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"AY 3 1980The person charging tnTs^material is re-sponsible for its return to the library fromwhich it was withdrawn on or before theLatest Date stamped below.Theft, mutilation, and underlining of books are reasonsfor disciplinary action and may result in dismissal fromthe University.To renew call Telephone Center, 333-8400UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN

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ENGINEERING LIBRARVUNIVERSITV OF ILLINOISURBANAj ILLINOIS

UNIVERSITY OF ILLIfURBANA, ILLINOIS 61801

CAC Document No. l83

IMPROVED EFFICIENCY OF TOTAL ENERGYSYSTEMS THROUGH WASTE HEAT ENERGY

UTILIZATION

Jerry Akira Tanaka

January 1976


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Digitized by the Internet Archivein 2012 with funding from

University of Illinois Urbana-Champaign


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CAC DOCUMENT No. l83

IMPROVED EFFICIENCY OF TOTAL ENERGY SYSTEMSTHROUGH WASTE HEAT ENERGY UTILIZATION

byJerry Akira Tanaka

Center for Advanced ComputationUniversity of Illinois at Urbana-Champaign

Urbana, Illinois 618OI

January 19T6

This research was conducted under a grant from the NationalScience Foundation.


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ABSTRACT

Increased efficiency of power systems is investigated withconsiderations for economic, mathematical and engineering feasibility.In particular, a study comparing two alternative modes of energyoutput for a nuclear power plant is discussed with conclusions andcomments as to maximum theoretical efficiency and optimal operatingconditions. Discussion of several current methods for improving idleplant capacity and optimal consumer demands is included.


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iiiSection TABLE OF CONTENTS Page1 . Introduction 12.0 Efficiency 33.0 Power System Description and Assumptions 5

3 . Reactor Model 53.2 Turtine Model 53 . Modified Steam Extraction Turbine Design 8

i+.O Execution of Project Analysis 10k.l Statement of Problem and Objectives 10k . 2 Methodology 10

5 . Conclusions and Results IT6.0 Notes on Improvement in Plant Idle Capacity 25T.O Calculation Of Optimal Operating Point For The Dual

Output System 28

Appendices:A Single Output Program 3kB Dual Output Program 37


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ivLIST OF TABLES

Table Page1 Heat Rates for Turbine Generators Applied with

GE Standard PWR 72 Seasonal Consumer Demands lU3 August 10 Consumer Demands 15k December 7 Consumer Demands l6


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VLIST OF FIGURES

Fig,voce Page1 PWR Turbine-Reactor System 62 Modified Steam Extraction Heat Processor , 93 Power Production as a F-unction of Heat Load Factor 12h Seasonal Variation Comparison Between Dual and Single

Function Plants l85 Hourly Variation in Efficiency on Aug. 10 for Dual and SingleF\inction Plants 196 HoTorly Variation in Efficiency on Dec, 7 for Dual and Single

Function Plants 207 Output Locus of Power Plant Operating Points 29


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viACKNOWLEDGMENT

The author wishes to acknowledge the assistance and helpful commentssupplied by Professors Robert Herendeen and Bruce Hannon of the Centerfor Advanced Computation and Professor B. G. Jones of the NuclearEngineering Department, all of the University of Illinois. Reviewand approval of this study was also granted by Professor Willis L. Emeryof the Department of Electrical Engineering at the University. Consider-able information and assistance was provided by R. W. Snyder and Don Cazerof General Electric 's Medium and Large Steam Turbine Division with techni-cal data and publications supplied by the United States Energy Researchand Development Administration at Oak Ridge Laboratories.

Extra thanks go to Mrs. Veronica Soltys for her efforts in theorganization and publication of this thesis.


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1.0 INTRODUCTIONThis project investigates the possibility of increased efficiency

for power plants through the use of waste heat created within thesystem. By using a dual output system, as opposed to the more con-ventional single output electrical network, it is theoretically possibleto convert some of this waste heat to useful purposes. Limits to thisproblem are set by the maximum work output possible under the firstlaw of thermodynamics and the engineering feasibility of such a plant [l].Practical limitations on steam pressures, temperatures, environmentaland cost considerations are but a few of the many factors which shouldbe analyzed for a complete study of a project of this size. To eliminatemany of these problems, while trying to remain as close to reality aspossible in our models, this study has attempted to simulate many of thedesign features of power plants already in existence or proposed. Anysimplifying assumptions made are duly noted within.

