strategy op operation and theme for control a …

STRATEGY OP OPERATION AND THEME FOR CONTROL

OF A SOLAR-FOSSIL HYBRID ELECTRIC PLANT

by

KARAN LEA WATSON, B.S. IN E.E., M.S. IN E.E.

A DISSERTATION

IN

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for

the Degree of

DOCTOR OP PHILOSOPHY

Approved

Accepted

December, 1982

f\i^ /'-y fA

TV

ACKNOWLEDGEMENTS

I would like to express my sincere appreciation to

Dr. John D. Reichert and the rest of my committee. Dr.

John Craig, Dr. Wayne Ford and Dr. John Murray, for their

guidance with my research. I am also Indebted to Travis

Simpson who helped make working for the Crosbyton Solar

Power Project such an enjoyable experience.

Very special gratitude is extended to Sandra and Melvln

Branch, Rose Kuehler, Brenda Coker, and Tom Zolnerowlch

for far surpassing the title of friends by helping to get

this paper into print.

I could not finish my acknowledgements without express

ing my gratefulness to my Mother and Father for the strong

foundation they have provided for my life, and offering

my thankfulness to God.

11

CONTENTS

ACKNOWLEDGEMENTS 11

ABSTRACT vli

LIST OP TABLES ix

LIST OP FIGURES x

CHAPTER I THE SOLAR-HYBRID ELECTRIC POWER PLANT 1

CHAPTER II THE PROPOSED POWER PLANT 10

2.1 The Solar Gridiron Concept 11

2.2 Plant Operation 27

2.2.1 Typical Daytime Plant Operation 29

2.2.2 Fossil Fuel Operation 32

2.2.3 Stand Alone Solar

Operation 33

2.2.4 Special Operations 34

2.3 The Plant Equipment 39

2.3.1 Water Treatment Complex 4 0

2.3.2 The Deaerator 4l

2.3.3 The Peedwater Pumps 43

2.3.4 The Trublne/Generator

System 43

2.3.5 The Condenser 46

2.3.6 The Cooling Tower 46

2.3.7 The Auxiliary Superheater... 47

2.3.8 The Steam Storage Tank 4 9

ill

2.3-9 The Desuperheater 49

2.3.10 The Contact Cooler 50

2.3.11 The Fossil Boiler 50

2.3.12 The Plash Tank 53

2.3.13 The Solar Collectors 54

2.3.14 The Solar Boilers 57

2.3.15 The Plant Piping 58

CHAPTER III SOLAR BOILER OPERATION STRATEGY 62

3.1 The Solar Boiler Operation Modes.... 63

3.1.1 The Quality Mode 63

3.1.2 The Default Mode 65

3.1.3 The Auxiliary Modes 66

3.2 The Annual Solar Penetration 68

3.2.1 The Annual Energy Required by the Turbine 68

3.2.1a Continuous Pull Load 70

3.2.1b Daytime Pull Load-Nighttime Half Load. 73

3.2.1c Daytime Full Load-Nighttime No Load... 75

3.2.Id Relationship Between ALERT and Energy Consumption 76

3.2.2 The Annual Energy Captured by the Solar Boilers 80

3.2.2a Power Delivered by the Solar Boilers-Power Tables 84

IV

3.2.2b Frequency Tables-The Bright Eyes Tables 95

3.2.3 Evaluation of the Solar Penetration 102

3.3 The Strategies of Operation IO8

3.3.1 The Q Strategies 109

3.3.1a The QD Strategy Il4

3.3.1b The QAD Strategies.. II6

3.3.1c The QCAD Strategies. 120

3.3.2 The D Strategies 120

3.3.2a The DQ Strategy 126

3.3.2b The DAQ Strategy 127

3.3.3 Comparison of Strategies.... 128

CHAPTER IV TACTICS FOR SOLAR BOILER CONTROL 135

4.1 Basic Control Philosophy I38

4.2 The Control System Model l42

4.2.1 The TMR System Model l44

4.2.1a Model Performance -Small Perturbations. l46

4.2.1b Model Performance -

Large Perturbations. 148

4.2.2 The TMRW System Model l48

4.2.2a Model Performance -Small Perturbations. I65

4.2.2b Model Performance -Large Perturbations. I67

4.3 The Controllers I67

v

4.3.1 The T Controller 172

4.3.2 The M Controller I87

4.3.3 Comparisons Between T and M Controllers 204

CHAPTER V RECOMMENDATIONS 209

REFERENCES 2l4

APPENDIX A THE TMR EQUATIONS 215

APPENDIX B THE TMRP EQUATIONS 217

APPENDIX C THE POWER FACTOR TABLES COMPUTER CODE 219

APPENDIX D STUDY OP NUMBER OP GRIDIRONS TO USE IN

THE PLANT 224

APPENDIX E THE STEAM TABLE CURVE PIT 230

APPENDIX P THE VALVE RESPONSE CURVES 232

APPENDIX G THE CONTROLLER COMPUTER CODE 236

APPENDIX H RESPONSE CURVES FOR VARIOUS CONTROLLERS.. 244

VI

IBSTRACT

The Crosbyton Solar Power Project has proposed a design

for a solar-fossil hybrid elctric power plant„ Tnis plant

will utilize ten Solar Gridirons and a fossil fuel boiler to

produce 5 MWe on a steady and reliable basis. Before the

final design for this plant can be made, detailed

operational procedures must be defined. This study

considers strategies, methods, and procedures for operating

and controlling the Solar Gridiron. Specifically, two

elements of sclar boiler operation were investigated.

The f irst effort was to develop a basis for selecting

the solar boiler operation modes for use under various

conditions. A mode is defined by the state of the fluid

exiting the boilers. A criterion for switching from one

mode to another, in order to improve plant performance, is

referred to as a solar boiler operational strategy. for

this study several strategies were investigated in an effort

to find procedures which provide the most effective capture

vn

, ; * « 5 ^

and u t i l i z a t i o n of s o l a r energy for t h e p l a n t . Severa l

s t r a t e g i e s were found which improve t he expected ^ l an t

performance. However, the f i n a l d e c i s i o n between tnese

s t r a t e g i e s nJust u l t i m a t e l y i n c o r p o r a t e eco:nomic

c o n s i d e r a t i o n s beyond the scope of t h i s s t u d y .

The second e f f o r t r e l a t e l t o b o i l e r o p e r a t i o n ,

considered in t h i s stu(3y, d e a l t with c o n t r o l of the f l u id

through t h e b o i l e r s . A c o n t r o l system provid ing r a p i d , yet

s a f e , c o n t r o l of the s o l a r b o i l e r s i s fundamental ly

d i f f e r e n t t han a c o n t r o l system fo r a f o s s i l b o i l e r . for

f o s s i l b o i l e r s , an o p e r a t o r can c o n t r o l the f i r i n j r a t e to

produce the airount and q u a l i t y of steam d e s i r e d . For s o l a r

b o i l e r s , s o l a r a v a i l a b i l i t y d i r e c t l y i n f l u e n c e s the b o i l e r

ou tpu t , and t h e r e i s no way to e f f e c t i v e l y c o n t r o l the s o l a r

power r each ing the G r i d i r o n . An e f f e c t i v e and v e r s a t i l e

con t ro l scheme for t h e s o l a r b o i l e r s , developed dar ing t h i s

s tudy, i s d e s c r i b e d in d e t a i l .

v m

LIST OP TABLES

3.1 Annual Energy Requirements for the Turbine -ALERT 77

3.2 Power Table: T^^^ = 1000°P 89

3.3 Power Table: T • = 900°P 90

3.4 Power Table: T , = 800°P 9I - out ^

3.5 Power Table: T = 700°P 92

3.6 Power Table: T ^ = 500°P 93

3.7 Annual Frequency Table for March, I98O -

March, I981 99

3.8 December, I98O Frequency Table 100

3.9 February, I98I Frequency Table 101

3.10 Approximate Mode Loss Penalty Factors IO6

3.11 Solar Penetration for Q and D Strategies 132

3.12 Comparison of Strategies 133

4.1 Favorable Parameters for the T Controller 178

4.2 Favorable Parameters for the MController 193

IX

LIST OP FIGURES

2.1 Spherical Reflector Ray Tracing. 13

2.2 Conical Focal Zone with a Cylindrical Receiver 15

2.3 Optical History on an Aligned Receiver for ^ = 0° 17

2.4 The Solar Gridiron 19

2.5 Solar Boiler Efficiency vs Solar Inclination... 26

2. 6 The Proposed Hybrid Power Plant 28

2.7 Fossil Boiler Heating of Solar Boiler Steam Lines 36

2.8 Solar Boiler Heating of Solar Boiler Steam Lines 37

2.9 Water Treatment System 42

2.10 Turbine Steam Requirements for Generating Electricity 45

2.11 Auxiliary Superheater 48

2.12 Fossil Boiler 51

2.13 Proposed Solar Gridiron 55

2.14 Solar Mirror Panel Configuration 56

2.15 Heat Loss in Insulated Pipe Carrying 900°P Steam 59

2.16 Temperature Loss in Insulated Steam Line Between Solar Receiver Outlet and Steam Storage Tanks 60

3.1 Turbine Cycle 78

3.2 ADVS Data and TMR Prediction 86

3.3 Decision Tree for Q Strategies 112

3.4 Annualized Average Power Capture for QD Strategies II5

3.5 Annualized Average Boiler Efficiency for QD Strategies II7

3.6 Annualized Average Power Capture for QAD Strategies II8

3.7 Annualized Average Boiler Efficiency for QAD Strategies 119

3.8 Annualized Average Power Capture for QCAD Strategies 121

3.9 Annualized Average Boiler Efficiency for QCAD Strategies 122

3.10 Decision Tree for D Strategies 125

3.11 Annualized Average Power Capture for QD Strategies With Different Frequency Tables.... 129

3.12 Annualized Average Power Capture for QAD Strategies With Different Frequency Tables (BETs) 130

3.13 Annualized Average Power Capture for QCAD Strategies With Different Frequency Tables.... I3I

4.1 Control Systems for the Regulation of Fluid Temperature at the Solar Boiler Outlet 137

4.2 Solar Boiler Process Loop for the ADVS 139

4.3 Solar Boiler Process Loop for Proposed Plant.. l40

4.4 Control System for a Solar Boiler l43

4.5 Plow Diagram for the TMR System Model 145

4.6 Actual Controller vs TMR Controller l47

4.7 Actual System vs TMR System Large Step Up in M 1 9

4.8 Actual System vs TMR System Large Step Down in M 150

XI

4.9 Actual System vs TMR System Large Step Down

i" IDN 151

4.10 Actual System vs TMR System Large Step Up

i^ ^DN 152

4.11 Plow Diagram for the TMRW System Model 153

4.12 Delayed Valve Performance 156

4.13 Optical History on an Aligned Receiver for xJ2. = 30° 159

4.14 Piecewise Linear Approximation of the Optical Profile on an Aligned Receiver for xJZ. = 0°.... I60

4.15 Actual Controller vs TMRW Controller I66

4.16 Actual System vs TMRW System Large Step Up in M 168

4.17 Actual System vs TMRW System Large Step Down in 11 I69

4.18 Actual System vs TMRW System Large Step Down in I „ 170

DN

4.19 Actual System vs TMRW System Large Step Up

in ^DN 171

4.20 The T Controller 173 4.21 The Response of the T Controller to Large

Step Up in I^^ 179

4.22 The Response of the T Controller to Large Step Down in I„„ I80

DN 4.23 The Response of the T Controller to Large

Ramp Up in I^^ 1^^ 4.24 T Controller Response to Large Ramp Down

in I 1 2 DN

4.25 The Response of the T Controller to Small Past Oscillations in I^^ ^^3

4.26 T Controller Response to Large Fast Oscilla-,. . - r l04

DN

xii

4.27 The Response of the TController to Small Slow Oscillations in I I85

4.28 The Response of the T Controller to Large Slow Oscillations in I_ „ I86

4.29 The Response of the T Controller to Large Step Down in T„ I88

s 4.30 The Response of the T Controller to Large Step

Up in T 189 ^ s

4.31 The M Controller 190 4.32 The Response of the M Controller to Large Step

up i" IDN 19^

4.33 The Response of the M Controller to Large Step Down in I 195

4.34 The Response of the M Controller to Large Ramp

up in IDN 19^ 4.35 The Response of the M Controller to Large Ramp

Down in I ,, 197 DN

4.36 The Response of the M Controller to Small Past Oscillations in I„„ 198

DN 4.37 The Response of the M Controller to Large Fast

Oscillations in I_ ^ 199 4.38 The Response of the M Controller to Small Slow

Oscillations in I .. 200 DN

4.39 The Response of the M Controller to Large Slow Oscillations in 1 ,, 201

4.40 The Response of the M Controller to Large Step Down in T 202

s 4.41 The Response of the M Controller to Large Step

Up in T 203 s

4.42 Alternate Response of the T Controller to Large Step Up in I^^ 206

Xlll

4.43 Alternate Response of the T Controller to Large Step Down in I 207

4.44 Alternate Response of the T Controller to Large Oscillations in I 208

xiv

CHAPTER I

THE SOLAR-HYBRID ELECTRIC POWEB PLANT

Since 1976 the Crosbyton Solar Power Project, CSPP, of

Texas Tech Dniversity has worked on a program to utilize

energy from the sun to produce high quality steam to drive a

turbine-generator for the production of electricity. The

CSPP incorporates the Solar Gridiron concept in the design

of an electric power plant. This concept is also known as

the Solar Bowl and Hemispherical Bowl concept. This concept

is emphasized by the CSPP because i t is one of the most

effective renewable energy conversion concepts providing

electricity to the public. The term effective implies high

technical performance at low costs.

For the private sector, the single most critical factor

for the acceptance of a renewable energy conversion concept

is the resulting price of the energy to be sold. Ti\e

technical aspects, such as efficiency of conversion, are

only important as they effect the cost of the proauct. In

t h i s study only t e c h n i c a l a s p e c t s of the power plant

proposed by the CSPP were d i scussed . In order to make a

comparison of t h i s concept with other renewable energy

conversion concepts a breakdown of the projected l i fe t ime

system costs can be found in CSPP Volume VIII .

The CSPP has already demonstrated the Solar Gridiron

concept with a sub-commercial s ca l e system, the Analog

Design Ver i f ica t ion System, ADVS. This system has been in

operation cont inuously s ince January , 1980. Data col lec ted

on t h i s system were used to ver i fy perfcrraance predic t ion

models of Solar Gr id i rons . Data and experience gained from

the ADVS lead to a prel iminary design of a 5 MWe hybrid

power p lan t . A hybrid plant u t i l i z e s both a renewable

energy source and a convent ional energy source.

All so l a r or wind energy conversion concepts are

handicapped by a low capaci ty f ac to r . Therefore they must

be coupled in some manner with a thermal energy s torage

system, and/or nuclear or f o s s i l fue l e l e c t r i c generation

(CP 8 ) . The ef fec t of thermal s torage on product c o s t s make

a plant which uses convent ional energy sources for backup.

r a t h e r than thermal s t o r a g e , more a c c e p t a b l e . The CSPP

proposes a s i n g l e - s i t e p l a n t for steam g e n e r a t i o n , with

so l a r and f o s s i l e n e r g y , fed t o a common t u r b i n e - gene ra to r

system.

Ten 20C foot d iamete r Solar Bowls have been

incorpora ted in t h e des ign of t h i s 5 MWe power p l a n t . The

ten s o l a r c o l l e c t o r s can p r o v i d e t h e steam t o produce 5 MWe

at peak t imes ( i . e . , op t imal p o s i t i o n and b r i g h t n e s s of the

sun) ; however, a t any o the r t ime t h e d e f i c i t of steam

a v a i l a b l e from the s o l a r c o l l e c t o r s w i l l be made-up by a

f o s s i l - f u e l e d b o i l e r . Because s o l a r b r i g h t n e s s , which can

be a r a p i d l y f l u c t u a t i n g p a r a m e t e r , d i r e c t l y i n f l u e n c e s the

amount of s team the s o l a r c o l l e c t o r s can p rov ide , a steam

s to rage tank i s u t i l i z e d in the p l a n t . The tank a l lows the

f o s s i l b o i l e r t o be tu rned up to c a r r y more load , in the

event of r e d u c t i o n of t he steam from the s o l a r iDoilers,

without d i s r u p t i n g t h e flow of steam to the t u r b i n e . This

tank i s t h e only t h e r m a l s t o r a g e element i n the proposed

s o l a r - f o s s i l hybr id p l a n t .

The goal of t h i s power p l an t i s t o supply as much as

poss ib le of the required load (up t o 5 MWe) from so l a r

energy. The percent of the t o t a l annual required energy

which can be provided by the s o l a r c o l l e c t o r s i s ca l l ed the

solar p e n e t r a t i o n . Once a concept for so la r energy

col lec t ion ( e . g . . Solar Bowls) has been chosen, the plant i s

operated in order t o maximize solar pene t ra t ion . This

maximizing procedure involves : 1) f inding the best modes

( i . e . , the temperature and pressure of the f lu id ex i t ing the

solar b o i l e r s ) ; 2) f inding the bes t s t r a tegy ( i . e . , the

switching from one mode of operat ion t o another) for the

operation of the s o l a r b o i l e r s ; and 3) finding the best

theme for c o n t r o l l i n g the s o l a r b o i l e r s ' output in the

desired modes.

