of merit must measure economic performance. Given the power plant application, the cost of electnclty xs chosen as this measure As a contrastmg example, the proper figure of merit for a safety system is risk. The computational framework for evaluatmn of the effects of system stmphficaUon upon plant electricity cost ts shown schematically in fig. 3
The four major cost categories are those of capital, fuel, replacement power and operation and mainte- nance. Tins delineation is not new. However, fig. 3 reflects the fact that the treatment of replacement power and O&M costs m the stmphficatton method is differ- ent from standard power plant economic analysis tn that the effects of system sxmpliflcatlon upon availabil- tty and operattonal costs are computed through a more realtStlC treatment than has been used previously. In the past such costs were addressed by means of various empirical (and static) cost multtpliers upon capital costs. In the stmpllficatlon method, the capital cost analysts ts performed using present worth analysis whale the fuel cost computatton involves a thermodynamic analysis
FIGURE OF 1 MERIT IN , ELECTRICITY
l COST ,[ CAPITAL COST [
11 REPLACEMENT ELECTRICITY COST
tS MPLIFICATION --[UN I TY rHUMAN ERROR' ] ?[ PRO.A.ILITY ?--AW'LA"ILITY I r
IFUNCTIO~AL RFL'A"IL~T" } - - J
Fig 3 Diagram of impact of system slmphficatlon on electri- city cost
38 P H Seong V P Manno, M W Golay / Apphcatton of a power plant ~tmphflcatwn
INITIATING SYSTEM HUMAN ItlI\IAN [ INAL SYSFFM STATE DI AGI',OS|S CORRFCFIO\ STATE
F i g 4 M m g a t e d f a d u r e p r o b a b i l i t y
and uses a fuel cost data base These are s tandard practtces and are not discussed further.
The esttmatlon of avadabdlty reqmres two pmces of reformation - the mechanical system rehabfltty and the
human error probablhty Thts requirement reflects the fact that system performance depends upon both me-
chanical integrtty and human operation of a system The art of estimation of the mechanical rehabthty is the
more mature. It benefits from more developed esuma-
tlon methods and available data bases The tools of
probablhst ic rehablhty assessment have advanced to the
point of s tandar&zat ion and can produce reasonably
accurate estimates of system performance subject to the
constraint of availability of adequate mformatmn, such as is the case with components having relatively well
documented failure and repair charactenstms (e.g, pumps, valves, control subsystems) The specific tech-
tuque whach ~s employed m this evaluation model is that of fault tree analys~s [25] of the system at hand The pnnclpal hnutanons on the uUllzatmn of these tech- tuques are the t reatment of data uncertainty and the
mchasmn of common cause and common mode fadures
m the analys~s. Whale these factors are important to note, they are of less concern than the difficultms of
human error probab~hty esumates
There are three categories of human errors (1) errors
of commlssmn, whmh involve the m~sperformance (rather manual or cognmve) of a correctl~ tdennfied acuom (2) errors of om~ssmn, when the correct act ~s not Menu- fled, and (3) gratmtous errors, where unnecessary acts exacerbate a situation. The current model does not
address gratmtous errors but these are recogmzed as an ~mportant area of future work The stanstmal aspects of manual human actmns assocmted w~th commission er-
rors have been the subject of most of the hterature of " h u m a n factors" [26], and reasonably accurate est> mates of such error rates can be made However, lhe
{ S ucCes s I V [ | "%,,...,,,~l ( D e s l r e d ~ S t a t e 1 !/"q-------t/'N
( S T A N D B Y M O D E ) ( F M L E D M O D F ) A B S O L U T E C O N D I T I O N A l .