To determine the comparative efficiencies of both systems, twomathematical models were created representing all internal cycles inthe power plant from material gathered from GE and the reactor divisionof Oak Ridge Laboratories [2, 3], These models were programmed on anIBM 360 for mass calculation of dynamic load points. Results fromthese programs reveal the true system efficiency at all operating timesfor fluctuating seasonal and daily demands.

Our definition of efficiency here is an operational one defined bytaking the total useable Btu's or MW's delivered divided by the totalenergy created by the reactor.


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2The problem of fluctuating daily loads is also taken londer considera-

tion to improve the use of idle capacity within the power plant as muchas possible. This helps provide for maximimi utilization of potentialpower within the system since standby capacity represents a significantcost to utilities today.

It is hoped that the conclusions and alternatives arrived at withinthis study may provide some insight into the many environmental andenergy connected problems generated by our power systems today. Itis well known that these plants are one of the major causes of thermalpollution. With our constant demand for electric power rising eachyear it has become increasingly important that a solution to the amountof waste heat generated by alleviated. The environmental and efficiencyproblems are thus directly linked, with increased waste heat utilizationoffering a prime method for partial solution to these problems.


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2.0 EFFICIENCYThe study of efficiency evolves around the First Law of Thermo-

dynamics which claims that, due to increased entropy, one cannotconvert all generated energy into useful work. This is caused bythe constant degrading of energy within the system to higher entropy,lower quality heat. The work output divided by the heat input givesthe theoretical efficiency for ovir system [i].

The efficiency equation for conversion of energy to mechanicalwork i s :

T - T T_2 _2 ^ -L _ _2T T1 1

where T represents the absolute temperature of the initial hot reservoirand Tp the absolute temperature of the condensed cold reservoir Ik], Forthe PWR plant modeled in this study, typical warrented thermal propertieslist T at about 590F or 58'3K for a 2U39 MW reactor and 90F or305K for T , the condensed water temperatvire . This gives a theoreti-cal efficiency value of kf.Cfo. This figure would be applicable for asingle output conventional nuclear electric generating station l2]. Oncethe system has been altered for dual purpose outputs, our operationaldefinition is used to describe the additional use of steam since theCarnot cycle definition is not applicable. The value kj .6% may be

used as an indication for comparison between the actual operatingefficiency of the single output plant and its theoretical limits. Fiirtherlimitations on the dual output system arise only from the fact that the


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hentropy of the cycle attains such a high level that mechanical work oruseful transference of energy becomes impractical for conventional usesof heating, air conditioning and electrical generation l5].

Some preliminary studies involving the dual generation of steam andelectricity suggest that the practical limitations for this system mayappear to be around 90^, theoretically. This is a vast improvementover the usual k'J .6% limit [3].


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5

3.0 POWER SYSTEM DESCRIPTION MP ASSUMPTIONS3.1 Reactor Model

The system iinder study involves modeling a standard GE PWR(pressurized water reactor) with a 100^ warranted thermal output of2U39 MWt. This is used in conjunction with an appropriate steam generatoror heat exchanger to provide a low radioactive secondary cycle enablingsafer steam usage and easier control (Fig. l) [6] . Operating pointswere obtained from GE performance data and used to construct a straightline segment model for the reactor turbine combination (Table l) [2],

3.2 Turbine ModelA GE model TCi+F-38 turbine was matched to the PWR reactor to give a

maximum electrical output of 837.8 MWe at 2^+39 MWt reactor output.Operational assumptions made on the system include 100^ moisture separa-tion, constant losses due to components outside the turbine- condenserregion, full throttling method of steam control and minor fluctuationsin efficiency due to slight -variance in t\arbine back pressure. Themaximum error in output power due to small differences in back pressure

using 2 inches Hg as a standard was +1.8^ and -2.2^ at 1220 MWt. Alloperating levels below ^0% of the warranted thermal capacity were ex-trapolated from the last operating segment given in the tiirbine data.Plotting of the data in Table 1 indicates only slight variation fromlinear performance down to 50^ thermal capacity. Miiltiple preheatstages are used at all temperatiores to preheat the outgoing secondarycondensed water flow to ii20F before return to the steam generator.A three segment turbine is used to drive the generator which will supply


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hiI-O)>-VitroI-o


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TABLE 1. Heat Rates for Turbine GeneratorsApplied with GE Standard PWR

Warranted thermal output = 2i+39100 KWFinal feedwater temperat\ire at warranty = U20FCondensate storage tank flow = 30000 Ibs/hr.