The modes in which t o opera te the so la r bo i l e r s were

cpnsidered when the design of the in t e r f ac ing between so la r

and f o s s i l s i d e s of the proposed plant was done. The so la r

boi le rs in t h i s p lan t must produce steam at 1000°F, 900 psia

in order for the f l u id to go d i r e c t l y t o the steam storage

tank, SST. This i s referred to as the Quality Mode. Any

time the s o l a r b o i l e r s do not operate in the Quality Mode,

the exiting fluid must not be sent to the SST. In these

cases the exiting fluid can be used to preheat the feedwater

to either the fossil boiler or the solar boilers. These are

referred to as default modes. The only other modes in which

to operate the solar boilers that are plausii)le for this

plant are referred to as the Auxiliary Modes. In these

modes superheated steam is produced by the solar boilers but

below 1000°F. This steam must pass through a superheater

(the same one fossil boiler output passes through) before i t

enters the SST.

A strategy for operating the solar boilers establishes

under what solar conditions (brightness and position) to

switch from one solar boiler mode to another in order to

increase annual solar penetration. This study has defined

and analyzed strategies for increasing the solar penetration

of the proposed plant. Statistical data for solar

conditions during the year, March, 1980 through March, 1981,

have been used in the analysis of various strategies. These

data, collected at the ADVS in Croscyton, hdve been

organized in the form of Frequency Tables summarizing solar

brightness and solar inclination correlations. The annual

energy collectable by Solar Bowls is predicted. The plant,

including machine efficiency and operating points, described

in the next chapter was utilized to calculate the annual

energy required. All of this data provides the necessary

basis for calculating solar penetration under various

strategies. One final point which should be recognized is

that a relatively simple strategy for boiler operation is

desired. Nevertheless, the study includes five mode

strategies.

The evaluation of the strategies primarily involves

comparison of the resulting annual solar penetrations.

However, qualitative analysis of parasitics present in

various modes, which do not direclty effect solar

penetration, are also considered-

In calculating the solar penetration of various

strategies perfect control is assumed. That i s , the exact

state called for in a mode of operation is assumed to be

obtained instantaneously and continuously. While this is

the desired response of the system, in order to maximize

solar penetration, i t is not realizable. The control of the

f lu id s t a t e in the s o l a r b o i l e r s i s accomplished oy using a

d i g i t a l computer t o produce ac tua t ing s i g n a l s for the valves

which r egu la t e the amount of water en te r ing each b o i l e r .

The algori thms used in the computer are refer red to as the

c o n t r o l l e r .

The c o n t r o l l e r which allows the s h o r t e s t s e t t l i n g time

in the response of the f lu id s t a t e to any parameter

var ia t ion i s best for increas ing so la r pene t ra t ion .

However, because of the ma te r i a l s of the bo i l e r s and of the

ent i re system, l a rge overshoots cannot be t o l e r a t e d . Even

swings of ^Q% when operat ing in the 1000°F range put

excessive s t r e s s on the ma te r i a l s . Therefore, a c o n t r o l l e r

which minimizes s e t t l i n g t ime, overshoots , and o s c i l l a t i o n s

i s d e s i r a b l e . The I n t e g r a l of the Time mult ipl ied by the

Square of the Error , ITSE, index q u a n t i t a t e s these f ac to r s

well. In t h i s s tudy, a c o n t r o l l e r which minimizes the USE

was des i red .

The s o l a r b o i l e r model developed by Dr. John D.

Reichert and Dr. L. Davis Clements, and expanded to include

the e n t i r e c o n t r o l loop by Reichert and Enayet J iwani , has

8

been employed t o f i n d the b e s t c o n t r o l l e r . This model

i n c l u d e s s o l a r b r i g h t n e s s , s o l a r i n c l i n a t i o n , wind speed ,

and t h e mass flow r a t e of water e n t e r i n g the b o i l e r s . One

more improvement was neces sa ry i n o r d e r t o s tudy t ae

t r a n s i e n t r e sponse of a Solar Bowl sys tem. The t r a n s p o r t

delays as we l l a s t h e energy s t o r a g e c h a r a c t e r i s t i c s of the

system had t o be i n s t a l l e d in the model. This improvement

of t he model was a pr imary goal of the s t u d y .

Once t h e n e c e s s a r y improvements were made i n the system

model, two themes fo r c o n t r o l l e r s were i n v e s t i g a t e d . In the

f i r s t , c o n t r o l of the e r r o r i n the e x i t i n g f l u i d t empera ture

from t h e d e s i r e d ( s e t poin t ) t empera tu re has been ana lyzed .

Such a c o n t r o l l e r i s c u r r e n t l y being u t i l i z e d a t the ADVS.

In the second theme, c o n t r o l of the e r r o r in the mass flow

r a t e from t h e d e s i r e d mass flow r a t e i s s t u d i e d . Tae

des i red mass flow r a t e i s much harder t o determine than the

desired t e m p e r a t u r e because i t i s a f u n c t i o n of txie d e s i r e d

temperature of t h e e x i t i n g f l u i d , the s o l a r b r i g h t n e s s , the

so lar i n c l i n a t i o n , and o the r v a r i a b l e s -

A controller is defined by the theme which i t uses and

the values of gain parameters in the algorithm. Both or the

two controller themes are analyzed for different types of

solar brightness activity, such as large and small steps in

the intensity, rarap-like increases and decreases, and even

sinusoidal variations. Gain parameters which decrease ITSE

are found. At this point a switching function from tneme

to theme or from one value of gain parameters to another has

been devised. The optimum switching function is the

simplest function which significantly reduces the overall

error of the system response.

In the following chapter the hybrid plant proposed by

the CSPP has been described. Chapter III presents the

analytical procedures and results for operating strategies

for the solar boilers. Chapter IV outlines the procedures

and results of the analysis of various solar boiler control

tactics. The last chapter describes the recommended

operation of the 5 MWe hybrid power plant based on the

results found in Chapters III and IV.

CHAPTER II

THE PROPOSED POWER PLANT

The p l an t proposed by the Crosbyton Solar Power

Pro jec t , CSPP, i nco rpo ra t e s t en Solar Gridirons in tandem

with a f o s s i l fueled b o i l e r in order to produce steam for a

tu rb ine-genera tor system. This p lan t would be able to

provide more e l e c t r i c energy than i s present ly consuined by

the c i t y of Crosbyton, Texas. The p l an t i s to ae a unique

i l l u s t r a t i o n of newly developed technology in renewable

energy sources combined with convent ional technology in a

s i n g l e - s i t e e l e c t r i c generat ion system. The CSPP proposed

such a p l a n t , in 1974. Since then the Project has

constructed and operated a sub-commercial sca le Solar Bowl.

This sub-commercial system, known as the Analog Design

Veri f icat ion System, ADVS, has been in continuous operat ion

since January 23, 1980. The data co l l ec ted on the 65 foot

diameter Solar Bowl have been used to confirm the

performance model for Solar Bowls made in 1978. Confidence

10

11

in the system model as well as ADVS experience have allowed

the CSPP to prepare extensive design details for the

proposed 5 MWe hybrid power plant. These details and a cost

analysis of the proposed plant are reviewed in the CSPP

Report Volume VIII. A brief description of the Solar

Gridiron concept incorporated in the plant designed follows.

2-1 The Solar Gridiron Concept

The Solar Gridiron concept incorporates a quartersphere

reflective surface to collect and concentrate solar energy.

This energy is focused onto a solar receiver, or boiler.

The reflective surface does not move. Because the sun moves

some part of the system must move if concentrated energy is

to be captured. In the Solar Gridiron concept the small

solar receiver is the only system component which must track

the sun. The reflective surface, composed of mirror panels,

redirects sunlight passing through the aperture of the solar

collector to the focal region. The spherical nature of the

collector surface results in a line focus when the aperture

is illuminated by a point source. The focal line interval

lies on the line passing through from the center of

12

cu rva tu re of the c o l l e c t o r and t h e c e n t e r of t he s u n . The

focal l i n e i n t e r v a l e x t e n d s from the r e f l e c t i v e s u r f a c e na i f

way to the c e n t e r of c u r v a t u r e . As t h e po in t source moves,

the f o c a l l i n e moves a t the same angu la r r a t e .

The sun i s on ly approx ima te ly a p o i n t s o u r c e . The

ac tua l f oca l r eg ion i s a f rustum of a s l ende r cone wnose

ver tex angle i s e q u a l t o the angu la r s i z e of the sun . Tnis

con ica l f oca l zone i s cen t e red on the foca l l i n e (d i r ec ted

to the c e n t e r of t he sun) and l i k e w i s e moves as t a e s o l a r

pos i t i on changes with r e s p e c t t o t h e c o l l e c t o r s . The s o l a r

r e c e i v e r i s kept in t he f o c a l reg ion in order to cap ture

so la r energy ( f igure 2 . 1 ) .

The t e r m s s o l a r r e c e i v e r and s o l a r b o i l e r a r e often

used i n t e r c h a n g e a b l y . In a more g e n e r a l c o n t e x t , t he name

" rece ive r " should be used, because not a l l a p p l i c a t i o n s

involve b o i l i n g a f l u i d . In the p r e s e n t c o n t e x t , the s o l a r

r ece ive r i s a c t u a l l y formed of two components: 1) the

so lar b o i l e r and 2) the b o i l e r suppor t s t r u c t u r e which

maintains t h e b o i l e r shape or p r o f i l e . The shape i s

important in regard t o c a p t u r i n g t h e concen t ra t ed s o l a r

13

>XIALMAY

center of curvature

R<

nlfLtCTIHO tUfKfACl

. n iCI ivEn

Figure 2.1 Spherical Reflector Ray Tracing

energy from the collector. To produce high quality steam,

the ideal solar receiver would be in the shape of a conical

frustum, matched to a perfectly spherical collector surface.

However, considerable cost savings can be achieved by the

use of a cylindrical receiver in the proposed Solar Bowls.

This means that some of the solar energy directed to the

conical focal region is not intercepted by the solar

receiver. Such a cylinder is illustrated in Figure 2.2.

[The angle is exaggerated in the figure to illustrate the

nature of the mismatched. ] Because perfect mirrors are not

required, the angulor size indicated in Figure 2.2 is

matched to an "effective sun size." It is convenient to

relate mirror surface imperfections to an effective (larger)

size of the solar disk. In other words, i t is convenient

for design purposes to pretend that the mirror surface is

perfect, but that the solar disk is imperfect; surface

errors are mapped to disk errors, effectively enlarging the

solar disk. It is cost effective to use mirror surfaces

with an RMS surface normal deviation of aDout 0.06°. This

provides a focal zone equivalent to that from perfect

mirrors with an effective solar disk diameter of 1 degree

(twice actual size).

a \ ;

V

Angle detemiined/\ by the / \ effective i ^ ;sun size. -^^ .

pd. 1 1 * [Exaggerated.]

EFFECTIVE SUN

15

7K

R

Midpoint of frustrum

/

/

/

/

/

/

Figure 2.2 Conical Focal Zone

With a Cylindrical Receiver

16 4

The concentration factor along the length of the focal

region when the sun is aligned with the aperture normal is

shown in Figure 2.3. Notice the low ratios at the end of

the receiver near the reflective surface. Due to lower

concentration ratios in the focal region near the reflective

surface, the mismatch between receiver shape and focal

region does not result in significant losses in total power

capture. Since the cylinder is slightly too large at the

top, the peak concentration is slightly reduced.

The support structure of the receiver is covered by

helically wound parallel tubes which compose the solar

boiler. Water is pumped through these tubes from the

bottom, the end nearest the mirrors, of the receiver to the

top, the end nearest the center of curvature of the Bowl, of

the receiver. The temperature of the fluid exiting the

solar boiler can be regulated by the mass flowrate of the

feedwater.

The position of the sun not only establishes where tae

solar receiver must be positioned, but also the total amount

of sun light which reaches the collector's reflective

I

17

O

+-> fO S-

-M

QJ

o-C_3 to

12 V

o

O t

p-CD Lf)

OJ JD 13

4-)

O S-o OJ r-^ r— .

•r— O

JD

S-03

f —

o O (/) LO r-H CU

J Z +J

en c o

1 ^

CD rO , C 3

CM O) ( J fC '—-

M - +-> S- CU =5 O) to ^ -

S-o O IT) +-) <N O

O) 1 —

r— o o OJ

o x : o +J CO

E o s

M-

(U CJ c

o fC i n + J ro CO

o , o J-

II

%-O

4 -

J-

> o OJ

cc • u cu c CD

ro

c o >> J-o

+-> (/)

«3

u

Q-O

CO

CM

O) J-

C7)

o in

oos 0S2

18

surface. The power en te r ing the bowl depends on the

aperture which the sun sees (Figure 2 . 4 ) . The aper tu re

appears pe r f ec t l y c i r c u l a r to the sun, due to per fec t

alignment along the ape r tu re normal, a t only two moments

during each year . This i s because the sun must not only be

in the proper plane with regard to the time of day

(east-west) , but a l s o in the proper plane with regard to the

day of the year (nor th -sou th) - The angle between the

aperture normal and the ray through the c o l l e c t o r center of

curvature and the cen t e r of the solar d isc in ca l l ed the

inc l ina t ion ang le , v=Jc_ . The aper ture area which the sun

sees i s e l l i p t i c a l most of the time and can be found by:

Aperture Area t he Sun sees

= (the c i r c u l a r aper tu re area) cos J 2 . . (2.1)

The c i r c u l a r aper tu re area has a 200 foot diameter for

the power g r i d i r o n s proposed for the Crosbyton p lan t . The

sub-commercial s c a l e ADVS has an ape r tu re diameter of

65 fee t . The value of Uc depends on the time of day, day

of the year, and l oca t i on and geometry of the Solar Bowl.

The i n c l i n a t i o n angle may be obtained from the formula:

19

c o J-

s-fO

o c/)

<u JZ

m

c\j

S-ZJ

U -

20

cos yJl_ = cos 6 c o s (x-y) COSx + s i n 6 s i n (A-y) (2.2)

where

6 = s o l a r d e c l i n a t i o n a n g l e (from c e l e s t i a l

e q u a t o r ) and i s e s s e n t i a l l y c o n s t a n t f o r any g iven

day [ V a l u e s o b t a i n e d from an Ephemer is t a b l e . J;

X = l a t i t u d e of t h e c o l l e c t o r s i t e (33.625 d e g r e e s

a t Crosyb ton) ;

Y = t h e t i l t a n g l e of t h e bowl , t h e a n g l e t h r o u g h

which t h e a p e r t u r e normal i s t i l t e d s o u t h of

v e r t i c a l ;

T = l o c a l a p p a r e n t t i m e ( t h e hour a n g l e of the sun

wi th r e s p e c t t o t h e l o c a l mer id ian ) .

The S o l a r G r i d i r o n s a r e t i l t e d t o improve a n n u a l s o l a r

c o l l e c t i o n . In t h e n o r t h e r n h e m i s p h e r e a s o u t h e r n t i l t i s

d e s i r a b l e . A t i l t e q u a l t o t h e l a t i t u d e of t h e bowl would

maximize a n n u a l e n e r g y c a p t u r e . At t h e Crosby ton l a t i t u d e ,

a t i l t of 15 d e g r e e s w i l l p roduce 85% of t h e pe r fo rmance of

a c o l l e c t o r t i l t e d t o t h e f u l l l a t i t u d e a n g l e . E f f e c t i v e

cos t r e d u c t i o n i s a c h i e v e d by s e l e c t i n g the t i l t a n g l e t o De

about 15 d e g r e e s .

21

The performance of a Solar Gridiron i s determined by

uncontro l lable f a c t o r s such as so la r pos i t i on , so la r

i n so l a t i on , and wind speed, and a lso by c o n t r o l l a b l e f a c t o r s

such as Gridiron design and maintenance, and mass f lowra te .

All of these f ac to r s are encompassed in the system model

developed for Solar Gridirons by the CSPP. The model i s

used to determine the amount of s o l a r power which i s

t ransferred t o , or captured by the bo i l e r feedwater.

The power captured by a s o l a r bo i l e r i s the amount of

power, Pp, t r an s f e r r ed i n t o the working f l u i d . Dr. L.

Davis Clements and Hariharan Shankar developed a computer

simulation which modeled the performance of Solar Gridiron

Boi lers . This model, r e f e r r ed t o as the Taermal Fluid

Analysis Program, TFAP, takes in to account parameters such

as: wall shape and t h i cknes s , m a t e r i a l s , pressure

var ia t ions , gas a c c e l e r a t i o n , f r i c t i o n f a c t o r s , void

f rac t ions , c e n t r i f u g a l e f f e c t s , l i qu id forced convect ion,

steam superheat ing , and film boi l ing (HS). The TFAP model

uses as i n p u t s : feedwater i n l e t temperature and p res su re ,

wind speed, phys ica l Solar Bowl parameters, d i r e c t normal

inso la t ion , as well as energy concentra t ion p r o f i l e s along

22

the r e c e i v e r . These p r o f i l e s of energy along the rece iver

were ca lcu la ted for various i n c l i n a t i o n angles by the

Approximate Azimuthal Average Approach, AAAA, computer code,

developed by Cr. John D. Reichert and Hipsua Leung (HL) .

Such p r o f i l e s are shown in Figure 2 . 3 . The TFAP model uses

these inputs for var ious mass f lowrates and i n c l i n a t i o n

angles to determine Pp.