P R O B A B I L I T I E S P R O B A B I L I T I E S P , p "
0 9025 0
S t a t e 2 ,, ~ 0 0475
[State 4 ~ 0 0025
Fig 5 Four possible states of a two-valve system when the probabdlty of a valve open is 0 95
Standby mode
1 1 1 1 - - + P2 - - + P~ - - +/ '4 log2-- = 0 5727 H = reformational entropy = P2 l o g 2 p~ l°ga P2 l o g : P~ /°4
Faded mode 1 1 1
H D = D E P O S S = P2 * l°ga ~-2. + P3* l°g2 p3- ~ + / 4 * log: Pa ~ =1 147
[P,* condmonal probabdlty of system state i when the system is m an undesired state]
0 4~70
0 45"/0
0 0257
P.H Seong, V P Manno, M W Golay /Apphcanon of a power plant stmphficatton 39
dependence of cognitive errors such as in system diag- nosis upon system design is an area that lacks a sub- stantial conceptual framework of credible empirical data. The necessity for inclusion of this category of model can be appreciated from a rexqew of fig. 4 which depicts the human rehability analysis in an event tree framework.
The ideas discussed in this section are reported more completely in refs. [3] and [29]. In an evaluat/on of the human contnbution to system unavailability emphasis is placed upon the expected fequency of human success in diagnosing the condition of a system which has failed to operate as intended. It is assumed that the system will have a set of possible configurations or states. Among these only one, termed the des/red state, will be the state which it is intended that the system occupy at a particular moment. The identity of the des/red state may change with the passage of time. In a well-designed system the probability of the desired state will be large and that of any other state, an undesired state, will be small.
These ideas are illustrated in fig. 5, which shows a two-valve hydrauhc system. In this example the state where a fluid is permatted to flow, that with both values open, is the desired state. The remaining three states, each of which has at least one valve closed, are all undestred. For this example it is assumed that the probability that a valve will actually be open when it is intended that the valve be open is 0.95. The correspond- ing state probabilities are shown in fig. 5.
Three alternative condmons are of practical interest for a system, as follows:
- The system is operating as intended. - The system is in standby status. - The system has failed to operate as intended, and
is, thus, in one of the undesired states. The respective conditional probabilities of the system state are different for each of these condinons. When the system is operating as intended and a perfect signal indicates this to be the case (e.g., when fluid is seen to be issuing from the system of fig. 5), the conditional probabthty of the desired state is unity and that of each indesired state is zero. Under this condition the uncer- tainty of the system is nil as the true condition of the system is known with absolute certainty.
When the system is in standby status the probability assignments of fig. 5 for the standby situation apply. It is seen that the desired state is far more likely than any other. If one were to search for the true system state it would be most efficient to search first for the desired state for this reason. Then if the system were found not to be m that state an efficient search would proceed
next to the two single-failure states successively, and after those, finally, to the remaining double-failure state.
When the system is known not to be in the desired stated (e.g., with the example of fig. 5 when fluid does not issue from the piping system) the conditional prob- ability of the desired state is equal to zero. Correspond- ingly the condmonal probabihtles of the remaining must be re-normalized such that their sum is equal to unity This renormahzatlon is illustrated in the example of fig. 5 for the failed system situation. It is seen in that example that the number of likely states has doubled, with the conditional probability of each of the single failure states being slightly less than one half. In di- agnosing this system the most efficient search would begin with one of these states. However, the probability of not finding the true system state would be 0.55, rather than 0.10 as in the situation where the system IS in the first interrogation in standby status.
The uncertainty of a system is quant/fied by the reformational entropy, H, through the relationship:
H = - ~ p, log2p,, (1) t = l
where n = number of system states, and p, = probablhty of the t-th state. For a system known to be in the desired state the value of H is equal to zero, as the system has no uncertainty For the standby and failed system situations of the example of fig. 5, the respective values of the entropy are 0.5727 and 1.147 It is seen that the value for the failed system is approramately double that for the system on standby, reflecting the fact that the number of highly likely states of the former is twice that of the latter. The entropy ~s used as an indicator of the complexity of the system under consid- eration.
A postulate of the work reported here, which has been confirmed, is that the number of questions, (~) , which must be asked in order to diagnose a system IS a unique function of the system entropy. It has been shown [29] that ( h ) obeys the relationship
(~ ) -- ½2 n. (2)
This relationship has been shown to hold, at least approxamately, without regard for the number of com- ponents in the system or the particular values of the state probabilities.