TCUF~38 2 stage reheat cycle - Output in MW

Percent of reactor warranted thermal outputinal ExhaustPressure

1..5

2.,0

2..5

100 88 T? 50838.3 7^2.3 626.6 399.1837. 7i^l.O 623.8. 391.9835.6 7ii0.0 6l8.6 383.2


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8

3.3 Modified Steam Extraction Turbine DesignFig. 2 shows the schematic design for the modified proposed turbine

system for steam extraction. GE provides many turbines equipped forautomatic extraction at all temperatiires and a variety of capacities [?].This steam, taken at a temperatvire slightly higher than UOOF would flowthrough heat exchangers to reheat the district heating supply steam to300F. Data for a typical steam extraction system was provided by thereactor division of Oak Ridge Laboratories [3]. Performance for thecombined electric-steam system may be calculated directly through theuse of steam tables and evaluation methods for industrial power plants [?].For this study, the data given by Oak Ridge was deemed sufficient fordrawing initial conclusions on the system design.

This steam at 300F would then be pumped from the source generatingstation by means similar to those in use for steam today and used forabsorption air conditioning of homes and commercial buildings duringthe summer and space heating in the winter [8]. A more detailed descriptionof this system appears in Section U.2.


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TURBINE TURBINE TURBINE

REGULATOR Y X~ TO CONDENSER

DISTRICT HEATING STEAMHEAT EXCHANGERS oPUMP

FIGURE 2. MODIFIED STEAM EXTRACTION HEAT PROCESSOR


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10i+.O EXECUTION OF PROJECT ANALYSISk.l Statement of Problem and Objectives

We seek a method of comparison for our two alternative output modesof power production (with processed steam output and without) to determinewhich, when applied to a typical dynamic load, will yield the highestefficiency in terms of actual utilized power. The data given by GE andOak Ridge provides the basis for evaluating both power sources along allfeasible operating points [2,3]. By comparing the amount of utilized MW'sfor both steam and electric consiomption, we will be able to determine underwhat conditions each system is the most efficient in addition to comparingboth systems \inder similar operating modes.

k.2 MethodologyThe efficiency calculations for mass data points were carried out

by the two computer programs listed in Appendices A and B.For calculation of the single output electrical efficiency, a simple

program utilizing the straight line segment input-output data for thereactor was formulated. For this study, zero loss due to transmissions

between source and load was assumed. Therefore, the demand applied tothe source was matched directly by the source output in MWe. Three linesegments were used to describe the complete operating conditions forthe source. Data is read in off the card reader in MWe as electricaldemands by consumers for a given time interval. The data is matchedwith a corresponding reactor output in MWt which is used as the basisfor system input power. Efficiency is then calculated by taking theconsumer demands divided by the reactor output power. Each of these


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11The dual load calculation becomes more involved as ve attempted to

match each load characteristic with the appropriate soTorce output whiletrying to maintain a minimum reactor operating level. To achieve this,system data utilizing the modified extraction turbine network describedpreviously was used for locating the appropriate reactor output levelproportional to the steam utilized and electrical demand. Maximimielectrical output from the source was set at 83T.8 MWe. In our calcula-tions, peak demands for electricity did not exceed 837 MWe. Data on theelectric and steam load demands are read in initially as seen in Appendix B.Excessive demand for electricity is then checked. Corresponding heat loadis then calc\ilated from the utilized steam demand read in. This takes intoaccoxont all transmission steam losses from turbine extraction to residentialdelivery. Once the heat load factor is determined, steam generator energymay be calculated in utilizing both the heat load and the current electricaldemand. This calculation determines the reactor power output needed tosupply the desired amount of extraction steam while still allowing theturbine to produce the desired amount of electrical output. A plot of thisfunction reveals the percentage loss in generating ability as larger quan-tities of steam are extracted (Fig. 3) [3].

Efficiency of the system is calculated by combining the utilized steamand electric loads read in, divided by the steam energy generated or thereactor output power. Each of these operating factors is listed in theprogram output along with the corresponding demands shown in Appendix B.This program automatically adjusts the source's output to the particulardemands with the minimum reactor output level.


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12

>occillzucroI--ozUJou.

S 30>-

20

10 -

DUAL SYSTEM

SINGLE SYSTEM\,

' ' ' ' ' ' ' I I I I i_12 2 4 6 8 10 12 2 4 6 8 10 12

A.M. P.M.