Dr. John D. Reichert made "phenomenological" curve f i t s

to the data generated by the TFAP model in 1978 (EC). These

curve f i t s a r e r e f e r r ed to as the TMR equations and are

shown in Appendix A. The TMR equat ions model the power

captured by the f lu id in a so lar oo i le r with five

parameters. These parameters are the Solar Bowl attendance

fac tor , a ( u n i t l e s s ) , the d i r e c t normal i n s o l a t i o n ,

IrjM (KW/m ) , the s o l a r i n c l i n a t i o n angle , ^Jl- (degrees) ,

the wind speed, V (mph), and the mass flowrate of f lu id w

through the r e c e i v e r , M(lbm/hr). The attendance fac tor takes

in to account so lar energy losses which occur before the

energy reaches the s o l a r b o i l e r wal ls . Parameters such as

mirror r e f l e c t i v i t y , f r ac t ion of r e f l e c t o r surface shadowed,

receiver t r ack ing accuracy, and boi ler wall ab so rp t i v i t y are

23

a few of t h e f a c t o r s considered in a - An accura te

" t h e o r e t i c a l " value of a may be pred ic ted for a Solar

Gridiron once the f i n a l design i s complete. The measured

values observed for t h i s a w i l l vary only as tne system

qual i ty parameters change ( i . e . , mirror surface may become

d i r t y , thus decreasing r e f l e c t i v i t y ) . The value of a can be

considered as a very slowly varying function (constant for a

whole day) during normal Solar Gridiron opera t ion .

The a predic ted for the 65 foot diameter bowl at the

aovs was

oiju = 0-686.

For the pre l iminary design of the 200 foot diameter

gr idirons for the proposed p lant

"TH = 0 . 7 2 4

These ca lcu la t ions a re found in CSPP Volume 7. The r a t i o of

the actual a t tendance fac to r for a Bowl to the predic ted

attendance fac tor i s c a l l ed the spec i f i c a t tendance, a . Ihe

24

s p e c i f i c a t t e n d a n c e fo r the ADVS i s u s u a l l y between 90% and

1005i.

The TMR e q u a t i o n s f ind Pp by keeping an account of the

d e s t i n a t i o n of a l l of t he power, PJM* which e n t e r s the Solar

Gridiron a p e r t u r e .

where

AjP = nominal g r o s s ( c i r c u l a r ) a r e a of a p e r t u r e

Ip,., = d i r e c t normal i s o l a t i o n DN

\SL = i n c l i n a t i o n a n g l e

Then t h e power which r e a c h e s t h e s o l a r b o i l e r , w a l l s , P|,, i s

given by

P„ = a B j ^ , J L ) P i , . (2-a)

Where B ( o2-) ( r e f : Appendix A) i s a f u n c t i o n a c c o u n t i n g

for m u l t i p l e r e f l e c t i o n s of t h e s o l a r e n e r g y by t h e m i r r o r s .

F i n a l l y t h e power i n t h e f l u i d , P p, i s g i v e n by

P = a P J2.5) F " F W

25

where Op is the "fluid power captured factor", a complicated

function which models the solar boiler efficiency. The Or-

factor accounts for the radiative and convective losses of

the boiler.

Figure 2.5 illustrates the dependence of Or on several

of its parameters. For an insolation of 912 W/m , each

curve in the figure represents a different outlet

temperature of the solar boiler fluid. The vertical dashed

line on the graph shows that the boiler efficiency can be

varied, for constant solar insolation and inclination, by

changing the outlet temperature. A change in outlet

temperature is accomplished by manipulating the feedwater

mass flowrate. The management of the value of o^ ^s one

concern in the development of stategies for operation of a

solar electric power plant. The feedwater control in the

process loop must be accomplished in such a way that the

boilers perform as effectively as possible, consistent with

the function of the plant.

Because the performance of a Solar Gridiron system

depends on many uncontrollable factors, an electric power

26 Lf)

CVJ

LO

in C>J U 3

LO

LO

LO

CM LO

LO

LO

CM

LO

CO

LO 32

.

to O)

gre

(de

LO

CM

LO

CM CM

LO

LO

*

CM

LO

LO

CM

c:

CJ

o CO

(/) >

u c <u

•r—

o

o CO

i-

o CO LO

CM

(U S-3

cn

A'ouapL^j.3 jaL.Loa -i LOS

27

plant system must have the support of either an energy

storage capability or a reliable and controllable companion

energy source. The plant which CSPP has proposed utilizes

fossil fuel as a campanion energy source.

A schematic of the proposed Solar-Fossil Plant is shown

in Figure 2.6. There are various ways in which the plant

may be operated. The choice of how to operate the plant

depends greatly upon solar conditions. The path which the

feedvater takes to reach the turbine i s determined by how

the plant i s being operated. A description of plant

operation under various conditions follows.

2-2 Pl nt Operation

Steam for the turbine can be supplied completely by the

solar boilers, or completely by the fossil fueled boiler if

necessary. Typical daytime operation utilizes steam

provided both by the solar boilers and by the fossil fueled

boiler. There are special operational procedures which must

be observed during start up and shut down of the solar

boilers and at nighttime. These special procedures are

described in a subsequent section.

28

c

S -

o a.

$_

>> zc •o (/) o Q . O s -D-

CM

Qi J -

cn

29

2 . 2 . 1 T y p i c a l Dayt ime P l a n t O p e r a t i o n

During t y p i c a l day t ime p l a n t o p e r a t i o n , some

s u p e r h e a t e d s t e a m i s p r o v i d e d by t h e s o l a r b o i l e r s and t h e

r e s t i s p r o v i d e d by t h e f o s s i l b o i l e r . The p a t h of t h e

feedwater can be t r a c e d on F i g u r e 2 - 6 . The f e e d w a t e r f o r

t h e b o i l e r s i s p r e s s u r i z e d by t h e f e e d w a t e r pumps. The

f l o w r a t e t o each b o i l e r i s r e g u l a t e d by v a l v e s c o n t r o l l e d ijy

a computer o r s e n s o r s . Va lves on t h e i n l e t s i d e of t h e

s o l a r b o i l e r s a r e c o n t r o l l e d t o r e g u l a t e t h e t e m p e r a t u r e of

t h e e x i t s t e a m . The f l o w r a t e of f e e d w a t e r t o t n e f o s s i l

b o i l e r i s r e g u l a t e d by a v a l v e which r e s p o n d s t o a water

l e v e l s e n s o r i n t h e b o i l e r drum.

The s t e a m p r o d u c e d by t h e v a r i o u s b o i l e r s i s combined

in t h e steam s t o r a g e t a n k . The tank a l s o p r o v i d e s b u f f e r

s t o r a g e ; i . e . , s e r v e s a s a s m a l l energy s t o r a g e d e v i c e which

wi l l p e r m i t t ime f o r t h e f o s s i l b o i l e r t o i n c r e a s e i t s

f i r i n g r a t e , whenever s o l a r s t eam p r o d u c t i o n d r o p s , w i t h o u t

i n t e r r u p t i o n of t h e s t eam flow t o t h e t u r b i n e .

The f i r i n g r a t e of t h e f o s s i l b o i l e r chaa;^es i n o r d e r

to m a i n t a i n a s e t v a l u e cf t h e p r e s s u r e i n t h e s team s t o r a g e

30

tank. The set-point value is approximately 300 psi above

the pressure required at the turbine inlet. The pressure in

the steam storage tank also determines the pressure of steam

exiting the solar boilers. Thus, solar boiler exit pressure

is determined and regulated by the fossil boiler.

An auxiliary superheater lies in the flow path between

the boilers and the steam storage tank. This superheater is

necessary in crder to control and maintain the temperature

of steam entering the steam storage tank at a set value.

This set-point value i s about 50°F above the desired turbine

inlet temperature. Fossil boiler steam requires the

auxiliary superheater because the boiler itself works to

regulate steam pressure, not the temperature. Solar boiler

steam temperature is regulated by feedwater flowrate

control. However, i t i s more effective under some solar

conditions, due to solar boiler efficiency, Or , to produce

steam at temperatures lower than required by the steam

storage tank. If the solar steam is at tne desired

temperature, it is sent directly to the steam storage taD/..

If the solar steam needs additional heating, it passes

through the auxiliary superheater.

31

The steam which enters the turbine must be finely

controlled. The steam storage tank absorbs many of the rapid

transients in the steam state. The pressure of the turbiiie

inlet steam is fine tuned by the sensor controlled valve

following the steam storage tank. The temperature of the

turbine inlet steam is fine tuned by the desuperheater

preceeding the turbine. Precise control of the temperature

is obtained by a spray of feedwater, at 219°F, into the

steam exiting the steam storage tank.

Finally, steam passes through the turbine-generator

system. The flowrate through the turbine is controlled by a

governor. As the load on the generator varies the flowrate

through the turbine varies. The flow through the turbine

exits at a lower temperature and pressure than i t entered,

but i t is s t i l l steam. The steam exiting the turbine enters

the condenser where i t is condensed and cooled- This

condensate is then returned to the deaerator before i t is

cycled through the plant again.

32

2-1-2 Foss i l Fuel Operation

The p l an t can opera te in a mode in which the f o s s i l

fueled bo i l e r provides a l l of the t u rb ine steam. At such

times, the so la r b o i l e r s may be completely shut down or may

be producing hct water , r a the r than steam. If tae so la r

bo i l e r s a re shut down, during nightt ime operat ion for

example, the feedwater i s p ressur ized by the feedwater

pumps, and sent to the f o s s i l b o i l e r . The flow and i t s

control are ca r r i ed out in the exact ly the same manner as

for t y p i c a l daytime opera t ion , except tha t no steam i s

contributed by the s o l a r b o i l e r s . If the solar iDoilers are

operating as p rehea t e r s for the f o s s i l b o i l e r s , during low

insolat ion per iods during the day, for example, much or a l l

of the f o s s i l b o i l e r feedwater wil l pass through the so la r

boi le rs f i r s t . The water en ter ing the f o s s i l oo i l e r should

be at l e a s t 50°F below s a t u r a t i o n in order to prevent

excessive noise in t h e b o i l e r drum. Therefore, the fluid

exit ing the so la r b o i l e r s passes through the contact cooler

so t ha t the water can be cooled, if necessary, oefcre

entering the f o s s i l b o i l e r . The water i s evdporated and

superheated in the f o s s i l b o i l e r . Less f o s s i l fuel i s

33

required since the water has been preheated- The path of

the steam exiting the fossil boiler is identical to the path

followed when preheating is not available.

2.'1*1 Stand Alone Solar Operation

Only on rare occasions will the plant operate with

steam produced only by the solar boilers. Even when solar

conditions are sufficient for the solar boilers to provide

the required turbine steam load, the fossil boiler snould

not be completely shut off. Unlike solar boilers, fossil

boiler wall materials are not designed to endure frequent

thermal transients. Additionally, if the fossil boiler were

completely shut off and solar steam production was

interrupted, due to clouds for example, i t would take over

30 minutes to bring the fossil boiler up to handle the load.

Such operation would necessitate a huge steam storage

capacity in order to avoid interrupted service. Therefore,

the fossil boiler, should always operate and maintain i ts

temperature, even if i t is producing only a minimal amount

of steam. In the event of a fossil boiler failure, or

during a maintenance cycle, however, the solar boilers could

34

s t i l l opera te if s o l a r cond i t ions warranted. The feedwater

flowrate to the s o l a r b o i l e r s would be con t ro l l ed to

regulate t he steam temperature . The steam s torage tank

would s t i l l be used, and the a u x i l l i a r y superheater would

increase the economy of operat ion if used. The pressure

would be regula ted by the valve following the steam storage

tank ins tead of by the f o s s i l b o i l e r . The steam would flow

through the desuperheater , the t u r b i n e , and in to the

condenser. In t h i s operat ion mode, there i s no back-up for

the so la r b o i l e r s other than the small buffer provided by

the steam s to rage tank . Thus, any i n t e r r u p t i o n s of more

than a few minutes would i n t e r r u p t the p l a n t ' s e l e c t r i c a l

output. The p lan t i s designed to allow stand-alone

s o l a r - e l e c t r i c opera t ion on occasion, but not for basel ine

operation in such a mode.

2.2.JI Special Operat ions

At c e r t a i n t imes spec ia l ope ra t iona l procedures must be

followed to insure smoother system performance. These

procedures do not necessa r i ly have d i r ec t influence on the

p lan t ' s e l e c t r i c a l production, and therefore have been

35

neglected in the r e s t of the s tudy . However, they w i l l be

br ief ly reviewed h e r e . One of these procedures i s required

during the s t a r t up of the s o l a r b o i l e r s every day. ihe

insulat ion of the piping car ry ing steam from the so la r

boi lers has a heat s to rage capac i ty . If these pipes are

cold when steam f i r s t s t a r t s through them, the in su la t ion

will rob much of the s t eam ' s energy before i t can reach the

res t of the p l a n t . This could even r e s u l t in sa tura ted

rather than superheated f l u id reaching the p lan t .

Therefore, t he steam pipes must kept up to temperature a l l

night or must be heated every morning before the so lar

boi lers can provide steam for e l e c t r i c a l production. Tnese

pipes may be heated by passing steam from the f o s s i l bo i l e r

through the pipes and slowly bleeding i t out near the solar

bo i l e r s . Another method of hea t ing the pipes i s t o cycle

solar boi ler fluid through the steam pipes but not in to the

steam s to rage tank (or a u x i l i a r y superheater) u n t i l

superheated steam can be assured. In t h i s case tae so la r

boiler output completely bypasses the turb ine and re tu rns to

preheat the f lu id a t the s o l a r b o i l e r i n l e t . These

operational procedures are i l l u s t r a t e d m

Figures 2.7 and 2. 8.

36

</) <v c

0)

in s -0)

o CO J -ro O

t/7

cn e rC

o CO

to o

CM

$-3 cn

37

1/1 (V c

Qi

t o

J-<v

o CO i-rm

'o

o CD

ro (U zc i.. Qi

O

s -

ro

O to

00

CM

Q} J -Z3

cn

-•^^iSemu^

38

During cold weather a s p e c i a l procedure i s required to

insure t ha t no water f reezes in the s o l a r b o i l e r s a t night .

One method i s to completely dra in the f l u i d out of the so lar

bo i l e r s . A l t e r n a t e l y , warm water can be c i r cu l a t ed through

the so l a r b o i l e r s . There i s a bypass l i ne (not shown in

Figures 2.6-8) through which s o l a r b o i l e r feedwater can be

directed i n t o a heat exchanger assoc ia ted with the

condenser. Such water i s heated by ex t r ac t ing waste heat

from the t u r b i n e exhaus t , thus reducing the work load of the

cooling tower . The heated water can be cycled through the

solar bo i l e r s to e l imina te the danger of f reez ing . i f t h i s

option i s used the cooling tower water c i r c u l a t i o n can be

reduced or even s topped , depending on the amount of steam to

be cooled. This method i s a t t r a c t i v e i f the f o s s i l bo i le r

i s operat ing; i . e . , i f the p lan t i s operat ing a t n igh t . If

the fo s s i l bo i l e r i s not opera t ing , then there wi l l be no

exhaust steam to cool in the condenser. Thus, there would

be no hot water to c i r c u l a t e through the so la r b o i l e r s .

Under freezing c o n d i t i o n , one would then have to c i r c u l a t e

unheated water or dra in the r ece ive r s .

39

These e x a m p l e s of s p e c i a l o p e r a t i n g c o n d i t i o n s a r e

given t o i n d i c a t e t h a t c o m p l e t e p l a n t pe r fo rmance i n v o l v e s

many f a c t o r s — n o t j u s t t h e f a c t o r s d i r e c t l y i n f l u e n c i n g

e l e c t r i c a l p r o d u c t i o n . However t h e a n a l y s i s of p l a n t

performance made i n s u b s e q u e n t c h a p t e r s i s n o t conce rned

with t h e s p e c i a l o p e r a t i o n p r o c e d u r e s .

Z'A The P l a n t Equipment

Only a few p i e c e s of equipment have t o be used in t h e

p lan t t o merge t h e s o l a r s i d e of t h e p l a n t wi th t h e f o s s i l

s i d e . Much of t h e equipment i s s h a r e d by the two s i d e s of

the p l a n t . This i s an a d v a n t a g e of a s i n g l e s i t e with

renewable and c o n v e n t i o n a l e n e r g y s o u r c e s .

The major p i e c e s of equ ipmen t s h a r e d by t h e two s i d e s

of t h e p l a n t a r e : t h e wa t e r t r e a t m e n t complex , the

feedwater d e a e r a t o r , t h e f e e d w a t e r pump, t h e t u r b i n e -

g e n e r a t o r s y s t e m , t h e c o n d e n s e r , t h e c o o l i n g t o w e r , t h e

a u x i l i a r y s u p e r h e a t e r , and t h e c o n t r o l s y s t e m . The

equipment whose s o l e pu rpose i s t o s u p p l y an i n t e r f a c e

mechanism between t h e s o l a r and f o s s i l s i d e s of t h e p l a n t

a r e : t h e s t e a m s t o r a g e t a n k , t h e d e s u p e r h e a t e r , t h e c o n t a c t

40

cooler, and the heat exchanger associated with the condenser

(mentioned in the preceeding subsection) . This leaves the

fossil boiler and flash tank on the fossil side, and the

Solar Bowls on the solar side. Brief descriptions of each

of these major pieces of equipment follow.