This relatmnship may be understood by consldenng the diagnosis of a system of N components for which all possible states have the same probability value. When the number of system states is n the value of p, is equal to 1/n. For this system the value of ( h ) is equal to
40 P H Seong V P Manno, M W Golay / Apphcatton of a power plant slmphficatlon
n / 2 Tins is because no sequence of searching for the true system state ~s more efficient than another or than a perfectly random search. For tins system the entropy has the value log2n, from winch the result
n = 2 n (3)
IS obtained, as is that of eq. (2). The system for winch the probabdlty of each state has the same value is partmularly interesting since it has the least number of possible states of any system having the entropy value H
An especxally interesting case ~s that of the system where all possible states have probainhtles of value zero except for the single fadure states. The number of possible states is equal to the number of system compo- nents For tins mua t lon the value of ( h ) is given as
( h ) - N 1 H 5 - 7 2 (4)
The result
N = 2 H = N D, (5)
where N D is termed the dlagnostm number of compo- nents. The approxamatmns imbedded m eq. (5) apply to well-designed systems winch must be dmgnosed due to fadure but for winch the absolute failure probabili ty for each component is small Use of eq (5) pernuts com- parison of disslrmlar systems m terms of dmgnostlc complexity. The approxamate equivalent number of sys- tem components for a failed system having a con&- tmnal entropy value of H is given by N D. The relatwe complexity of systems of dfffenng values of H (termed HD) is indicated by differences m the corresponding values of N D. The complete definitmn of H D is dI- agnostm entropy for a faded system hawng a single perfect system signal. It is notable that N D and ( h ) increase exponentially as functmns of H.
A concept winch is used subsequently in the analysis of system rehabihty is that of the probabili ty of failure to diagnose a failed system correctly w~tinn a hrmted number, j , of lnterrogatmns. When the interrogation of a fmled system is performed in the descending order of state probabdmes, P f ( j ) is seen to obey the rela- tranship
J
P r ( J ) = 1 - ~ p,. (6) l = l
An ~mportant aspect of these concepts is that when a group of human subjects was asked to dmgnose differ- ent failed CFS examples it was seen that the values of
( h ) , Pf(3) and P f ( 5 ) correlated ver~ well with corre- sponding results obtained from eqs (2) and (6)
The challenge is to identify a measure of design simplicity winch can be correlated with the human error probablhty. In the work reported here the measure that has been identified as being useful for tins purpose is the information entropy, H, [27] subject to the cond> tlon that the system is in a failed or undesirable state
The most important aspect of these formulatmns is that they can be demonstrated empirically 0 .e , through actual human performance experiments) that P~ and H D can be correlated Therefore, the quantlflcatmn of H D winch involves a mathematical calculation can be used to estimate the human probabdlty of dlagnosuc success and thus to complete the event tree calculation depicted schematically in fig. 4
4. Application to representative designs
Use of the evaluation method is now demonstrated through a comparat ive analysis of three candidate CFWS The first is the BVPS-2 system depicted in fig 1 and table 1. Two alternative configurations are con- structed by selective modification of the BVPS-2 sys- tem One system has less hardware and the other more hardware than the BVPS-2 system. The underlymg logic, winch is employed m the creation of these two alterna- tives, reflects the qualitative development Instory sum- marlzed earlier, removal of components which have small effects upon the thermodynanuc efficiency, ellrmnatlon of active components as a general goal, focus upon subsystems winch have Instormally been sources of plant unavallablhty and exploiting the poten- tial for alternative component utlllzatmn
The first alternatwe, simpler, system ~s designated as System 1 System 1 has two fewer low pressure heaters and no fifth point heater dram cooler The drmns are cascaded down, thus ehminatmg dram pumps and tanks The three feedwater pumps are changed to variable speed motor-driven pumps and each is rated for 50% ot full flow (vs using two 50% and one 30% pumps as with BVPS-2) System l is shown schematmally m fig. 6. The BVPS-2 system is designated a System 2
The tinrd, more complex, system winch is desagnated System 3 has two condensate pumps, two feedwater pumps, two booster pumps, a dram pump and ad- dmonal motor-operated valves. System 3 is depicted in fig 7
The major active C F W S components of the three systems are illustrated in figs. 8a through 8c System 1 has 23 active components with four stage of feedwater
P H Seong, VP Manno, M.W. Golay / Apphcatton ofa powerplant slmphficatton
. . . . . . . . . . . . . I r . . . . . I t r I I I I
- - It. _ -_~_-_.- - : : . . . . . . - -
i L . . . . . . . . .