FIGURE 6. HOURLY VARIATION IN EFFICIENCY ONDEC. 7 FOR DUAL AND SINGLE FUNCTIONPLANTS


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21Such fluctuations in the dual output system are a result of theefficiency of the steam extraction and heat transfer process.

Examination of Fig. 5> the daily efficiency chart for August 10,reveals even wider fluctuations. As shown previously in Fig. 3, thissystem becomes extremely efficient as more steam is extracted from theturbine cycle, up to the maxim\;mi allowable for minimal electric genera-tion. This study found the early morning hours to be those of greatestsystem efficiency. This was due primarily because of moderate steamdemands and lower electric output. Many people may be running theirair conditioners at almost constant levels from the hours of 11 P.M.to 6 A.M. This, coupled with a possible drop in electric usage fromlighting and appliances after 12 P.M. could provide the necessarycharacteristics needed for improved efficiency. Higher steam demandsduring mid-hours with equally high electric demands forced the generatingplant to full capacity but with reduced overall efficiency. Sustainedhigh electric usage into the early evening hours with a gradual sl\jmpin steam demand due to lowe'r ambient temperatures caused a further dropin the efficiency as the demand curve approached one similar to the

single output system. Significant improvement in system performanceis maintained throughout this period, however.

Fig. 6 shows the corresponding efficiency curve for a typicalwinter day, December 7. The curve is similar in form to the summer onewith shifts occurring during the early morning hours and through theafternoon. Steam usage appears to maintain a much more even demand,since the majority of this is used for home heating (Table h) . Thepeak levels for steam are slightly higher than during the summer but


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22evening levels are significantly higher due to space heating duringperiods of low temperatures. The electric demands seem elevated fromsummer levels hut with much the same proportions. Together these twodemands create a slightly lower system efficiencies during the hours ofT P.M. to 10 A.M. and increasing efficiency during 11 A.M. to 6 P.M.when compared to the summer graph.

Additional consideration in evaluating coal-fired generating plantsas compared to nuclear systems should take into account energy lossdue to chimney heat and the heat exchange process. Conventional fossil-fuel plants release approximately 15 to 20 percent of their totalboiler heat into the atmosphere during steam generation while 5 to 10percent of the total energy in a PWR nuclear steam cycle is lost insteam generation through heat exchangers [h] . By using the proposedsystem of steam for residential use, an additional 5 to 10 percent lossis incurred within the system by using the extra steam generation forthe district heating supply. A comparison of total generating powerbetween the PWR v. fossil-fuel plants reveals a 10 percent improvementin cycle efficiency for the conventional fossil- fuel system, dueprimarily to the use of higher steam temperatures and pressures withinthe system enabling more efficient heat-energy transfers. Because ofthe high risks involved in using high pressure systems in nuclear plants,conventional coal-fired systems are currently able to operate moreefficiently in generating electric power [h] . Direct steam extractionfor the district heating supply in the conventional system will alsoimprove total efficiency by eliminating the lossy heat exchanger usedfor isolation purposes in the nuclear system.


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23Another item to be considered in such a residential heating

system is the possible risk to the population from accidental exposureto radioactive effluents. Studies utilizing statistical and probabal-istic techniques indicate that the possible mortality risk factorassociated with a nuclear as opposed to a coal-fired accident are atleast an order of magnitude larger for typical plant malfunctions orrelease of operational pollutants to the air at the plant site [12].An additional risk factor may exist if such a nuclear accident shouldsomehow cause radioactive particles to be transmitted in such quantityas to deliver harmful doses of radiation through the district heatingsupply to the residential sector. Although the use of a third enclosedsteam system reduces this probability to a minimum, daily low leveldoses and the existence of the threat of nuclear accident and exposuremust be taken into consideration in evaluating such a project. Useof a coal-fired generating plant could eliminate this additional highrisk.

It should also be noted that these results have not been costadjusted, since this study covers an engineering as opposed to aneconomic analysis of power plants. Recent investigations have foundthat fuel and fuel cycle costs associated with nuclear power plantshave risen to considerable levels in recent years making the use ofnuclear as opposed to coal fueled plants highly questionable. Inaddition to these fuel costs are the large capital reqiiirements neededto fund nuclear power systems, all of considerable importance inevaluating proposed power plants [13].