2.3.1 Water Treatment Complex

Service water from the city water supply is used for

make up water for the solar boilers and fossil boiler, to

supply the cooling tower water, and for domestic use at tae

plant site. The water is prefiltered by three charcoal

filters to remove chlorine, iron and rust, and other solids.

All the water is then treated in a demineralizer utilizing

an electro dialysis process. Chemical feeds are eliminated

during this stage. This water is then stored in an

intermediate storage tank.

Some water from the intermediate storage tanK is

utilized in the cooling water tower. In addition, some of

the water from the intermediate storage tank passes through

a softener to a reservoir for domestic services and for the

cleaning the gridiron mirror surface.

4 1

Boilers requ i re a high q u a l i t y water. The in termedia te

storage tank water t o be used by the b o i l e r s passes through

two ion exchange p o l i s h e r s which remove pos i t ive ly charged

ions and nega t ive ly charged ions from the water. This water

i s stored in a 10,000 gal lon tank and i s refer red to as the

make-up water . The water t reatment complex i s i l l u s t r a t e d

in Figure 2 . 9 .

2.3.2 The Deaerator

The deaerator removes a i r and noncondensible gases from

the boi ler feedwater. A s torage tank in the deaerator i s

maintained a t a cons tant water leve l by a con t ro l valve

operated in response t o a leve l cont ro l f l o a t . Therefore,

laake-up water can be added to the condensate from the

condenser to compensate for f o s s i l bo i l e r blowdown and other

system l o s s e s . Ext rac t ion steam from the turbine i s used to

heat the make-up water and condensate in a preheating

compartment. This water i s heated nearly to boi l ing

temperature t o remove the bulk of the noncondensiDle gases.

The water then passes through t r ays t o complete deaera t ion

before going to t he deaera tor s torage tank.

42

c c

•«< o

>•

o o. ca

o »- o > -O u l •— «rt

o> c a.

o -x o — «j a:

Q

E?8

—v

V

0 0 •»-» »^ 0

m o

^ L 1

/ f I i

-/

1

f , I '

f .

ectr

oc

&U

1

i on

F1U

j a

1

i

^

i

1 -m 0

^ «< «

0 • <

GC O O

3

o o. — 1 - 0

— CO

o u>

Q

1- o > ^ » « O

.— o -o • • ^ cn t/> ^^

TJ C w o

5 ^

(U 4->

CO

C

 o

o

43

2 .2 -1 The Feedwater Punrs

Three v e r t i c a l , s i n g l e s t a g e c e n t r i f u g a l pumps a r e

mounted in p a r a l l e l under t he d e a e r a t o r . Two of t he pumps

each handle ha l f of t h e feedwater flow for t he f o s s i l and

so lar b o i l e r s . The t h i r d pump i s on s t andby , and

au tomat i ca l ly s t a r t s on l o s s of e i t h e r one of the o p e r a t i n g

pumps. Since the pumps supply both f o s s i l and s o l a r

b o i l e r s , they o p e r a t e a t n e a r l y c o n s t a n t ou tpu t , r e g a r d l e s s

of t he s p l i t between f o s s i l and s o l a r p o r t i o n s . The nominal

o u t l e t p r e s s u r e of t h e pumps i s 1500 p s i a , in o rde r t o

supply the p r e s s u r e drop through the s o l a r b o i l e r s . The

f o s s i l b o i l e r does not have as g r e a t a p r e s s u r e drop as the

so lar b o i l e r s , so t h e e x t r a p r e s s u r e i s dropped a c r o s s a

feedwater va lve in f r o n t of the f o s s i l b o i l e r .

2'!'a The T u r b i n e / G e n e r a t o r System

The steam t u r b i n e o p e r a t e s a t a c o n s t a n t speed t o d r ive

the e l e c t r i c gene ra to r with a cons t an t frequency o u t p u t . A

tachometer on the t u r b i n e works i n con junc t ion with the

turbine governor t o c o n t r o l t h e steam f lowra te so t h a t a

constant t u r b i n e speed w i l l be maintained even under vary ing

generator l o a d s .

44

The steam t u r b i n e i s a key element of the system,

because the turb ine e f f ic iency determines the amount of

e l e c t r i c a l output which can be generated by the ava i l ab le

steam. In other words, i f the t u rb ine e f f ic iency i s

extremely low, more so la r b o i l e r s or a l a rger f o s s i l boi ler

might be requi red t o obtain a net output of 5 MWe.

Off-the-shelf t u rb ine designs were s o l i c i t e d by FW Energy

Applicat ions, I n c . , of Livingston, New Jersey and examples

of i n l e t steam f lowrate requirements are shown in

Figure 2.10. These t r u b i n e s requi re an i n l e t steam s t a t e of

850°F, 900 p s i a . Even though tu rb ine 2 in the Figure looks

to be more d e s i r a b l e due to a higher e f f ic iency , cost

considerat ions may make turbine 1 a be t t e r choice.

Therefore both of these tu rb ines are considered in the plant

analysis in Chapter I I I .

The generator proposed for the p lant i s a 6,000 KW,

3 phase, 60 Hz, 2 .5 KV, 7,500 KVA ,b rush le s s , synchronous

generator. A 6 MWe generator i s used so tha t a t l e a s t 5 MWe

net can be de l ive red to the power gr id a f t e r accounting for

the operat ing load of the p l a n t . The generator con t ro l unit

adjusts the genera tor output to conform in frequency, phase,

and voltage a s requi red by the u t i l i t y power g r i d .

45

E JP

O, O o

5 o

-E ta 0) -M to

O)

o

c JO u 3

l="Standard" turbine at 900 psia and 850°F

2=Special turbine at 900 psia and 850°F"

oL 1 2 3 4 5 6

Gross Generator Output. HW a t 0.8 PF

Figure 2.10 Turbine Steam Requirements for Generating Electricity

46

2.3-5 The Condenser

The condenser withdraws steam from the turbine ex i t and

condenses i t by r e j e c t i n g heat to the cooling tower water.

The condensate i s c o l l e c t e d in a hot wel l , a v e r t i c a l tank

located below the main condenser. Two pumps operate in

p a r a l l e l , responding t o a l iqu id l eve l sensor in the hot

well t o con t ro l the flow of condensate t o the deae ra to r . A

third pump i s a v a i l a b l e on standby. The temperature of the

condensate in the hot well i s con t ro l l ed by the flowrate of

the cooling tower water .

2.J.6 The Cooling Tower

The cooling tower cools the cooling tower water. The

flowrate of the cool ing tower water i s varied by a con t ro l

valve to r egu la t e the temperature of the condensate in the

condenser hot wel l . Three pumps pressur ize the cooling

water. Two of the pumps serve as 50% flow pumps, and tne

third pump i s on s tandby.

The cooling tower i s a dual module double-flow tower.

The tower has two 40 Hp 2-speed fans . Cooling water i s

cooled with a i r by r e j e c t i n g heat t o the atmosphere. The

47

cooling tower has a cont inuous blowdown of ^% to maintain

water q u a l i t y . There i s a l s o a 2% water l o s s t o evaporation

and a 0.255 l o s s t o d r i f t . These l o s s e s amount to anout

90,000 Ibm/hr and are compensated with water from the

intermediate s torage tank of the water t reatment system.

2.3.7 The Auxil iary Superheater

The function of the a u x i l i a r y superaeater i s to provide

steam at a constant temperature to the steam s torgae tank,

SST. Or ig ina l d i s cus s ions considered only f o s s i l boi le r

steam enter ing the a u x i l i a r y supe rhea te r . However, plans

for r a i s ing l e s s than SST qua l i ty steam proauced by the

solar b o i l e r s to the appropr i a t e temperature with the

auxiliary superhea te r have been made. One of tae

inves t iga t ions of p l an t opera t ion discussed in Chapter I I I

u t i l i z e s t h i s idea . Ihe a u x i l i a r y superheater has been

sized to provide a 200°F temperature inc rease for f u l l load

steam, regard less of whether the steam i s provided by the

fossi l bo i l e r a lone , by the so la r b o i l e r s , or by a

combination of the sources . The o u t l e t temperature i s

regulated by the burner and/or the d i l u t i o n a i r in tne

superheater (Figure 2 .11) .

48

Flue Gas Out

Hot Air In

Blower Air Preheater

To Steam Storage Tanks

Gas In

Auxiliary Superheater

- A A A A - ^ -roiD Fossil Boiler

Figure 2.11 Auxiliary Superheater

49

2.3-8 The Steaa Storage Tank

The s t e a a s torage tank, SST, a c t s as a "flywheel" in

the system as we l l as the i n t e r f a c e point of f o s s i l bo i l er

steam and s o l a r b o i l e r steam. The SST maintains a steady

steam supply for the turbine in s p i t e of f luc tua t ions in the

solar bo i l er outputs due to rapid i n s o l a t i o n f l u c t u a t i o n s .

The f o s s i l bo i l e r r e g u l a t e s the pressure in the steam

storage tank at approximately 1175 p s i a . In the event of a

drop in so lar steam production, the steam storage tank has a

capacity of approximately 10 minutes of f u l l load steam.

During t h i s t ime the f o s s i l b o i l e r increases i t s f i r i n g rate

in order to pick up the load, and continues at the increased

f iring rate u n t i l i t has recharged the SST.

2-2-9 The Desuperheater

The desuperheater and the control valve between i t and

the steam storage tank contro l the s t a t e of the steam at the

turbine i n l e t . The valve reduces the steam pressure about

300 psi under normal f u l l load or part load turbine

condit ions. The desuperheater maintains the turbine i n l e t

temperature. I t does t h i s by c o n t r o l l i n g the rate of 219°F

feedwater sprayed i n t o the superheated steam l i n e .

50

2- i - i9 The Contact Cooler

The contact cooler i s necessary because a t t imes the

output from the s o l a r b o i l e r s serves as preheated f lu id for

the f o s s i l b o i l e r drum. The contact cooler i s used to

ensure that t h e temperature of the water enter ing the f o s s i l

boiler drum i s beneath the sa tu ra t ion temperature (531°F a t

900 p s i a ) . The contac t cooler adds b o i l e r feedwater from

the deae ra to r , a t 219°F, to the preheated f lu id in order to

keep the temperature belcw s a t u r a t i o n . The advantages for

operating t h e s o l a r b o i l e r s as feedwater p rehea te r s are

discussed in Chapter I I I .

2-3.11 The F os s i l Boi le r

The f o s s i l b o i l e r , i l l u s t r a t e d in Figure 2.12 i s a

packaged steam genera tor which produces superheated steam

from boi ler feedwater. The bo i l e r has an evaporation

section and a superheat ing s e c t i o n . I t has a dual fuel

system so i t can operate on gas or o i l . Two spec ia l

requirements have been speci f ied for t h i s b o i l e r which are

not normally quoted by bo i l e r manufacturers. The f i r s t

special requirement i s a b o i l e r turndown r a t i o of 12-to-1

51

To Auxiliary Superheater Superheater

Wvn 1

From Contact Cooler

Drum Overflow to Flash Tank

Oil or Gas In

A- From Feed Pumps

Flue Gas Out

i Hot Air

IN

Air Preheater

Fossil Boiler

t^

81owdown to

Flash Tank

Figure 2.12 Fossil Boiler

52

rather than the usual 6 - to -1 quoted for o f f - t h e - s h e l f

turbines. This turndown r a t i o w i l l allow greater fuel

conservation during the t imes when the so lar b o i l e r s can

provide aost of the steam load. The second s p e c i a l

requirement i s a f a s t e r than usual rate of load change for

the b o i l e r . Normally, a maximum load change of 10%/minute

i s quoted by t o i l e r manufacturers. The des igners of tne

proposed p lant have asked for a larger rate of change so

that steam s torage can be kept to a minimum. That i s , i f

the f o s s i l bo i l e r i s f a s t e r to respond to increased load

demands, which can be very sudden due to f l u c t u a t i o n s in

inso la t ion , then l e s s steam need be stored in order to

provide a s teady steam flow to the turbine . The boi ler

manufacturers have increased the load change rate to

20Vininute through s p e c i a l burners and design. The f o s s i l

boiler can, t h e r e f o r e , increase from a minimum flow of

9000 Ibm/hr, to a maximum flow of 70,000 Ibm/hr, in about

5 minutes. This maximum flow provides not only tae required

turbine i n l e t at f u l l load but can a l s o , s imultaneously,

recharge the steam s torage tank.

53

The f i r i n g ra te of the f o s s i l bo i l er i s contro l led to

regulate the pressure in the steam storage tank. Tne amount

of feedwater entering the b o i l e r i s contro l l ed oy a valve

working i n conjunct ion with a water l e v e l sensor in the

f o s s i l b o i l e r drum. The i n l e t water can be between 219° F

and 531°F. Increased i n l e t temperature reduces the f o s s i l

fuel required to b o i l the water. However, t h i s a l so

decreases the heat a v a i l a b l e in the superheater s ec t ion of

the bo i l er . Thus, the o u t l e t temperature of the bo i ler

steaa w i l l be lower. The aux i l i ary superheater must

compensate with a higher f i r i n g ra te .

A continuous blowdown of about 3% of the operating

flowrate i s required i n the f o s s i l bo i ler - This i s

necessary to maintain water q u a l i t y . The blowdown water i s

about 570°F and i s used to heat the make-up water or the

boiler feedwater in the deaerator.

2'2'12 The Flash Tank

If an exces s of feedwater i s sent to the f o s s i l bo i ler

drum, due to a sudden increase in preheated feedwater from

the solar b o i l e r s , for example, the excess i s sent to the

54

flash tank. This avoids losing the high quality water. The

steam from the flash tank is sent to the condenser and added

to the turbine exhaust steam. The exit water is then sent

to the condenser hot well-

2-3.12 The Solar Collectors

The proposed plant calls for ten quartersphere solar

collectors. These collectors have a radius of curvature,

B , equal to approximately 115 feet. The rim angle of the

quartersphere is 60 degrees, and the tilt angle is 15°, as

illustrated in Figure 2.13. The aperture diameter is

approximately 200 feet. Ten collectors of this size will

provide enough steam to produce 5 MWe at peak solar

conditions of brightness and position.

The reflective surface of each collector is composed of

approximately 2160 mirror panels. These panels are similar

in design to those used in the ADVS, illustrated in Figure

2.14, except that the honeycomb will be aluminum instead of

paper. The front of the panel is a glass mirror which has

been pressed into the desired curvature (radius 115 feet).

These mirrors are made of inexpensive float glass with a

56

c o

.f—

+J ro $-3 cn

c o o

c ro a. i-o $-

rO

O t o

CM

3 cn

57

s i lvered backing. They demonstrate approximately 88%

r e f l e c t i v i t y . The nirror i s glued to an aluminum honeycomb

structure, which holds the mirrors in t h e i r curved form and

serves as a shock absorber for the mirror. Such panels can

withstand the impact of 1.5 inch diameter h a i l s t o n e s

travel ing i n excess of 100 MPH. This design claim was

tested in the laboratory and substant iated by the panel

performance on the ADVS. The CSPP has proposed an o n - s i t e

f a c i l i t y for the manufacture and r e h a b i l i t a t i o n of mirror

panels.

1-1*11 The Solar Boilers

Twenty tubes , each approximately 445 fee t long, with

0.375 inch outer diameter and 0-25 inch inner diameter make

up each so lar t o i l e r - To reduce c o s t s , the f i r s t 268 f e e t

(portion nearest the r e f l e c t o r surface) i s TP 439 s t a i n l e s s .

This i s the low temperature end of the b o i l e r . A small

plenum then connects the s t a i n l e s s s t e e l tubing with Inconel

617 s t e e l tubing for the l a s t 176 fee t of the tube. The

Inconel tubing i s able to withstand the s t r e s s high

temperatures and thermal cyc l ing which occur near the top of

the rece iver .

58

2.3.15 The Plant Piping

Not a l l of the plant piping w i l l be discussed here, but

the piping and i n s u l a t i o n running between the so lar b o i l e r s

and the c e n t r a l p lant are re levant . This piping i s

s ign i f i cant because the Solar Gridirons are s i tuated at much

greater than usual d i s t a n c e s between b o i l e r s and turbines .

Three pipe l i n € S serve the s o l a r b o i l e r s . One provides the

feedwater. Another c a r r i e s turbine bound steam to e i ther

the steam s torage tank or the a u x i l i a r y fuperheater. The

third c a r r i e s output f l u i d which can more e f f e c t i v e l y be

used as preheated feedwater for the f o s s i l b o i l e r . All of

th is piping i s i n s u l a t e d .

Because the steam pipe l i n e s from the so lar b o i l e r s the

steam storage tank are so long (maximum bo i l er d i s tance:

1300 feet) , the pipe diameters are varied to reduce heat

losses . Figure 2 .15 i l l u s t r a t e s heat l o s s e s to be expected

for d i f f e r e n t pipe diameters and insu la t ion th i cknes se s .

Figure 2.16 shows temperature l o s s e s expected for various

steam f lowrates from the s o l a r b o i l e r s . These l o s s e s are of

special concern because the s o l a r b o i l e r s must be operated

so that the temperature of the steam reaching the steam

storage tank i s above turbine qua l i ty .

59.

c

ro (U

+-> CO

o o o CT>

c •r->> i-i~ ro

<_)

Q) O.

•a ta

3

CO

o

ro

LO

o o O O CM

CM

<U i-

U i - J q / n j g ) adi^j j o ^ooj j a d SSOT ^PSH cn

60

160^

140

Single Receiver 1300 ft from Storage Tank

c to

O! <0 u o

o

o s->

CU

u

E o s-

CL o u o

s.