Fig 6 Slmphfied power conversion system design 1 (m two trams)
41
r . . . . . . . . . i i r I -11-- - I
I / I lJm~/1UI I I I
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42 P H Seong, V P Manno. M W Golay / Apphcatton of a power plant slmphficatto~
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Fig 8 (a, top) Actwe components configuration of stmphfied condensate feedwater systems System 1, (b, middle) Acuve components configuration of medium complexity beaver Val- ley Power Station-2 condensate feedwater system System 2, (c, bottom) Active components configuration of complex con-
densate feedwater system System 3
heating. System 2 has 29 active componen t s with six stages of feedwater heating. System 3 has 40 acttve componen t s wxth six stages of feedwater heating. The es t imat ion of the h u m a n error con t r ibu t ion to system unaval labdi ty is based upon use of the concepts out- l ined previously. The computa t ion of the mechanical or funct ional reliability contr ibut ion, which is per formed using fault tree analysis, reqmres the provis ion of a
componen t rel labdl ty and repair da ta base. Two ahe l - nat ive data bases are employed for per formance of two
separate system evaluat ions The purpose ~s dlustrat lon of the sensltlVtty of the results of an evaluat ion to differing umforml ty m the expected rates of componen t failures The da ta base which is employed in the ana l ) - sis of Case A utlhzes generic indust ry data for the actwc componen t s [28] The o ther data base. employed in the analysis of Case B, is a modif icat ion of tha t of Case A m which the p u m p failure rates are made umform These two data bases are hsted m table 2 A d d m o n a l reformation, mcludlng p lan t power rating, cost data, economic per formance factors and addi t ional h u m a n error per formance at t r ibutes , which are required for the overall evaluat ion methodology calcula tmns are hsted In
table 3 The calculat ion of system availabdlty, taking into
account b o t h mechanica l and h u m a n con t r ibu t ions to lost aval lablhty, is per formed as follows The system ~s assumed to become unavai lable for full power opera tmn due to refueling, shu tdowns due to major repmrs of long dura t ion and due to t rans ients which take the plant off-line for short dura t tons Each of these classes of outage is character ized by a mean t~me to failure and a mean tame to repair, respectively, as shown in table 2 The h u m a n con t r ibu t ion to lost avadabaht) arises m t ransients winch lead to forced outages It is assumed tha t the p lan t ~s designed w~th remotely-act ivated sys- tem recovery features which would pernn t valves or pumps which were to fall to operate properly to be reset and placed back in service m rime to keep the plant runn ing if their fadure were detected quickly
Discount rate 0 06 (yr- a ) Plant hfetime 35 years Pump cost $5 0 x 103 Valve cost $1.0 × 105 Feedwater heater cost $1 5 x 10 6
Correction error probablhty 0.01 Lucky success probablhty 0.01 Number of interrogations
allowed in diagnosis 3
The sequence of events leachng to a forced p lant outage of ei ther long or short dura t ion is indicated m fig. 4. The outage event sequence consists of the follow-
mg - an imtxal system failure, - an a t tempt by the p lant operator to diagnose the
failure, and - an a t tempt to restore the fatled componen t s to oper-
ation. The different success and failure pa ths are indicated in fig. 4.
In system diagnosis ~t ~s assumed tha t the p lant operator ~s t ra ined to search through the system states in the descending order of state probabil i ty , and ff the analyst canno t identify the true system state in three interrogat ions that the dmgnos~s ~s unsuccessful, the lat ter assumpt ion is used as a surrogate for the case of the analyst having only a l imited amoun t of t ime for dmgnosis. The probabi l i ty of successful diagnosis in calculated f rom eq. (6). U p o n successful diagnosis it is assumed that the probabi l i ty of correct ing the system failure is P 3 a s U p o n unsuccessful &agnosis it is also possible, bu t very unhkely, to correct the failure. The p robab lh ty value of P3bs is used for this event.