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2kWith increased energy utilization within the pover plant, a vast

decrease in the amount of waste heat results. This means less condenser

water being dumped into lakes and streams, much less. While notcompletely eliminating the problem of thermal pollution from wasteheat, this report shows that the amount which must be eliminated canbe cut by as much as ^G%. Although a city supplied by an electric-steam system may require large alterations in the current system orconsiderable planning for a new city, the possible savings in efficiencyand environmental protection make this plan well worth considering.About fifty large power stations currently supply both electricityand steam for residential and commercial use, the largest beingConsolidated Edison's New York plant which supplies Manhattan [5].Although these are of the coal burning type, a new dual reactor underconstruction in Midland, Michigan, will possess the potential fordelivering I38O MWe for consumer use and large amounts of processedsteam to the Dow Chemical Company by steam extraction for industrialuse [1^].


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256.0 NOTES ON IMPROVEMENT IN PLANT IDLE CAPACITY

Due to the vineven dynamic power demands of consiimers , constant

feedback is necessary within the system to detect these fluctuationsand provide the necessary changes in generation capacity. A majorityof power plants are designed to operate most efficiently in the regionnear maximum capacity. At nimerous periods where less than maximumgeneration is required, efficiency is lost within the system. Becauseof this, it would be much to everyone's advantage to seek out a methodwhereby the load curves would become essentially constant. Thiswould allow our power plants to be designed over a very narrow, highlyefficient operating region.

Upon consideration of this problem and by comparing the results inSection 5-0, we see that the evening period to early morning is one ofdecreased electrical demand. If this curve could be shifted evenlyby dropping peak demand periods with a minimal raising of the slumps,it would be ideal.

Several methods now under consideration or in current use forcoping with this problem and encouraging energy conservation are,adjustments in the utility rate structures, promotional advertisement,and methods for storing potential energy during periods of low consumerdemand

Many state utility commissions have enacted or are studying thepossibility of flattening current rate structures to discourageexcessive power use formerly encouraged by offering lower rates forgreater consumption. This usually involves the use of differentialpeak load pricing for daily and seasonal demands, and marginal cost


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26pricing, as opposed to the more conventional average cost pricing. Thecommissions feel that by flattening residential, commercial, and

industrial rate structures, charging flat rates for excess power levelsand using differential pricing, additional electrical energy conservationcan be achieved vhich may help with the peak loading problem. [15]

Since the energy shortage, utilities have boosted the number ofprom.otional ads for energy conservation, although the net effect ofthese on lowering peak demands appears controversial at this time.The aim of these ads is supposedly to make people more energy consciousand, therefore, encourage better energy conservation. It can bedebated whether or not these ads have done more to promote the utility'sinstitutional image as opposed to helping ease the peak demand problem [l6]

Many research groups, including the Electrical Power ResearchInstitute, Oak Ridge Laboratories, and a number of university researchteams, are currently investigating numberous methods for storing vastamounts of potential energy during off-peak load times to help evenout the demand curve for electrical power plants. Pumped storage ofwater at hydroelectric power plants into reservoirs is already in

use at several sites across the nation [9]. Magnetic field storage ofpotential energy in large superconducting inductors and low frictionmagnetic bearing flywheels appear to offer an efficient method formass energy storage at a possible efficiency of ninety-five percent.Other options including compressed air storage and molten galbers saltheat energy are being investigated and have thus far shown promisingresults on small scale tests. These methods have yet to be installed ona wide scale at existing power plants, but may one day provide an


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27

answer to the fluctuating load problem [IT].These characteristics of uneven demands and idle plant capacities

have existed for decades and appear may continue until such time astechnology allows for the creation of a power plant capable of efficientpower generation along all operating levels, or an efficient, practicalstorage device is found able to handle the excess power demands createdby our fluctuating load factors


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28T.O CALCULATION OF OPTIML OPERATING POINT FOR THE DUAL OUTPUT SYSTEM

Given our system of two variable outputs, we would like to come

to some conclusion as to an optimal operating point, taking into accountenergy costs and profits. An optimal mix of processed steam andelectric output may be calculated utilizing joint products theory.This method will combine a plot of the power plant's possible operatingpoints with a family of curves defined by the energy costs of eachpoint and the revenue generated by each operating point [l8] . Byminimizing energy costs and maximizing profits, two optimal operatingpoints will result, which should coincide if utilities are actuallystriving for maximum energy efficiency with maximum profits.