« S-<u o. E

120

100

20OF Ambient 90OF Ambient

80

60

40

20

0 J _ 1000 2000 3000 4000 5000

Flow per Receiver, Ib/hr

Figure 2.16 Temperature Loss in Insulated Steam Line Between

Solar Receiver Outlet and Steam Storage Tanks

61

The power p lan t b r i e f l y described in the preceding

subsection has been used t o analyze the opera t iona l

considerat ions for a hybrid p lant . The ana lys i s was

performed in order t o optimize the use of the renewable

energy source , the sun , and conserve the conventional energy

sources, o i l and g a s . The procedure and r e s u l t s of t h i s

analysis a re given in the next s ec t ion .

CHAPTER I I I

SOLAR BOILER OPERATION STRATEGY

The S o l a r G r i d i r o n s may be o p e r a t e d i n many modes. A

mode i s d e f i n e d by t h e i n t e n s i v e s t a t e of t h e steam e x i t i n g

the s o l a r b o i l e r ; i . e . , by t h e t e m p e r a t u r e and p r e s s u r e .

For e l e c t r i c power p l a n t s . . due t o t h e n a t u r e of the

r a d i a t i v e and c o n v e c t i v e l o s s e s of t h e s o l a r b o i l e r s , under

some s o l a r c o n d i t i o n s t he b o i l e r may be more e f f e c t i v e l y

used by p r o d u c i n g f l u i d a t l e s s than t u r b i n e q u a l i t y . T h i s

i s why a S o l a r B o i l e r O p e r a t i o n a l S t r a t e g y , S-30S, i s

n e c e s s a r y . A s t r a t e g y d e f i n e s the c o n d i t i o n s under which

the b o i l e r w i l l be s w i t c h e d from one mode to a n o t h e r ; e . g . ,

from a t u r b i n e - q u a l i t y mode t o a p r e s s u r i z e d ho t water mode.

S t r a t egy deve lopment and s e l e c t i o n i s d i r e c t e d toward

maximizing t h e s o l a r p e n e t r a t i o n of t h e power p l a n t .

Converse ly , t he p l a n t must be des igned t o f a c i l i t a t e use o t

s t r a t e g i e s p r o v i d i n g good p e n e t r a t i o n . The s o l a r

p e n e t r a t i o n , a , i s a r a t i o of t h e annua l energy d e l i v e r e d by

62

63

the s o l a r b o i l e r s t o the annual energy required by the

t u r b i n e . Only energy captured by the b o i l e r s which i s

usable by t h e p l a n t i s c o n s i d e r e d in the annual energy

de l ivery- The f i r s t s t e p t o f i n d i n g an o p e r a t i o n a l s t r a t e g y

i s to d e f i n e the modes of s o l a r b o i l e r o p e r a t i o n which can

be most e f f e c t i v e l y u t i l i z e d by the proposed p l a n t .

J - 1 ^h£ So lar B o i l e r Operation Modes

One of t h e advantages of the S o l a r Gridiron concept i s

the a b i l i t y t o produce t u r b i n e - q u a l i t y steam- The

d e f i n i t i o n of " t u r b i n e - q u a l i t y " depends on tae turb ine

s e l e c t e d f o r the p l a n t .

3-1-1 The Qua l i ty Mode

The s e l e c t i o n of a t u r b i n e for the proposed Crosbyton

plant i n v o l v e s h e a t ba lance as wel l a s c o s t a n a l y s i s . FW

Energy A p p l i c a t i o n s I n c . , obta ined pre l iminary b i d s from

turbine manufacturers and analyzed p lan t performance (FW) .

The present recommendation i s a t u r b i n e whose operat ing

i n l e t steam s t a t e i s 850°F, 900 p s i a . This s t a t e

e s t a b l i s h e s , f or p r e s e n t purposes , a lower l i m i t for the

64

temperature of the "turbine-quality steam mode". for

simplicity, this mode will be referred to as the Quality

Mode.

Another factor involved in the Quality Mode definition

is the long distance from the solar boiler outlet to the

turbine (ref: Chapter II). Figure 2.15 illustrates the

nature of losses to be expected from the piping between the

receivers and the steam storage tank. Figure 2.16 presents

various examples suggesting the temperature losses to be

expected. Depending upon conditions, a temperature drop

between 20° F and 140 °F can be anticipated. In the proposed

plant concept, the outlet pressure for the solar boilers is

determined directly by the turbine requirement. In the

guality mode this pressure will be set and regulated by the

fossil boiler. This pressure will be maintained at the

solar boiler outlet regardless of the exit temperature. For

a fixed fossil boiler pressure, the solar boiler modes are

then defined by the exit temperature. As mentioned in

Chapter II, however, the fossil boiler will not serve as the

regulator in all modes. Based upon the turbine and piping

losses, the Quality Bode, QM, for the solar boilers in the

65

proposed p lant i s de f ined t o be 1000°F, 900 ps ia a t the

bo i l e r e x i t .

3-1-2 The Defau l t Mode

I f q u a l i t y mode steam becomes i m p r a c t i c a l because of

high l o s s e s (very low f l o w r a t e s ) , then t h e s o l a r b o i l e r s can

be used a s f eedwate r p r e h e a t e r s for t h e f o s s i l b o i l e r . In

t h i s s i t u a t i o n enough water w i l l be s en t through the b o i l e r s

to assure t h a t t h e e x i t i n g f l u i d i s l i q u i d . Because the

boi l ing t e m p e r a t u r e of water a t 900 p s i a i s 531 °F, the

Default Mode, DM, i s defined fo r o p e r a t i o n of the s o l a r

boi ler with o u t p u t a t (not more than) 500°F. This lower

temperature i n s u r e s a dec rease in the r a d i a t i v e and

convective l o s s e s a t t h e s o l a r b o i l e r wa l l s and, t h e r e f o r e ,

greater b o i l e r e f f i c i e n c y ( r e f : F igure 2 . 5 ) . Under

automatic c o n t r o l , t h e DM i s def ined t o be 500°F, 900 p s i a ,

and the c o n t r o l sys tem w i l l main ta in t h a t e x i t s t a t e . In a

looser s e n s e , a l l e x i t f l u i d which can not be c l a s s i f i e d in

one of t he e t h e r def ined modes (during of t r a n s i e n t

condi t ions , f o r example) i s c a l l e d Defaul t Mode f l u i d and i s

directed t o the c o n t a c t c o o l e r and d e l i v e r e d as preheated

feedwater to the f o s s i l b o i l e r -

66

Based on the discussion above, one might think that the

solar boilers should always operate in the Default Mode so

that the boiler efficiency would be higher due to lower

losses. This i s not the case, however, because there i s a

limit on the flowrate of preheated water which can be used

by the fossil boiler. During peak solar conditions, if all

the solar boilers were to be operated in the DK, at least

three times tec much feedwater would be produced. because

all of this energy could not be utilized by the plant, the

excess would have to be thrown out. Only the energy used

can effect solar penetration.

3.1.3 The Aux iliary Modes

The presence of the auxiliary superheater at the fossil

boiler exit makes other solar boiler operation modes

plausible. Such modes produce steam, but below the

temperature level of the QM- Such steam must be transported

to the auxiliary superheater before entering tae steam

storage tank- Boiler outputs such as: 900°F, yOO psia;

800°F, 900 psia; and 700°F, 900 psia may be used to define

these auxiliary modes, AM. Use of AM's requires greater

67

complexity i n the contro l system for the aux i l i ary

superheater, AS. I f the AM«s are defined i sothermal ly , as

in the examples above, then the AS must respond to a time

varying f lowrate t o d e l i v e r isothermal output to the SST-

Alternately , i f the AM's are defined by fixed f lowrate

s p e c i f i c a t i o n s , then the AS must respond to time varying

in le t temperatures t o d e l i v e r isothermal output to the SST.

A c o s t - b e n e f i t a n a l y s i s i s necessary before committing to

the use of AM's: does the increased solar penetration

jus t i fy the increased complexity and cost of a more

complicated AS and a s s o c i a t e d contro l s? A proper ana lys i s

of the c o s t - b e n e f i t s i t u a t i o n for AM's was outs ide the scope

of the present s tudy .

The goal of t h i s study was to eva luate the switching

function, between modes or s t r a t e g y , for solar boi ler

operation. From t h i s point of view, the greater the annual

solar penetrat ion predicted for a s t ra tegy , the more

desirable the s t r a t e g y . Thus, a method for comparing

penetration was required .

68

3-2 The Annual So la r P e n e t r a t i o n

The annua l s o l a r p e n e t r a t i o n , a , i s the r a t i o of the

annual energy d e l i v e r e d by the s o l a r b o i l e r s t o t n e annual

energy used by t h e t u r b i n e . The energy cap tu red by the

bo i l e r s must be d e l i v e r e d i n t o the QM, the DM, or i n t o an

AM. If too much DM f l o w r a t e occurs (more than can be sen t

to the f o s s i l b o i l e r ) , then t h e excess does not c o n t r i b u t e

to the annua l energy d e l i v e r e d . The p rocedures fo r

p red ic t ing t h e energy r equ i r ed and the use fu l s o l a r energy

del ivered a r e d e s c r i b e d i n Subsec t i ons 3 . 2 . 1 and 3 . 2 . 2 ,

r e s p e c t i v e l y .

I'Z"! The Annual Energy Required by the Turbine

The annual energy r e q u i r e d by t h e t u r p i n e , ALERT,

depends on t h e e l e c t r i c load served by the g e n e r a t o r . The

generator load changes every t ime a sw i t ch i s thrown in the

load g r i d . T h e r e f o r e , a b a s i c assumption necessary in order

to pred ic t ALEET c o n c e r n s the g e n e r a t o r load- The e l e c t r i c

load s c e n a r i o may be assumed t o be almost a n y t a i n g .

However, some assumpt ions a re obvious ly c l o s e r t o what i s

expected of t h e p l a n t . The ALERT for t h r e e d i f f e r e n t annual

69

e l e c t r i c loads was considered. The three loads are: 1)

continuous f u l l l o a d , 6 flWe, supplied by the plant 24 hours

a day, 365 days a year; 2) f u l l load during the so lar

boiler operat ion-hours (defined below) and half load at a i l

other t imes; and 3) f u l l load during the so lar bo i l er

operating hours and no load the res t of the time. Ful l load

i s defined to be 6 MWe so that the plant can operate i t s own

pumps, l i g h t s , and other equipment, and s t i l l supply 5 MWe

net to the e l e c t r i c power gr id .

The meaning of "solar boi ler operation-hours" i s

determined by the Solar Gridiron design, not by i n s o l a t i o n

conditions. The operating time i s es tabl i shed by

considering only the sun»s p o s i t i o n . The sun must be high

enough in the sky so tha t the rece iver can he placed in the

focal reg ion , which l i e s on the l ine determined by the

Gridiron's center of curvature and the center of the so lar

disc. The CSPP Solar Gridiron system has been designed so

that the rece iver can track the sun whenever the i n c l i n a t i o n

angle, ^ , (ref: Eg. 2.2) i s l e s s than 75°. Operation of

the Gridiron outs ide of t h i s angular range would r e s u l t in

very l i t t l e a d d i t i o n a l energy capture. The number of so lar

70

boiler operat ion-hours in a year i s (for J? = 7 5 ° ) a MAX ' •

function of x and y , the l a t i t u d e and t i l t ang le . At

crosbyton, Texas ( ^ = 3 3 . 6 2 5 ) , for a 15 ° t i l t angle , there

are 3585 operat ion-hours i n a year. Thus the s o l a r sytem

Operation-Year = 3585 hours. (3, i)

3.2.1a Continuous F u l l Load

The bas ic d e f i n i t i o n of continuous f u l l e l e c t r i c load

i s : 6 MWe, 24 hours per day, 365 days per year. This

araounts to

(6 flWe) (24 hrs/day) (365 days/year) = 52,560 MWe-hr/year.

This i s a much greater annual e l e c t r i c load than the c i t y of

Crosbyton present ly requ ires . Therefore, i f tne plant i s to

operate e f f e c t i v e l y under t h i s assumption, a buyer for the

excess energy produced must be a v a i l a b l e . The CSPP plant i s

planned to serve a large g r i d , which, in turn, serves

Crosbyton.

71

The energy r equ i r ed by the tu rb ine to produce 6 MWe

depends on t h e steam mass f lowra te , tu rb ine i n l e t condi t ions

and the genera to r . The mass flowrate requirements for the

turbine genera tor systems considered for t h i s plant were

given in Figure 2 . 1 0 . This f igure shows, for two d i f fe ren t

turbines, the t u r b i n e i n l e t steam flowrate required to

deliver a spec i f i ed gross e l e c t r i c a l output . Both tu rb ines

require i n l e t steam a t 850^F and 900 ps ia and dr ive t a e same

e lec t r i c gene ra to r . Turbine 2 i s more e f f i c i e n t , because i t

requires l e s s steam in the same s t a t e to produce the same

e lec t r i ca l output as tu rb ine 1.

From Figure 2 .10, the steam flowrate required by

turbine 1 to produce 6 MWe i s approximately 59,500 Ibm/hr.

Turbine 2 r equ i r e s about 55,000 Ibm/hr. The steam, a t 850°F

and 900 p s i a , has a spec i f i c enthalpy of 1422 Btu/lbm.

Therefore, t h e steam power required at the turb ine i n l e t s

are:

6 (59,500 Ibm/hr) (1422 Btu/lbm) = 84.6 1 x 10 Btu/hr

for turbine 1 ; and

72

6 (55,000 Ibm/hr) (1422 Btu/lbm) = 78 .21 x 10 Btu/hr

for turbine 2 .

The annual energy required by each turbine is found by

multiplying the power required to produce 6 MWe by the time

6 MWe is to be produced. Therefore the annual energy

required (at the inlet) by each turbine when 6 MWe is

continuously produced is:

6 ALERT = (84.61 x 10 Btu/hr) (24 hr/day) (365 days/year)

12 = C.7412 xlO Btu/year

for turbine 1; and

ALERT = (78.21 x 10 Btu/hr) (24 hr/day) (365 days/year)

12

= 0.6851 X 10 Btu/year

for turbine 2 .

73

3.2.1b Dayt ine F u l l Load - N ight t ime Half Load

In the event t h a t no p o t e n t i a l buyer e x i s t s for any

excess energy produced by the p l a n t , the product ion r a t e

wi l l vary d i r e c t l y with the Crosbyton demand. For the

present s t u d y , r a t h e r than model the Crosbyton demand in

great d e t a i l , a f u l l load demand of 6 MWe w i l l be assumed

for the s o l a r b o i l e r o p e r a t i o n a l hours and a h a l f load

demand of 3 MWe w i l l be assumed f o r the remaining nours of

the year. As mentioned in s e c t i o n 3 . 2 , t h e number of

operat ional hours i n a year i s 3585 hours . There are

5175 remaining hours i n a year .

The power r e q u i r e d at any t ime, by e i t h e r of the

turbines under c o n s i d e r a t i o n , to produce 6 MWe has a lready

been found i n t h e p r e v i o u s s e c t i o n . In the same manner,

using Figure 2.10 a g a i n , t h e steam power required t o produce

3 MWe i s a l s o found. For t u r b i n e 1 t h i s ( i n l e t ) power i s :

(32,500 Ibm/hr) (1422 Btu/lbm) = 4 6 . 2 2 x 10^ dtu/hr

and for t u r b i n e 2 t h e i n l e t power required to produce 3 MWe

i s

74

6 (29,000 Ibm/hr) (1422 Btu/lbm) = 41 .24 xlO B t u / h r .

The a n n u a l energy r e q u i r e d (a t t h e i n l e t ) i s found by

the sum of t h e p r o d u c t s of i n l e t power r equ i r ed and the t ime

t h i s power i s r e q u i r e d . The re fo re , t h e annual i n l e t energy

required fo r the two t u r b i n e s when the load has been halved

at n ight i s

ALERT = (84.61 x 10 Btu /hr ) (3585 h r s /yea r )

+ (46.22 X 10 Btu /hr ) (5175 h r s / y e a r ) 12

= 0.5425 X 10 Btu /year

for t u r b i n e 1; and

ALERT = (78.21 x 10^ Btu /hr ) (3585 h r s / y e a r )

+ (^1-24 X 10 Btu /hr ) (5175 h r s / y e a r ) 12

= 0.4938 X 10 Btu/year

for t u r b i n e 2 .

75

3.2.1c Daytime Full Load - Nighttime No load

The plant is assumed to operate during the solar boiler

operating hours at full load 6 MWe, and no load at night.

While this may or may not be an actual operating procedure

for the proposed plant, there is interest in this limit for

the calculation of solar penetration. This is because a

plant with essentially no energy storage capacity can not oe

expected to have any contribution from solar energy whenever

the Solar Gridirons cannot operate. Therefore, this

approach does not penalize the solar penetration for night

time hours when no solar energy could possibly be collected.

The calculation of the energy required by the turbine

calls for two factors. The power the turbine requires to

produce 6 MWe (ref: subsection 3.2-la) and the time the

plant produces 6 MWe, In this case, 6 MWe are produced

3585 hrs/year- Therefore, the annual energy required (at

the inlet) by the turbine is

6

ALERT = (84.61 xlO Btu/hr) (3585 hr/year) 12

= C.3033 X 10 Btu/year

76

for t u r b i n e 1 , and

6 ALERT = (78.21 xlO Btu/hr) (3585 hr/year)

12 = C.2804 X 10 Btu/year

for t u r b i n e 2 .