Each b ranch of fig. 4 then has an associated p rob- abdity, which ~s used m combina t ion w~th mean nm e to fatlure data m the calculat ion of the final system fatlure ra te (FSFR). The imtial system failure rate, the ra te of events imt ia tmg a t ransient or of refuehng, is obtaaned taking into account only mechamcal failure data. I t is seen m table 4 tha t the effects of opera tor diagnosis is to render F S F R < ISFR, sometimes substantially. No te tha t the specific h u m a n error which appears in this
analysts is failure to d iagnose and rmngate af ter three
at tempts. This is clearly an arbi t rary specif icauon based on intuit ion.
The results of the various eva lua tmns are sum- marized in tables 4 and 5 which present the three system compar isons based upon Case A and Case B data, respectwely. In bo th comparisons, the d iagnosnc entropy, HD, increases with system complexaty as is expected. For a gtven system the absolute values of H D are higher m Case B due to the greater uniforrraty among componen t s of the rehablh ty data, bu t the frac- t ional changes of the value of H D between systems are the same in bo th cases. As expected, the var ia t ions of Pt and ( n ) reflect tha t of the ent ropy The &agnost ic n u m b e r of components , ND, is notewor thy m that ~t is subs tanual ly lower than the actual n u m b e r of compo- nents m Case A and nearly equal to the actual n u m b e r of componen t s m Case B. This fact i l lustrates the point tha t a system with more uniformly & s t n b u t e d unde- sired state probabdl t les is ha rder to diagnose. Compar i - son of systems m terms of H D also provides a measure which can be apprecia ted in concrete term, i.e., the n u m b e r of componen t s m a system.
The h u m a n effects upon the mltml system failure rate (Le., dmgnost lc effects o ther than f rom acnons) are not included in the current model due to a dear th of useful da ta and the lack of a conceptual framework.
Table 4 Results of the economic A
evaluation using failure data m Case
System 1 System 2 System 3
Number of active components 23 29 40
H D 4 067 4 304 4 812 N D 16 792 19.757 28.275 Pf (3) 0 588 0 564 0 639 (~ ) 8.015 9 392 13.800 ISFR a ( /yr) 1 419 3 444 8.807 FSFR b (/yr) 0 834 1 941 5.624 Avmlabflity 0 92448 0 91785 0.90735 c Fuel cost saving ($) - 2.01 × 107 0 0 c Replacement
c Total electnoty cost saving ($) 3.55 × 107 0 - 7 39 × 107
d ISFR = Imtlal System Failure Rate b FSFR = Final System Fadure Rate c Net present savings at the start of station operation
Such actions represent an area of impor t an t future work. A m o n g such h u m a n cont r ibu tors to init ial system failure are errors in maintenance , manua l errors and cognitive errors in operat ions and gratui tous error, where needless act ions are taken which impai r p lan t op- erations. Hence, the I S F R values do not reflect a sensi- tivity to any h u m a n per formance contr ibut ions .