Fig. T reveals the locus of points for our model plant if maximumpower generation is considered. Revenue maximization will be calculatedfirst. The joint products equation defining profit in terms of theoutput quantities is:

R = p q + p qe e s s

Where R is the total revenue as a function of the quantities of steamand electricity delivered for customer use, q and q , and the pricecharged per quantity of steam and electricity, p and p . To maximizeprofit, we take the derivative of the revenue equation and set it equalto zero. This gives:

dR = pdq +pdq =0e e s ^s-p dq^s _ eP dqe s


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29

800

600

MWe 400

200 -

I I I I I I I L J L400 800 1200 1600 2000MW.

FIGURE 7. OUTPUT LOCUS OF POWER PLANT OPERATING POINTS


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30The ratio of dq /dq defines the slope of all possible revenue

curves which when placed on Fig. 7 determines for any fixed priceswhere the maximum revenue intersection will be with our operatingline. The critical slope is determined by the operating line which,for our example, is equal to -.188. To maximize profits, we find that-p /p must be less than the critical slope if all steam is to bes eproduced and greater than the critical slope if all electricity isto be produced. This is due to the linear operating line which weare using which causes the solution point to lie at one of the twoend points on the line, and the maximum profit being the largestsolution satisfying the revenue equation at a point coincident tothe operating line. As an example, if the average price of electricityis chosen to be $.02TT/KWe and the average price of steam to be$.0058i+/KWt , the slope of the corresponding revenue lines would be-.21 [19]. This indicates the utilities should be producing as muchsteam as allowable \ander technical limitations to maximize profits.If the price of steam is $.0032/KWt and electricity stays the same,-.116 is the revenue slope which says that maximum profit is attained

by producing only electricity.Energy costs are computed in a similar fashion by using an

energy cost equation:

E = cq +cq +bs s e eand comparing to the same operation load line. Slope conditions tominimize energy costs will be directly opposite those for maximizingrevenues. If -c /c is less than the critical slope, all electricitys e


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31should be produced. If -c /c is greater than -.188, maximum steams eshould be produced, b in the energy cost equation represents theenergy cost of capital for the power plant which is taJken to be aconstant and disappears when we differentiate the equation. To findc and c in practical given terms, we analyze our system as follows:s e

E = the total input energy into the systemb = energy cost of capitalQ = total steam produced by the steam generatorsc ' = energy cost of Q steamq ' = quantity of processed steam leaving the plantE' = energy of the processed steam leaving the plantq ' ' = quantity of steam used to drive the turbineE' ' = energy of the steam driving the turbineq ' = quantity of electricity produced at the generatorE' ' ' = energy of the electricity at the generatorq = net quantity of processed steam delivered to the loadq = net quantity of electricity delivered to the loade energy cost of electricity at the generator

E = Q + bsC ' = E/Qs s

E' = C ' q 's sE' = C ' q 's sC = E"/q ' = C ' q "/q 'e ess eE' " = C ' q ' = c ' E"e e e

c q = c 'q ' and c q = c 'q 's s s s e e e ec 'q ' c 'q 's ^s e ec = c =s q e q^s ^e


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32c 'q "q 's s e

c 'q "s s^e

c c 'q ' q q q 's s s e e sc q c 'q ' ' q q ' 'e ^s s s ^s s

If, using our model pover plant, ve assume electrical transmission

losses of Jfo and steam transmission losses of 20^, choose q as I56OMWT and q as 537 MWe from our operating line, we get an energy costslope of -.36. This indicates that maximvim electrical energy shouldbe generated for our case to minimize energy costs.

The optimal operating point is entirely dependent on the linelosses and the rates charged, which may yield a coincident point, butcan be adjusted in this case quite easily to be noncoincident as well.

We realize that our operating line and perhaps our family ofenergy cost and revenue curves will in reality be of nonlinear functionsThis would provide an optimal point other than the end points whichwould take into account all plant losses and internal system costs.We would like to point out, however, that even with our simplifiedlinear model significant results may be obtained concerning the optimaloperating conditions. We found that the prices charged can cause ouroptimal point to move from one end of the line to the other by onlyslight variations well within the boiinds of current national utility

rates [19]. With the line losses and linear approximation of capitalenergy costs, we also find that the utilities are maximizing energyefficiency if they produce only electricity under our model. With


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33better data on the actual operating conditions of the power plant andenergy costs , exact results could he obtained for any pover plant to

determine if the utility's goals of revenue maximization are indeed inconjunction or opposition to the energy cost and efficiency of theplant.