3-2-Id Relationship Between ALERT and Energy Consumption

The values for ALERT given in Table 3-1 represent the

energy reguired at the turbine inlets- Not all of this

energy is used by the turbine; some is recovered by the

cycle. In order to evaluate the solar penetration

(ref: Subsection 3.2.3), it is necessary to examine the

thermodynamic cycle and determine the energy used by the

turbine.

As illustrated in Figure 3-1, in the proposed plant

some steam is extracted from the turbine and mixed with the

turbine exhaust to produce 219°F feedwater- The temperature

of the extracted steam, T T ' ^^ less than d50°F, but

greater than 219° F- The work of the turbine is accomplished

across the teaperature difference between the 850 F inlet

Table 3.1

Annual Energy Requirements for the Turbines-ALERT

77

Full Load = 6MWe Half Load = 3 MWe

Turbine Steam Rates

Turbine 1: P

Turbine 2: Tl

T2

where

84.61 + (12.797)(L - 6)

78.21 + (12.323)(L - 6)

Steam Rate in MBtu/hr

Electrical Output in MWe

Year = 365 days = 8760 hrs

Daytime = Annual Operation - Hours of the Solar System = 3585 hrs

Nighttime = Annual Hours Solar System Not Operated = 5175 hrs

Load 1

Load 2

Load 3

Continuous Full Load

Daytime Full Load - Nighttime Half Load

Daytime Full Load - Nighttime No Load

12 ALERTS (given in MMBtu/yr where MMBtu 10 Btu

Turbine 1

Turbine 2

Load 1

0.7412

0.6851

Load 2

0.5425

0.4938

Load 3

0.3033

0.2804

78

Steam from Desuperheater

m

EXT

Boiler Feedwater

Figure 3.1 Turbine Cycle

79

temperature and t h e exhaus t t e m p e r a t u r e , T ryn- The exhaus t

temperature i s l e s s t han 219° F t o i n c r e a s e t h e e f f i c i e n c y of

conversion of f l u i d energy to usefu l work in produc t ion of

e l e c t r i c i t y .

The net e f f e c t of t h i s c y c l e , however, i s t h a t the

steam mass f l o w r a t e , M , e n t e r s the t u r b i n e at d50°F an i s

re turned a s system feedwate r a t 219°F. Ihe steam r a t e , P ,

(ref: Table 3 . 1 , F i g u r e 2.10) and t h e s p e c i f i c e n t h a l p y ,

h ocn# of 850°F steam a t 900 p s i a may be used t o o b t a i n the 8 50

mass f l o w r a t e ^

"T = ' ' T / ^ 5 0 (3.2)

The t o t a l mass th rough the t u r b i n e i n a year , then , i s

M = ALERT / hg^p , ( 3.3)

and the energy consumed by the t u r b i n e i s :

E = M , r h - h l = ( ^850 " ' 219 \ ALERT

' 850

= ALERT / 1.143 . (3.4)

80

The q u a n t i t y , ^ jn ' r a t h e r than t h e ALERT, i s r e q u i r e d for

the computat ion of s o l a r p e n e t r a t i o n .

3-2.2 The Annual Energy Captured by t h e Solar B o i l e r s

In o rde r to p r o j e c t annual energy c a p t u r e d , AEC, by the

solar b o i l e r s , one must c o n s t r u c t or f a b r i c a t e a b a s e l i n e

year of i n s o l a t i o n and weather da t a for the s i t e - In order

to use, as much as p o s s i b l e , t he a c t u a l ADVS s i t e d a t e ,

severa l Models or E s t i m a t o r s have been devised for

project ion purpose (CP 7 and KW). The t h r e e t ypes of

es t imators which have been cons ide red in p r ev ious CSPP

anaylses a r e :

I . The P r o j e c t e d Operat ion-Day Average (PODA) Model

P0^^ = 365/N I <Pp>j3 (HQPQ /3585 hrs) (3.5a) ^ '^^ N days

I I . The C lea r Sky F a c t o r (CSF) Model

CSF

III. The Statistical Projection (SP) Model

81

SP

<PF^AN,W = <^^F\>M * ^ F f ^ - ^ )

The q u a n t i t i e s <Pp>/\fyj# used i n Eqs . ( 3 . 5 ) , a r e a n n u a l i z e d

average powers ( f l u i d power , n o t e l e c t r i c a l power) added by

the s o l a r b o i l e r s , a v e r a g e d o v e r o p e r a t i o n - h o u r s o n l y . I n

o the r words

(3585 h r s ) / f = AEC. (3.6)

The q u a n t i t y <Ep>pj, u s e d i n t he POCA and CSF models , i s t he

average power added t o t h e f l u i d f o r a s p e c i f i c day.

In t h e PODA Mode l , a s e l e c t e d s e t of N days i s used fo r

ave rag ing p u r p o s e s t o g e t t h e a v e r a g e d a i l y energy added t o

the working f l u i d . M u l t i p l i c a t i o n by 365 g i v e s the

p r o j e c t e d a n n u a l e n e r g y i n c r e a s e d e l i v e r e d , and d i v i s i o n by

3585 h o u r s , t h e n , p r o d u c e s t h e power averaged ove r t h e

o p e r a t i o n - h o u r s . The q u a n t i t y ^npj) ^^ ^'^^ number of

o p e r a t i o n - h o u r s i n t h e s p e c i f i c day c o r r e s p o n d i n g t o <Pp ^ -

The CSF Model p r o j e c t i o n i s based on the Pes t days of

o p e r a t i o n e v e r r e c o r d e d a t t h e ADVS s i t e . The q u a n t i t y

'^Pc>nuAv i s t h e l a r g e s t d a i l y power a v e r a g e obse rved from r UjMAX

82

the ADVS s y s t e m . One then argues t h a t the maximum observed

value i s t h e b e s t t h a t the s y s t e m - s i t e - o p e r a t i o n can

ach ieve , and t h i s must correspond to a "very good day of

i n s o l a t i o n " . Other days in the year w i l l not o f f e r as l a r g e

a value for <Pp>nf l a r g e l y because the i n s o l a t i o n i s not as

good. Roughly s p e a k i n g , the CSF f a c t o r , then, i s t o be an

es t imate of t h e p e r c e n t of the time during the

operat ion-year t h a t the sky i s a s c l e a r as i t was at the

ADVS s i t e on t h e day of maximum observed performance

(]L| Ti 955 watts/m^) , assuming that t h e sky i s t o t a l l y

overcast a t a l l t h e o ther t i m e s . Appropriate CSF f a c t o r s

for the ADVS s i t e are probably about 75-803^.

The SP Model i s a g e n e r a l i z a t i o n of the PODA MOdel in

which the s i t e i n s o l a t i o n data i s averaged with a we ight ing

method i n d i c a t e d by the s u b s c r i p t W. A grea t v a r e i t y of

data weight ing methods may be used , depending on the t a s t e

and judgement of t h e u s e r . The PODA Method, l i k e a i l SP

Models, i s b iased by the date w e i g h t i n g . In the PODA

Method, data ga thered on a c e r t a i n day i s used to e s t i m a t e

"the energy t h a t would have been gathered that very day, i f

the s p e c i f i e d s o l a r s t r a d e g y (modes s e l e c t i o n s t r a t e g y ) had

83

been used." Such da i l y energ ies are then given equal weight

over the s e l e c t e d N days . Thus, the PODA Method might be

described as an SP Model employing equal ly weignted dai ly

energies. I t sould be noted t h a t , in a l l cases , a "solar

operating s t r a t e g y ' must be s p e c i f i e d i n order to determine

<Pp>., or <?^>r^ from the i n s o l a t i o n data. S t r a t e g i e s of

operation w i l be def ined and explained l a t e r in t h i s

s ec t ion .

I t i s p o s s i b l e t o include a variance band in SP Model

ca lcu lat ions . The quantity Ap in Equation (3-5c) represents

a standard d e v i a t i o n , a rms dev iat ion from the average.

A.^ = «Pp' > > - [ « P ^ » ' J (3.7)

For the present s tudy , an SP Model was s e l e c t e d . This

i s computed in the usual way: The power was scaled to

represent a s i n g l e "200-foot" gr id i ron , and then multipl ied

by 10 for the s o l a r system of the proposed plant (ten

gridirons) . Power s c a l i n g i s accomplished in an obvious

fashion, using the s i z e - a t t e n d a n c e f a c t o r s .

84

3.2.2a Power Del ivered by the Solar Boilers-Power Tables

Whenever a S t a t i s t i c a l Project ion (SP) Model i s used to

compute an average power for a so lar gridiron system, the

computation can employ a formula of the form:

where P i s a known funct ion expressing the instantaneous

fluid power which would be added by a s o l a r gridiron bo i l er

at a s p e c i f i c va lues of I„,, and ^J2_ under a spec i f i ed DN

solar o p e r a t i n g s t r a t e g y . The average g iven by

Equation (3 .8 ) i s a t ime-averaged power, but the sum i s

ac tua l ly performed over v a r i a b l e s I , and ^J2. which occur DN

in F(Ipjj^, \J2- )r a frequency t a b l e r e p r e s e n t i n g a g iven time

period observed a t the s i t e . The weight f u n c t i o n

F (IHM r sJL ) i s a normal ized j o i n t d i s t r i b u t i o n f u n c t i o n of

IpjM and >JL over some s p e c i f i e d t ime span .

One of the g r e a t s u c c e s s e s of t h e CSPP has been the

predict ion and the v e r i f i c a t i o n of the i n s t a n t a n e o u s b o i l e r

power f u n c t i o n s , P . The P f u n c t i o n s are obta ined from

the TMR e q u a t i o n s , a s e t of curve f i t s t o the output or the

85

TFAP b o i l e r a n a l y s i s code deve loped by the CSPP ( r e f :

subsec t i on 2 . 1 ) . The TMR e q u a t i o n s ( r e f : Appendix A)

demons t ra t e r e m a r k a b l e a c c u r a c y i n p r e d i c t i n g a c t u a l

g r i d i r o n b o i l e r p e r f o r m a n c e , a s has been s t r o n g l y v e r i f i e d

by t h e ADVS d a t a . Th i s a g r e e m e n t i s i l l u s t r a t e d i n

Figure 3 . 2 . In t h e s e f i g u r e s t h e a c t u a l , measured b o i l e r

performance and t h e TMR v a l u e s f o r t he same s o l a r d a t a a r e

e x h i b i t e d on a d a y - l o n g b a s i s f o r t h r e e t y p i c a l d a y s . Such

agreement i s found f o r e v e r y day of o p e r a t i o n ! The TMR

equa t i ons e x p r e s s t h e f u n c t i o n Pp (Irj*^ , ^ #M,Vyj) , where M i s

the mass f l o w r a t e t h r o u g h t h e b o i l e r . I n o r d e r t o use t h i s

func t ion i n E q u a t i o n (3.8) t h e v a r i a b l e s V , and M must be

s p e c i f i e d .

Because i t was not c o n v e n i e n t to c o m p i l e t r i p l e j o i n t

d i s t r i b u t i o n t a b l e s , ^ (Ir,M / ^ ' W^ ' ^^^ J t i n i s ^eed , V^, i s

simply s e t a t t h e c o n s t a n t v a l u e of 15 mph. T h i s f i x e d

value i s v e r y a p p r o p r i a t e fo r t h e Crosbyton s i t e . The

c e n t r a l i s s u e , however , f o r u s ing t h e f u n c t i o n

P (I , > J i , H , V ) i n Equa t ion (3 .8) i s t h a t H must be F DN W

specified as a funct ion of J^^ and ^ . A complete

specif icat ion of M as a function of 1^^ and v^ i s ca l led a

86

a-g l > -J

8 = is

o

g

C <"

si 2

o •t— +-> o

• o cu S -

-a «3

fC +-> <KS

Q

OO > Q

CsJ

ro

cu

<J)

^ g g § g 8 i

87

"solar operat ion s t r a t e g y " . Comparison of s eve ra l so l a r

s t r a t eg ies i s one of the c e n t r a l i n t e n t i o n s of the present

study.

For t h e s t r a t e g i e s considered in t h i s study,

"isothermal modes" were used. In other words, the so lar

boiler feedwater f lowra te , M_, i s cont ro l led to maintain a

specified b o i l e r e x i t temperature , T^ ^ . For such purposes,

Reichert has developed the TMRF equat ions , which allow

simple computation of M as a function of 1-^^ , \JL , T -.-j- , and

the relevant p r e s su re s . These equat ions are accurate enough

that they could be used for open loop control of the ex i t

fluid s t a t e of s o l a r g r id i ron b o i l e r s . The TMRF equations

were obtained d i r e c t l y from the TMR equations oy solving for

the M values corresponding to various values of Pp.

Parametric curve f i t s were then made to the r e su l t i ng values

of H. The TMRF equat ions are given in Appendix B-

Although the TMRF equations are simple to use d i r e c t l y ,

for purposes such as the computation indicated in Equation

(3-8), i t i s of g r e a t u t i l i t y to work ou t , once and for a l l ,

matrices r ep resen t ing P (I^.^ , ^ ) for various values of

80

T . « i t h s u c h " P o w e r T a b l e s " a v a i l a b l e , c o m p u t a t i o n of

 from E q u a t i o n ( 3 . 8 ) i s e x t r e m e l y f a s t , and i t i s a

t r i v i a l m a t t e r t o r e p e a t t h e c a l c u l a t i o n w i t h e t h e r

f r e q u e n c y t a b l e s , F ( I p ^ , x X ) , ( r e f : S u b s e c t i o n 3 . 2 . 2 b ) o r

f o r o t h e r s o l a r s t r a t e g i e s ( r e f : S u b s e c t i o n 3 . 3 ) . E x a m p l e s

of s u c h Power T a b l e s a r e g i v e n i n T a b l e s 3 . 2 - 3 . 6 .

The Power T a b l e s shown c o r r e s p o n d t o t h e f i v e v a l u e s of

T - 1000° F , 900 ° F , 800° F , 700° F , and 500°F - r e l e v a n t t o

t h e b o i l e r modes c o n s i d e r e d i n S u b s e c t i o n 3 . 3 . The c o d e

used t o g e n e r a t e t h e s e t a b l e s i s l i s t e d i n Append ix C. I h e

e n t r i e s i n t h e t a b l e s show t h e power ( i n K B t u / h r ) added t o

t h e f e e d w a t e r by t h e s o l a r b o i l e r i n a s i n g l e " 2 0 0 - f o o t "

s o l a r g r i d i r o n . T h i s i s t h e f l u i d power g a i n : e x i t

e n t h a l p i c power m i n u s t h e e n t h a l p i c p o w e r of t h e f e e d w a t e r .

[ " E n t h a l p i c p o w e r " i s mass f l o w r a t e ( i n I b m / h r ) t i m e s t h e

s p e c i f i c e n t h a l p y ( i n B t u / l b m ) . ] The f l u i d power g a i n s were

computed f o r a =95?i (a = 0 . 6 8 8 ) , V^ = 15 MFH,

^OUT ^ ^ ° ^ p s i a , and 1^^ = 219° F .

The 42 r o w s c o r r e s p o n d t o v a l u e s of 1 ^^ from

0-012 KW/m^ t o 1 .037 KW/m^ i n s t e p s of 0 - 0 2 5 KW/ia^. The 15

89

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z ^ - , C ~ — * •-.*»••*-«*— ••—^*/i«—i^^f-i^î,-' ir» - J -^ r* ~. - ™i cn ^ o*

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X Z x - ^ O O C y O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

93

-<" - -A» r t 0'>t»* > « - ^ - ^ j i A - . ~ ^ • # j « " . A — < - • . A p » , > A ^ 0»V"»-*»> r 3 A - . « 4 »«>» « 3 0-<">.N'O#> A 3 « - < " " AO # 1

to Q .

O O CJ>

II

•^ eO€ a->4 O-* « > * > » - - . O j # o ' ^ r > ' . A > A . » - g 0 O r S • * • — . A r Afw-W o l »'A-> ' 4 - . ^ ' > - j > s o"*»" o 04^ r # A '^x -< -« J j » > a - " ~ o ^ A r r . A ' A x l

o CT»

C\J

II

rA> A>^ O'XS * • D O - . f - • A ( ^ l A O 1A» 3-X » A«- 3 0^"AvAaxf f ' -« -A

• - r r A N - ^ J a - e y x"-a"Xi » I A - > < > J - . j > * ar-0«- . ->JT>Af~»O"VAA o'x>'3-»-r\-e or-y]

+-> 13 O

CL.

L o - ^ O J A > A r - - < / N > # a r M O O »• a> A*~-«<AO'-A~-Al O O <• a> • r f a - « A » - ' * 1 r - . . A C I A P - X - 3 > y : » ' 3 0 - » - . - < A » - > j * e A » » • . . A iA o O - o r - * ~ t o - " y y > ^ 3 " ' " * ; ^ ' ^ i f C ^ ; ?