The overall effect of h u m a n per formance on the F S F R and the system availabil i ty is small in the cases studied. This does not represent a failure of the model or imply a general conclusion that h u m a n per fo rmance a t t r ibutes are not impor tan t . The history of p lan t op- erat ions provides adequate proof of the lat ter point . The results reflect the characteris t ic of the systems selected for examinat ion in that the variabil i ty of mechanica l funct ional unrel iabi l i ty is a much s t ronger effect than tha t of h u m a n per formance contr ibut ion. It is recog- razed that o ther systems (especially very high reliabili ty system such as electronic controls) may have quite the opposi te sensitivity
Nevertheless, subject to the various hml ta t ions and assumptions , the results provide some interest ing in- sights which are unob ta inab le f rom extsting econonuc analyses. If the p lant opt imizat ion criteria were to focus only upon capital, fuel and s tandard O & M costs, as is the current practice; System 2 ( the actual BVPS-2 sys- tem) is seen as the opt imal choice among the three. This is true for b o t h sets of per formance data. However, if
the new methodology is employed. System 1 is seen to be more at t ract ive even though its the rmodynamic ef- ficiency is lower than that of System 2 and its capital cost savings are relatively small over the p lant ' s operat- Ing life System 3 is not preferred under any cir- cumstance
5. Critique and concluding remarks
The evaluat ion methodology discussed here requires bo th re f inement and appl ica t ion to other systems How- ever, it provides and advancemen t of the comprehensi - veness of the design process. The first area of improve- men t concerns deficiencies of the conceptual frame- work Two categories of needed improvement are First, deve lopment of models and data for a complete calcula- t ion of the figure of meri t of the design, such as a bet ter quant i f ica t ion of the influence of h u m a n per formance upon availabil i ty; and, for non-power p lan t applica- tions, the specification of al ternat ive figures of m e n t Second, the specif icat ion of the new overall evaluat ion f ramework for non-opera t iona l systems, such as a quan- t if ication of risk in evaluat ion of a safety system.
The next level of re f inement of the design methodol - ogy is the fur ther deve lopment of the various elements of the design evaluat ion model Experience to-date with opera t ional system analysis indicates tha t the area of h u m a n pe r fo rmance is the most deficient in terms of bo th theory and suppor t ing data. Some of the more impor t an t issues have been men t ioned - correla t ion of system design and per formance , ident i f icat ion of proper ma in tenance errors and gratui tous acts and evaluat ion of the utility of the event tree concept to thts quant i f ica- tion. Use of such improved design methods may lead to changes in the evaluat ions of the costs of ma in tenance with rep lacement of the current ly employed cost multi- plier methods . Quant i f ica t ion of mechanica l rehabll i ty remains a developing science, especially in the areas of da ta uncer ta in ty and applicabil i ty
In addi t ion to h u m a n error the economic costs of opera t ion and main tenance , of enhanced safety, and of cons t ruc t ion schedule disrupt ion, need to be taken into account as des ign-dependent variables. The econonuc cost con t r ibu t ions of capi ta l and fuel are adequately addressed with current practices. Deve lopment of non-opera t iona l system evaluat ion f ramework will pro- duce a new set of p rob lem areas
The specific example of the condensa te feedwater system is a useful first applicat ion, with overall positive results, of the evaluat ion methodology presented here. The current ly unachIeved goal of economical ly opt imal
P H. Seong, VP Manno, M W Golay / Apphcatton ofapowerplant stmphfwatzon 45
large central station power plant performance, as exem- plified by the detailed consideration of the CFWS evolution, is seen as resulting from deficiencies in the original specification of plant performance goals and from fadure to include all of them as optimization variables m the design process. The inclusion in the evahiat~on of realistic plant availability and operation and maintenance, ~s required. The further development and application of methodologies which reflect the com- plete set of dependent cost factors vail provade the technical community with tractable methods for achiev- ing the goal of design simphfication and will produce new generations of better performing power plants.
Acknowledgements
The support of this work by the EPRI Advanced Light Water Reactor Program is gratefully acknowl- edged.
Nomenclature
BVPS-2 CFWS FSFR GSSC /-/D
H ISFR LWR MSR ND N n
O & M Pf(J )
PWR P, SJAEC
Beaver Valley Power StaUon, Umt 2, Condensate Feedwater System, Final System Failure Rate (per year), Gland Seal Steam Condenser, diagnostic entropy for a failed system hawng a single perfect system signal, information entropy, Initial System Failure Rate (per year), Light Water Reactor, Moisture Separator Reheater, diagnostic number of components, number of system components, number of system states, average number of interrogations in system dmgnosis, Operations and Maintenance, human error probabihty to not diagnose suc- cessfully after j inquiries, Pressurized Water Reactor, probabihty of undesired state t, Steam Jet Air Ejector Condenser.
References
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46 P H Seong V P Manno, M W Gola2 / Apphcatlon of a power plant ~lmphftcatton
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