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3i^

Appendix A - Single Plant Output Program

IJOB1 PRINT 102 10 FOBM&T ( ItU. 128( * ) .///.'ilX.'CALCDLAT IQN n^ SINGLE OUTPUT PLANT EF

IF ir If NCY' .///, I'fX, 'CONSUMRH OFMANI) ( MH ) , 20X, ktACT OR OUfPUT (BTUf7


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35

Appendix A (continued)

_ cTLCUr&Tlbrr'OF~"srNGLE~bUTPUT PLANT" FFF IC I ENCYr.QNSllMFR DEMAND (MWJ REACTOR OUTPUT (BTU.S) PLANT EFFICIENCY (PER CENT)

430.00480.00_480.00480. 004?5.004 HO. 00430.00430.00430.00

0.491E 100.491E 100.491E 100.49 IE 100,440E 100.445E 100.445E 100.44SE 100.44&E 10

440.00480.00480.00

0.454E 10J).491 100.491E 10

33.3533.3533.3533.3532.9432.9932.99J2^ 9932.9933.0733.3533.35


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36

Appendix A (continued)

CALCULATION [)F SINGLE OUTPUT PLANT EFFICIENCY'

CONSUMER OFHAND (MW) REACTOR OUTPUT (BTU.SI PLANT EFFICIENCY IPER CENT)

38^.00 0.402E 10 32.57307.00 0.3316 10 31.64283.00 0.309E 10 31.26

288.00 0.3UE 10 31.35398.00 0.415E 10 32.71566.00 0.571E 10 33.8561A.00 0.615E 10 34.07614.00 0.615E 10 34.07600.00 0.602E 10 34.01562.00 0.567E 10 33.83494.00 ^ 0.504E 10 33.45494.00 0. 504E 10 33.45344.00 ^ 0.365E 10 32.13275.00 0.302E 10 31.12258.00 0.286E 10 30.81267.00 0.294E 10 30.98378.00 0.397E 10 __ 32.51525.00 0.533E 10 33.63559.00 _ _ 0.564E 10 33.81559.00 _ 0.564E 10 33.81550.00 0.556E 10 33.77512.00 0.521E 10 33.56 ___4fi9.00 _ 0.481E 10 33.23 , _469.00 0.481E 10 33.28


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37

Appendix B, Dual Plant Output Program

$JOBI PPINT 10I 10 F3HMAT ( IHl, i;?H ( ' * ) ,///,42X, 'CALCULAT ION OF DUAL OOTPur PLANT EFFIId ENr.Y'

,

///.^X.'C'JNSUMCR OFIANll ( 1 WT) ,5X , COrjSVJMeK DbMANO (MWF)'i?()X, 'PeACTUP OUTPUT (MWT) ,1'iX, 'SYSTEM EFFICie;4Clf IPtK CtNTJ',///!

CC CnNSUf'Ek DEMAND INPUT - IN MWT AND MW EC

3 I, BFAO 1 ,F,H4 I FORMAT! ?F7.2) -5 IFIt.EQ.O.) GO TO 56 IF(E.LE. 937.81 GO TO 2 _ .7 E=837.8

C - -C EFFICIENCY CALCULATION

8 2 HL=1.4556*H9 S3E = (E*. 12*HL)/.3 " " __-10 EFF=(EH)/SCE100.11 PKINT 3,H,E,S0E,EFF - - - . . __ _ ..,_..12 3 FQRMAT(l2X,F7.2,l8X,F7.2,23X,F7.2,31X,F6.2,/"13 GO TO * ~~~14 5 PRINT 615 6 FOPMATdHll ^16 STOP17 END ^ ' " ~"

SENTRY


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38

Appendix B (continued)

" - - . . .- CALCULATION OF DUAL OUTPUT PLANT EFFICIENCY

CONSUMCK DEMAND (MWT) CONSUMFR 06M4N3 (MWEJ RLACTOK OUTPUT (MWT) SYSTEM EFFICIENCy (PER CENT

500.00 480.00 1668. 0' 53.73505.00 480.00 1671.20 58.94520.00 480.00 1678.91 59.56520.00 430.00 1678.91 59. 5t.370.00 425.00 1440. US 55.21430.00 430.00 1485.61 57.89460.00 430.00 1501.03 59.29450.00 430.00 1495.89 58. (J3420.00 430.00 1430.48 57.41360.00 440.00 1479.06 54.09408.00 480.00 1621.37 54.77430.00 480.00 1632.67 55.74


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Appendix B (continued)