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? * . - ; : ^ : < : ^ x ^ * - t 7 * A - > A . A A T , A n > * J - M - M J M . V — - — • — -

I

y i ^ ^ ^ A i A ? * 4 - J * 4 - - « - ^ - A - i A m r > A A . - j r v ^ J w - - r ^ — O J - A

£ A »• r - f A y ir

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o

. 2 - S - j r - . ^ A O . A j y r<y r UJ A J o — a - r — M - ^ O K ^ x T ; ^ ^ 5 A m - J O > - - O ^ A . - . r i y > - - D * i A - . - > c c > - t f N * A , - < y x

" • . a y y - r y 0»A*^

A O A O - A ' _ — a — i s > a A

o;j;o;-:c:^;>:.;—o^^ô^--o-^2-Ar7s?*r;:'Â^ 3 42a3iAÂ.' *^^?^^- ' '"^-"" ' '-^"' ' '—'-'"^

tf^>^rr.^--ôr«^^--ao^y2-J^;S^S2,l^:i;r^-P£a^«-^-^^ •O a O-0lAW^J•.lf^ Arf> T J-•» * r^-^t^-^'

94

columns c o r r e s p o n d t o v a l u e s of t h e i n c l i n a t i o n a n g l e , UL ,

from 2 . 5 ° t o 7 2 . 5 ° i n s t e p s of 5 ° . These t a b l e s a r e

c o n v e n i e n t l y r e p r e s e n t e d a s m a t r i c e s indejced by i and j :

(^p)ij where i C £ 1 ,42] and j ^ £ 1 ,15] (3.9a)

where

I^^ = £ 0 . 0 1 2 + ( i - 1) (0 .025) ] KW/m (3 . 9D)

and

^ = 2.5 + ( j - 1 ) ( 5 ° ) . (3.9c)

These Power Table matr ices are conveniently used in

conjunction with the Freguency Tables , discussed iu the next

subsection, to compute the annual power delivered by solar

gridiron b o i l e r s .

95

3 .2 .2b F requency T a b l e s - The B r i g h t Eyes T a b l e s

As i n d i c a t e d in t h e p r e v i o u s s u b s e c t i o n , E g u a t i o n (3-8)

may be used t o compute t h e a n n u a l a v e r a g e power c o n t r i b u t e d

by a s o l a r g r i d i r o n b o i l e r . Th i s app roach r e q u i r e s the

func t ion F(Ipj^y s^ ) , a n o r m a l i z e d j o i i n t d i s t r i b u t i o n

func t ion of 1^^ and V»A-. o v e r some s p e c i f i e d t ime s p a n .

The CSPP f o r m u l a t e s and s t o r e s such a f r equency t a b l e ,

c a l l e d a B r i g h t Eyes T a b l e , BET, f o r t h e ADVS s i t e ( co-

l o c a t e d with t h e s i t e of t h e of t h e p roposed p l a n t ) fo r

every day f o r which a_t l e a s t f i v e h o u r s of ADVS o p e r a t i o n

data were t a k e n . U n f o r t u n a t i e y , t he ADVS s i t e p r o c e d u r e s

have been s u c h t h a t 'L.^ , ^JL d a t a i s n o t g a t h e r e d when t h e

r e c e i v e r i s i n t h e " s tow p o s i t i o n " . Al though t h e ADVS has

been o p e r a t e d eve ry day s i n c e J a n u a r y 2 3 , 1980, t h e r e c e i v e r

i s o f t e n s towed d u r i n g p e r i o d s of low i n s o l a t i o n

2

(I < 0.4 KW/m ) • T h u s , f o r a p p r o x i m a t e l y o n e - t h i r d of tne

days d a t a was g a t h e r e d i n t e r m i t t a n t l y f o r a t o t a l r e c o r d

length of l e s s t h a n f i v e h o u r s .

I n c l u d e d in t h e ADVS o p e r a t i o n da t a a r e r e a d i n g s of 1^

and t h e t i m e of day , r e c o r d e d e v e r y 20 s e c o n d s . The va lue

of ^ may be o b t a i n e d from t h e time ( r e f : Eg. ( 2 . 2 ) ) cy

96

c o n v e r t i n g t o l o c a l a p p a r e n t t i m e . To form a BET f o r a

given day , t h e v a l u e s of I and sJL. a r e ave raged over 15

c o n s e c u t i v e r e a d i n g (5 minu te i n t e r v a l s of t i m e ) . The

r e s u l t i n g v a l u e s , ^^nN^ ^"^^ ^ ^^ ^' ^^^ t hen used t o

l o c a t e a c e l l i n t h e same m a t r i x fo rmat used f o r t h e Power

Tables ( r e f : T a b l e s 3 . 2 - 3 . 6 and Eqs. ( 3 . 9 ) ) . In o t h e r

words, c e l l i n d i c e s i and j a r e d e t e r m i n e d suca t h a t

i ^ £ l , 4 2 ] and j ^ £ 1 , 1 5 ] (3.10a)

i > <^DN^/ 0 -0255 K8/m^ > ( i - 1) (3.10b)

j > < yJL >/5° > ( j - 1 ) . (3.10c)

The mat r ix F . . , of s u c h c e l l s i s used t o coun t t h e number of

occu r rences of t h e v a r i o u s <lnM>r ^ ^=^ ^ p a i r s . The F -j

matrix i s i n i t i a l i z e d t o z e r o , and t h e n the a p p r o p r i a t e

element i s i r c r e m e n t a e d by one fo r each 5 minute t ime

i n t e r v a l of d a t a . Such a t a b l e , comple ted f o r t h e e n t i r e

data r e c o r d f o r t h e day i s c a l l e d a UBET, unnormai ized BET.

The n o r m a l i z e d v e r s i o n , t h e BET, i s formed by d i v i d i n g each

t ry in t h e BET by t h e t o t a l number of e n t r i e s fo r t h e day . en

97

There a r e numerous ways t o combine s i n g l e day f r e g u e n c y

t a b l e s to r e p r e s e n t l o n g e r p e r i o d s of t i m e . I f one s imply

adds t h e n o r i a l i z e d BET m a t r i c e s f o r a number of days and

d i v i d e s by t h e number of d a y s , t h e r e s u l t i n g BET c o r r e s p o n d s

to " e q u a l l y w e i g h t e d d a i l y a v e r a g e p o w e r s " . I f , i n s t e a d ,

one a v e r a g e s n o r m a l i z e d BETs f o r a number of days with

averaging w e i g h t s based on t h e c o r r e s p o n d i n g

o p e r a t i o n - d a y l e n t h s , t h e n a PODA Model r e s u l t s

( ref : Eq. ( 3 - 5 a ) ) : " e q u a l l y we igh ted d a i l y e n e r g i e s " . I f

the OBETs f o r a number of d a y s a r e added and, t h e n , the

r e s u l t i n g TIBET i s n o r m a l i z e d , t h e n one h a s " e q u a l l y weighted

5-minute d a t a i n t e r v a l s " . T h e s e , and a l l o t h e r DETs, a r e

biased in one way o r a n o t h e r , as a r e a l l e f f o r t s t o

" c o n s t r u c t a t y p i c a l y e a r " .

For t h e p u r p o s e s of t n e p r e s e n t s t u d y , t h r e e BETs were

assembled, a l l by add ing d a i l y UBETs and n o r m a l i z i n g the

f ina l m a t r i x . The f i r s t , c a l l e d t h e " a n n u a l f re- juercy

t ab l e " was coirposed by add ing a l l of t h e UBETs from t h e 242

a v a i l a b l e d a y s be tween March 1, 1980 and March 1, 1981- The

second, c a l l e d t h e " F e b r u a r y , 198 1 f r eguency t a b l e " was

composed i n a s i m i l a r f a s h i o n from the a v a i l a b l e days from

98

t h a t month. The t h i r d , formed i n t h e same f a s h i o n , i s

c a l l e d t h e "December , 1980 f r e q u e n c y t a b l e " . These t n r e e

BETs a r e shown i n T a b l e s 3 . 7 - 3 . 9 . These BETs a r e r a t h e r

d i f f e r e n t from e a c h o t h e r , o f f e r i n g d i f f e r e n t p e r s p e c t i v e s

on the ADVS s i t e i n s o l a t i o n c h a r a c t e r i s t i c s . The d i v e r s i t y

of t h e s e t h r e e e BETs i s used to check the c o n c l u s i o n s

reached i n S u b s e c t i o n 3 - 3 -

Osing ( n o r m a l i z e d ) Bet m a t r i c e s o rgan i zed i n t he

fashion i n d i c a t e d by Eqs- (3 .10) and Power Tajj les i n the

format shown i n E ^ s . ( 3 - 9 ) , t h e formula given i n EQ. (3.8)

may be w r i t t e n :

42 15 P - .

 = .1 I ( p ) . . F . . = JTLIP'CM • (3.11) F i«l j=l ^ F'lj i j ^^ \ F [

The l a s t form shown p r e s e n t s t h e c o m p u t a t i o n a s e v a l u a t i n g

the t r a c e of t h e p r o d u c t of one of t h e m a t r i c e s witn t ne

t r anspose of t h e o t h e r -

I f t h e Power T a b l e m a t r i x i n E g u a t i o n (3.11) i s t aken

to be an " i s o t h e r m a l e x i t s t a t e " t a b l e , such as one of t h o s e

i l l u s t r a t e d i n T a b l e s 3-2 - 3 - 6 , t hen t h e a v e r a g e power

evaluated would c o r r e s p o n d to a " s i n g l e mode s t r a t e g y " .

99

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• ~ P-OC J ^ O ^ O O O ^ O JO O O O O O O O O 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C J , * 3 * 0 0 O J O w O J O J o o o >0 0 0 0 0 - ^ 0 3 0 o o o J OO J O O O 3 0 J O O

• » . « J O W A A lA A — O V r *•.% w O O J

r - ' J J o . ! J J o J o o J - ^ o ' J Jo*o-*o'J * o o j ' o o o ' J o J o o o o o j o o o o o o

•S ô :3 ' j ; j :o . ' J : * ' 'oo I J O J O O : O * J O O O . J O O . O .O . O O O .

o

^ _ Ao n . , o > J - 0 0 0 . ^ 0 . O J . O O O O O O O O C O ^ O O O O J O . . O . O O O O

O - o : c • J - J J o J - ' J ^ J - c o - J o - J - J j - J o J 3 0 0 0 , . 0 0 0 0 r . . 0 . 0 0 0 .

s -QJ

-^ J - 3 > ^ . ^ . 0 0 0 3 ^ 0 3 ' , 0 ^ < - . - 0 - ^ J ' 0 - 3 0 O > 0 0 3. q 0 - 3 0 . -

^ J , o J J J - > - > oo - O O J O J J J J«joo ^^ cr

fO . . , , , - - . - , - , 3 ' > o r - , o . O ( ' 0 ' 5 T " o o ' ' < " > > 4_) - . - ^ 3 . - - • ^ - ' - " i •: ; a ; V . ; ^ a i i • • • •

O ^ c : - 3 * J J : . : J * O ^ J O O J O O O O O O O O . > O O O O O O O > . O O O O O . . O O O J

7 r - > a ^ - < ^ A r - > a * - c ^ a * - > o * - J a * - » ^ 4 . - > a * - * a * - . > o * -

5 • • * J J J - L 4 r > r t r x » 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

a . . - . o o o o o o o c^'"'^^"'""^'"'"'^*''^""-''-^

102

such strategies are very poor for a solar-electric power

plant- The Strategies considered in Subsection 3,3 are

"fflultimode strategies". A "strategy decision function" is

used in multiicde strategies to switch from one Power Table

(from one controlled exit fluid state) to another, bajed upon

various test cr i ter ia related to 1^^ and ^.^ Once a

strategy has been selected, i t i s possible to devise a

single (nonisothermal) Power Table matrix for guickly

evaluating that strategy against various insolation

characteristics , (by using various matrices F-• in

Eg. (3.11)).

1-2.2 Evaluation of the Solar Penetration

The solar penetration a i s the fraction of the plant* s

a£2§s annual electrical energy which is derived from energy

delivered by the solar boilers. The penetration may also be

viewed as the fraction of the plant's overall fossil fuel

requirements which i s saved due to the presence of the solar

gridiron component-

Because the penetration is based on the gross

electrical power, and because the turbine is operated in tne

103

same thermodynamic cyc le a t a l l t imes , the penet ra t ion may

be computed as the r a t i o of the expected annual gr id i ron

energy used by the t u r b i n e to the t o t a l annual energy used

by the t u r b i n e . The t o t a l energy consumed by the tu rb ine i s

the quan t i ty ,

. '^850 " "219 \ ALERT

"850

given i n E q u a t i o n ( 3 - 4 ) . The ALERTs f o r t h e two t u r b i n e s

for each of t h e ' t h r e e l o a d s c o n s i d e r e d a r e g i v e n i n

Table 3 . 1 -

The g r i d i r o n e n e r g y used by the t u r b i n e i s s m a l l e r than

the q u a n t i t y .

AEC = <Tp>rtM (3585 OP-HRS)

defined in E q u a t i o n ( 3 - 6 ) , due t o l o s s e s o c c u r r i n g i n t h e

long f l u i d l i n e s from t h e s o l a r b o i l e r s t o t h e c e n t r a l

p lan t . For each of t h e s e modes t h e e n e r g y used by the

t u r b i n e i s g i v e n by

\ H -^<VH - «S.M'"H - "ML ' ^ ' " « ^ ''^=' " • ' ' '

104

where

<Pr>M • (3585 h r s ) i s t h e a n n u a l ene rgy d e l i v e r e d by the F M

s o l a r b o i l e r i n t o mode M ( b o i l e r e x i t t e m p e r a t u r e , T ) ,

M i s t h e a v e r a g e s o l a r b o i l e r mass f l o w r a t e whi le S,M

d e l i v e r i n g i n t o mode M,

h„ i s t h e s p e c i f i c e n t h a l p y (in Btu/lbm) of 900 p s i a M

f l u i d a t t e m p e r a t u r e T|^, and

h „, i s t h e s p e c i f i c e n t h a l p y of 900 p s i a f l u i d a t the ML

t e m p e r a t u r e T ML remaining a f te r l i n e losses,

The average mass flowrate for each mode i s given by

M S,M

<PF-M

hjVi - ^219

(3.13)

so that Equation 3.12 may be wr i t ten

S,M 1 -

^M " ^ L

hf - ^219

[<Pj_>j (3585 hrs)]

• ML • ^219

h ^ - h2 i9 J (AEC)

M

(3 . 14)

105

where (AEC)| i s t h e annua l s o l a r energy d e l i v e r e d i n t o mode

The s o l a r p e n e t r a t i o n r e s u l t i n g from mode M i s , t h e n .

M I

(1.143)

^ML " ^^219 ^850 \ (AEC)^

h850 - h2 i9 ALERT

h| j_ - 178 Btu/lbm

hj - 178 Btu/lbm

The t o t a l s o l a r p e n e t r a t i o n i s

(AEC) M

ALERT (3.15)

I ^ = M M ' (3.16)

where the sum i s over a l l modes used . The q u a n t i t i e s

(AEC)w a r e determined from the q u a n t i t i e s <Pp >^ , which

are obta ined in t h e cou r se of computa t ions of <Pp > under

any s t r a t e g y - The averaqe powers for each mode a re

considered in Subsec t ion 3 . 3 .

In t he absence of a complete f i n a l design for t he CSPP

plant , however, t h e r e i s some u n c e r t a i n t y in the l i n e l o s s e s

to be expected- In o t h e r words, the t e m p e r a t u r e s , T j^|_ , are

not Icnown a c c u r a t e l y - Seasonable v a l u e s , assurabed fo r the

various modes a r e shown in Table 3 . 1 0 , along with tne

corresponding va lues of t h e f a c t o r

106

Table 3.10 Approximate Mode Loss Penalty Factors

Assumed I'luuc a n

(at 900

QM

AM^

AM2

AM3

DM

psia) ^M

1000°F

900° F

800° F

700° F

500° F

"'"ML

900° F

820°F

740°F

660°F

480°F

Loss* -r

' AT

100°F 80° F

60°F

40°F

20°F

> Eq.(3.17))

1.095

1.102

1.108

1.116

1.056

107

hM| - h 2 i 9 \ / heso \ / h -178Btu/lbm^ % = I — =1.143M|^ 1(3.17)

h, - h2i9/ 1^850-^219/ \ h^""' ^ Btu/lbm,

in square b r a c k e t s i n Equation (3 .15 ) .

Because the mode l o s s pena l t y f a c t o r s , W , a re not

accura te ly known, f o r pu rposes of t h e p r e s e n t s tudy a

simplifying approx imat ion was made. The values of W» shewn

in Table 3-10 do no t e x h i b i t a l a r g e v a a r i a t i o n , and the

value shown for t h e DM i s probably u n r e a l i s t i c a l l y low.

Therefore, t h e va lue

¥ ^ = 1 .08 , (3- 18) M

independent of mode was used for the r e s u l t s presented in

Subsection 3 . 3 - Under t h i s assumpt ion , t he formulas given

in Eqs. (3.15 and 16) reduce t o :

a - (1.08) ^ ^ ^M (3.19a) ^ ALERT

and

„ . (1.08) ^ ^ ^ = (1.08) - ^ (3-19b) M ALERT ALERT

108

where AEC i s the t o t a l annual so l a r energy capture defined

in Equation (3-6)

1*1 The S t r a t e g i e s of Operation

There a r e two reasons for switching the so la r b o i l e r s

from one operat ing mode to another . The f i r s t i s to try to

aaximize the annual s o l a r pene t ra t ion , a. At f i r s t i t might

seem tha t opera t ing the so l a r b o i l e r s in the most e f f i c i e n t

manner a t each i n s t a n t would increase so lar pene t ra t ion .