. _- _. CALCULATION OF DUAL OUTPUT PLANT EFFrCIENCY

CONSUMER DEMAND (MWT) CONSUMER DEMAND (MWE) REACIOh OUTPUT (MWT SYSTEM EFFICIENCY (PER CENT)

420.00 384.00425.00 307.00430.00 283.00490.00 288.00580.00 398.00590.00 566.00570.00 614.00550.00 614.00530.00 600.00480.00 562.00425.00 494.00410.00 494.00330.00 344.00330.00 2^75.00350.00 258.00430.00 267.00540.00 378.00550.00 525.00555.00 559.00550.00 559.00540.00 550.00440.00 512.00370.00 469.00350.00 469.00

1345.18 59.771121.28 65.281053.26 67.691098.79 70.811468. :>6 66.601967.81 58.752098.71 56.422088.44 55.742036.99 55.471899.54 54.861671.28 54.991663.57 54.341181.30 57.06978.36 61.84938.63 64.781006.20 69.271389.18 66.081826.68 58.851929.24 5 7.741926.68 57.561895.07

.

57.521731.93 54.971569.50 53.461559.22 52.33


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REFERENCES

[l] William C. Reynolds, "Engineering Thermodynamics," McGraw-HillBook Co., N.Y., 1970, Ch. 2.

[2] M. K. Morrison, "Heat Rates for Turtine-Generators Applied withStandard APED Reactors," Report from GE Product Planning.Turbine- Generat or Marketing Division, Schenectady, N.Y., I969.

[3] A. J. Miller, H. R. Payne, M. T. Heath, M. E. Lackey, G. Samuels,E. W. Hagen, and A. W. Savolainen, "Use of Steam-Electric PowerPlants to Provide Thermal Energy to Urhan Areas," Oak RidgeNational Laboratories for the U. S. Atomic Energy Commission,Oak Ridge, Tenn. , 1971, Ch. 2, k.3.

[h] John I. Shoule, Environmental Applications of General Physics,Addis on-Wes ley Publishing Co., Menlo Park, Calif., 1975, Ch. ik.

[5] A. J. Miller, "Waste Heat Utilization," Proceedings of theNational Conference, Oak Ridge National Laboratories for theU. S. Atomic Energy Commission, Oak Ridge, Tenn., 1972, pp. 67-71.

[6] L. S. Tong and J. Weisman, "Thermal Analysis of PressurizedWater Reactors," American Nuclear Society, Hinsdale, 111.,1970, pp. 1-13.

[7] W. B. Wilson and D. L. E. Jacobs, "Shortcut Methods of EvaluatingAlternate Steam and Power Supplies for Industrial Plants,"Report from GE Industrial Engineering Section, extracted fromProceedings of the American Power Conference, Vol. XX, 1958.

[8] Garvey, Personal Communication on N.Y. Steam System, ConsolidatedEdison of N.Y., June, 1975.

[9] Communication with Professor Helm, Electrical EngineeringDepartment, University of Illinois, Urbana, Illinois, November, 1975

[10] Miller, "Waste Heat Utilization," pp. 72-75-[11] Miller, Payne, et. al, "Use of Steam-Electric Power Plants,"

Ch. 6.1, 6.2, 6.U.[12] T. H. Lim, "Some Quantitative Risk and Benefit Comparisons

from Generating Electricity of Coal-fired and Nuclear- fueledPower Plants," Department of Nuclear Engineering, Universityof California, Berkeley, California, 1972, pp. 18-20.

[13] Communication with M. Rieber, Energy Research Associate at theUniversity of Illinois' Center for Advanced Computation, Urbana,Illinois, November, 1975.


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[lU] Report on Midland Nuclear Plant, communication from ConsumersPower Co., Jackson, Michigan, July, 1975.

[15] R. Herendeen, K. Kirkpatrick, and J. Skelton, "Energy Conser-vation in Illinois: Report II," Energy Research Group,University of Illinois, Urbana, 111., 197^, pp. 21-23.

[16] Ibid, pp. 29-33.[17] Communication with R. Menendez, Research Assistant for theElectrical Engineering Department at the University of Illinois,

Urbana, 111., November, 1975.[18] J. M. Henderson and R. E. Quandt, "Microeconomic Theory,"

McGraw-Hill Book Co., N.Y. , 1958, pp. 67-72.[19] J. Tanaka, "Formulation of Computer Programs for the Energy

Cost of Living Model," Energy Research Group, University ofIllinois, Urbana, Illinois, 1975, pp. 20-25.


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