However, t h i s s t r a t e gy would r e s u l t in an over production of

hot water to be d i r e c t e d to the f o s s i l bo i l e r . Since any

excess water (above the turbine requirements) could not be

used by the f o s s i l b o i l e r (at constant l o a d ) , i t would not

contribute t o a . Therefore, the s t r a t egy capturing the

greatest amount of usable s c l a r energy wil l maximize o, not

the instantaneous b o i l e r e f f i c i ency , Op.

The second reason for switching from one mode to

another i s t o prolong the l i fe t ime of the so la r b o i l e r s .

During periods when the solar bo i l e r s a re operating with a

low eff iciency the temperature of the outer walls of tne

boilers are higher than the temperatures occurring a t higher

109

b o i l e r e f f i c i e n c i e s . T h i s c r e a t e s g r e a t e r s t r e s s on t h e

b o i l e r m a t e r i a l s and i n c r e a s e d t h e r m a l c y c l i n g . Thus , the

s o l a r b o i l e r e f f e c i e n c y , Op , should no t be a l lowed t o be

too smal l b e c a u s e t h e b o i l e r l i f e t i m e w i l l be d e c r e a s e d .

With t h e s e m o t i v a t i o n s f o r s t r a t e g i e s in mind, f i v e

bas i c s t r a t e g i e s were i n v e s t i g a t e d . The f i r s t t n r e e were

biased toward t h e Q u a l i t y Mode, QM. T h a t i s , t h e y a t t e m p t e d

to o u t p u t QM f l u i d u n l e s s t h e d e c i s i o n f u n c t i o n (CP 8}

forced the o p e r a t i o n t o an A u x i l i a r y , AM, or De fau l t Mode,

DM. These s t r a t e g i e s a r e r e f e r r e d t o a s Q s t r a t e g i e s . The

other two s t r a t e g i e s f a v o r e d t h e DM. They a t t e m p t e d t o

output DM f l u i d u n l e s s t h e d e c i s i o n f u n c t i o n s w i t c h e d the

b o i l e r s t o a n o t h e r mode of o p e r a t i o n . These s t r a t e g i e s a re

r e f e r r e d t o a s D s t r a t e g i e s .

1-J - l The 2 S t r a t e g i e s

The t h r e e b a s i c Q s t r a t e g i e s d i f f e r only i n t h e number

of modes u s e d : a two-mode s t r a t e g y , a th ree-mode s t r a t e g y ,

and a f i v e - m o d e s t r a t e g y . In each ca se t h e s t r a t e g y

dec i s ion f u n c t i o n ( r e f : Vol . V I I I , CSPP) was caosen to be

u . (I , >cJ^ , V , T ) w i t h V, f i x e d (for p u r p o s e s of -F * DN ' W ' OUT ' W

no

analysis only) a t 15 MPH- The s t r a t egy "decision funct ion"

i s the function which c o n t r o l s the mode s e l e c t i o n and

t r ans i t i on -

As explained in Subsection 3 .2 .2a , the function a i s

known well for s o l a r g r id i ron b o i l e r s , and relevant formulas

are given in Appendices A and B. As a matter of f a c t , for

the condi t ions

Vyj = 1 5 MPH

PQIJJ = 90 0 p s i a

T, . = 219 F (3.20) IN D« = 200 feet = gridiron aperture diameter

a = 955S (i-e-, a-n. = 0.688) I n

the values of Op (Ip^ , y j ^ ) may be obtained from

Tables 3.2 - 3.6, s e l e c t i n g the tab le appropriate to the

exit temperature of the mode. To obtain the value of Op,

one uses the fact t h a t : (tabular value of Pp) , «!)

g =

P

where (ref: Appendix A) the value of P, (for a s ing le

gridiron boi le r ) i s :

•"w = " C A „ g B j „ ( J L ) I D N " ^ - « -

Ill

2 KBtu m

' • ' " ' l ^ r ^ \ ' IN(^) IDN"^^ (3-22)

where the multiple bounce reflection factor, B ( ^ j ^ ) ,

varies monotonically froa 1„000 at >Ji = 0° to 0.977 at

J? =75° (ref: Appendix A).

The decision function, Oj-, for the three strategies is

compared at each instant (for each pair I pj , _J2 ) to a

threshhold value a TU * taken to be independent of mode. r , IH

The decision logic i s indicated in Figure 3-3. The decision

tree simply required that, at a l l times, the highest mode

that passes the threshhold test be used.

The three strategies considered are:

1) Two-Mode S t r a t e g y : QD

- u s e s o n l y t h e QM a n d t h e DM;

2) T h r e e - M o d e S t r a t e g y : QAD

- u s e s t h e QM, DM, a n d AM (T^^^ = 700°F) ;

3) F i v e - M o d e S t r a t e g y , C a s c a d e of A u x i l i a r y Modes:

QCAD

- u s e s t h e QM, DM,

*«1 t OUT = ^ ° ° ° ^ ' '

112

r

v_

5£r :5oiJ\R,

BoiL£RS IN

ReS£r EPILBKS To JLOXJJE K

jies_

M£^ ruRU OFF jgcxiXjs so ToTfiL SOLfiK FLDO<Slcc»^ 1

FIND

PF

use £Q. 3. To

FIND </2r>

5: XHPor

Figure 3.3 Decision Tree for Q Strategies

113

AM (T^^^ = 800° F) , and

Each of t h e s e s t r a t e g i e s i s paramet r ized by tne s i n g l e

parameter o^ j ^ , t h e b o i l e r e f f i c i e n c y th reshho ld -

The goal of t h e fo l lowing a n a l y s i s was to f ind the bes t

switching p o i n t , o^ j ^ , i n order t o maximize and

prolong the b o i l e r l i f e t i m e . I t should be mentioned t h a t

the a n a l y s i s accoun t s fo r a n o t h e r swi tching funct ion appl ied

by CSPP t o i t s s o l a r g r i d i r o n b o i l e r s - As may be noted from

gaps in the Power Tab les of s e c t i o n 3 .2 .2 t he re a r e some

values of I_ | and \JL fo r which QM w i l l never be used.

This i s because t h e f l o w r a t e c a l l e d fo r by these p a r t i c u l a r

condi t ions i s benea th a minimum f lowra t e th reshhold- In

order to a s s u r e t h a t no i n l e t va lves t o the s o l a r b o i l e r can

ever ge t s t uck i n a p o s i t i o n which complete ly shu t s off flow

to the b o i l e r , t h e va lves a r e not allowed t o c l o s e

completely. T h e r e f o r e , t he re i s a minimum flow which can be

provided t o t h e b o i l e r s . I f any mode c a l l s for a f lowra te

below t h i s minimum f low, then the mode of ope ra t ion must be

changed to one which w i l l not c a l l for such a low flow. The

miniiDua f lowra te t o a 200 foo t g r i d i r o n was taken t o be 800

114

Ibm/hr in t h i s s t u d y - This number was based on exper ience

with t he ADVS-

3.3.1a The QD S t r a t e g y

In the QD s t r a t e g y t he s o l a r b o i l e r s are opera ted in

the QM (1000°F, 900 p s i a ) , u n l e s s t h e value of o^ r a i l s

below a p r e - s e t t h r e s h o l d v a l u e , a- ^^ - If Or- in the QM i s

below Qp j ^ then t h e s o l a r b o i l e r i s opera ted in

the DM (500°F, 900 p s i a ) . The amount of DM water i s

compared with the maximum amount of water which the f o s s i l

boi ler can u s e . T h i s maximum a l lowab le f lowra te to the

f o s s i l b o i l e r i s taken to be 59,000 Ibm/hr (CP 8 ) ,

corresponding roughly t o t he c h a r a c t e r i s t i c s of t u r b i n e 1

(ref: Subsect ion 3 . 2 . 1 ) - I f more flow i s produced than

could be used by t h e f o s s i l b o i l e r , then the s t r a t e g y shuts

down g r i d i r o n b o i l e r s , one a t a t i m e , u n t i l t h e r e i s no

excess water produced.

Based on t h i s o p e r a t i o n s t r a t e g y t h e annual ized average

of the power c a p t u r e d , 1 0, by a l l t en Solar Bowls could

be found. F igure 3-U, shows the v a l u e s of <Pp > for QD

s t r a t e g i e s which have o^ j ^ from 0 t o 1. The peak in the

o o

o

115

.

o CXD

O

r>*

o t o

o un

o ^

o ro

O C\J

^ • ^

4-> fZ CU u S-cu Q .

c • 1 —

to cu

stra

tegi

Q

re fo

r Q

13 • M C^ ro

O

S-CU

s o O-

cu cn <a

Zi-P^O)

»«> L i_< :

t>

nnua

lize

d

< :

ure

3.4

CD

Ll_

o CO CVJ

CO m CVJ CJ) to m c\j

- M/n^aW < d> X 01

116

<P_>/ 26 ,225 K B t u / h r , which would a l s o r e s u l t i n t h e peak i n

a , o c c u r s when a p ^ ^ i s 0 . 5 . T h e r e f o r e , t he QD s t r a t e g y

which o p e r a t e s t h e s o l a r b o i l e r s i n the QM a s long a s a i s

50% o r g r e a t e r would p r o v i d e t h e b e s t s o l a r p e n e t r a t i o n . I f

the b o i l e r e f f i c i e n c y f a l l s below 50% then DM wate r i s

produced by t h e s o l a r b o i l e r s . F i g u r e 3 . 5 shows t h e a v e r a g e

value of Or f o r each QD s t r a t e g y .

3.3.1b The QAE S t r a t e g i e s

In t h e QAD s t r a t e g i e s t h e s o l a r b o i l e r s a r e o p e r a t e d i n

the QM u n t i l Or f a l l s below a d e s i g n a t e d Op y,, - When t h i s

occurs t h e b o i l e r s a t t e m p t t o o p e r a t e i n t he 700°F, 900 p s i a

AM. I f Or i s s t i l l below Op jLj,: t h e n t h e b o i l e r i s o p e r a t e d

in the DM- As b e f o r e , i f an e x c e s s of DM water i s produced

Solar G r i d i r o n s a r e s h u t down, one a t a t i m e u n t i l no e x c e s s

water i s s u p p l i e d .

The a n n u a l i z e d a v e r a g e power f o r QAD s t r a t e g i e s wi th

flp-j-^ r a n g i n g from 0 t o 1 i s shown i n F i g u r e 3 . 6 . The QAD

s t r a t e g y w i th Or- ju e q u a l t o 0 . 7 2 maximize t h e <Pp>, 28,020

KBtu/hr. F i g u r e 3 . 7 shows t h e a v e r a g e o^ fo r eacn CAD

s t r a t e g y .

117

o o

LO

o o

•S -.

C>J

to O)

CD (U

4-> ro i -

4-> CO

Q cy $-o

O

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3.3-lc The QCAD Strategies

In the QCAD strategies the solar boilers are operated

in the QM unless the value of a falls below a a . 1 1 the • F ,TH

boiler can not operate in the QM with a above the a_ _^ then r F, TrT

t h e b o i l e r i s o p e r a t e d i n an a u x i l i a r y mode which i s 100°F

below t h e QM t e m p e r a t u r e . I f Op i s s t i l l n o t a o o v e Op - rn then

an o p e r a t i n g p o i n t 100° F l o w e r i s t r i e d . The b o i l e r

o p e r a t i n g mode i s l o w e r e d i n t e m p e r a t u r e i n 100° f s t e p s i n

an a t t e m p t t o r a i s e o^ a b o v e ^cjit- I f t h e o p e r a t i n g p o i n t

r e a c h e s 700° F and o^ is s t i l l l o w e r t h a n o^ ju t h e n t h e

b o i l e r i s s w i t c h e d t o t h e DM.

The QCAD s t r a t e g i e s w e r e t e s t e d w i t h a r TU fi-'om 0 t o 1 . r , IH

The <Pp> v a l u e f o r t h e s e s t r a t e g i e s a r e shown i n F i g u r e 3 . 8 .

The peak v a l u e of <Pj .>, 2 7 , 6 2 0 K B t u / h r , o c c u r r e d when t h e

apTuWas 0 . 7 2 . The a v e r a g e o,- f o r t h e s e s t r a t e g i e s a r e r, In r

shown i n F i g u r e 3 . 9 -

hl'2 The D S t r a t e g i e s

The two D s t r a t e g i e s i n v e s t i g a t e d d i f f e r o n l y i n t h e

number of modes u s e d : a two-mode s t r a t e g y and a t h r e e mode

s t r a t e g y . i n e a c h c a s e t h e s t r a t e g y d e c i s i o n f u n c t i o n was

121 ro to

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123

based on t h e irass flow r a t e , M, through the s o l a r b o i l e r s .

The value of M can be p r e d i c t e d for any I ^ ^ , Jl^ , and

T c o n d i t i o n s by us ing t h e TMRF formulas found i n

Appendix B. The same c o n d i t i o n s (Eg. 3.20) assumed for the

Q s t r a t e g i e s were a l s o used for the D s t r a t e g i e s . With

these c o n d i t i o n s t h e va lues of M may be obta ined from Tables

3 .2 -3 .5 . S e l e c t i n g t h e t a b l e a p p r o p r i a t e t o tne e x i t

temperature of t he mode the value of M i s

( tabular value of Pr) M = ^ (3-23)

Ah

where

Ah = t h e change in s p e c i f i c en tha lapy of f l u i d s througn

t h e s o l a r b o i l e r and can be found on each t a b l e .

In t h e D s t r a t e g i e s the va lue of M Deing produced Dy

a l l ten bowls i s compared with a maximum al lowable K va lue .

This maximum value i s based on the f u l l load tlow

requirement for t u r b i n e 1,

' MAX " 59,000 Ibm/hr . (3.24)

124

If too ffluch flow i s o c c u r r i n g then t h e bowls a re switched

one by one t o a mode with lower flow r a t e s u n t i l the t o t a l

ten bowl M i s below f ^ . i f a l l t e n bowls a r e in the QM

and too much water i s s t i l l be ing produced then the bowls

are shut off one by one. As long as only ten bowls a re

considered t h e p r o c e s s of s h u t i n g off bowls i s not r equ i r ed

by t h i s p l a n t -

The d e c i s i o n f u n c t i o n fo r D s t r a t e g i e s r e q u i r e s t h a t

the mode or modes producing the g r e a t e s t combined bowl f low,

Hj be used, but never exceeding M ny . The dec i s i on t r e e

for t he s t r a t e g i e s i s found in Figure 3 .10 . The two

s t r a t e g i e s c o n s i d e r e d a r e :

1.) Two mode S t r a t e g y : DQ

- u s e s only t h e DM and t he QM

2.) Three Mode S t r a t e g y : DAQ

- u s e s t h e DM, QM and AM3 (TQ^J = 700 °F) .

For t h e s e s t r a t e g i e s t he value of the s o l a r b o i l e r

e f f ic iency , o^ , was not the b a s i s for any d e c i s i o n s . Even

though Or i s impor tan t to b o i l e r l i f e t i m e , these s t r a t e g i e s

favored t h e mode o r modes with the h ighes t Op va lues

au toma t i ca l ly .

125

6ET ^OLAR BoiLCRi rN

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REser SouiL, Ht&H£^

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Figure 3.10 Decision Tree for D Strategies

^J

126

3.3 .2a The DQ S t r a t e g y

In the DQ s t r a t e g y the s o l a r b o i l e r s are operated in the

DM as long a s M , t h e combined f l o w r a t e from a l l ten bowls ,

i s l e s s than M , t h e maximum f l o w r a t e regu ired by the

turbine (Eq. 3 - 2 4 ) - I f M e x c e e d s M„.^ for any I-.^. and

yJl^ c o n d i t i o n , t h e n one bowl a t a t ime i s swi tched to the

QH u n t i l M i s a g a i n l e s s than M .

The average annual f l u i d power captured x)y the DQ

strategy was fcund t o be

DQ = 29,513 KBtu/hr.

The average b o i l e r e f f i c i e n c y was

DQ <ap> = 98.4%

It was a l s o found t h a t 48.1% of the "^^ from DM output

and the remaining 51.9% from the 1000°F QM o u t p u t . At no

time did any s o l a r b o i l e r s have t o be shut down due to an

excess of output f low.

127

3.3.2b The DAQ S t r a t e g y

In t h e DAQ s t r a t e g y t h e s o l a r b o i l e r s a re opera ted in

the DM as long a s t h e combined b o i l e r f l owra t e , M , i s l e s s

than M ^ j . (Eq- 3 . 2 4 ) - I f M-j. exceeds Mj w , then one bowl

at a time i s swi tched to the 700° F AM u n t i l M-j- i s again

l e s s than M ,,.„ - I f a l l t en bowls are in the AM and M,- i s MAX I

s t i l l g r e a t e r than M ...^ , the bowls a r e switched one a t a MAX

time t o the QM u n t i l M^ i s l e s s than M,,.^ . With ten bowls T MAX

in t h e QM M^ w i l l n e v e r exceed M.,.„ , t h e r e f o r e , no bowls T MAX

are ever s h u t down-

The DAQ s t r a t e g y a c t u a l l y turned out to be a two mode

s t r a t egy for the t e n bowl p l a n t . I t never became necessary

to switch to the QM- The va lues of and < Op > were

found t o be

<Pp>P^Q = 30,979 KBtu/hr

"^F^DAQ = ^^-"^^

for t he DAQ s t r a t e g y - 27-9% of was acquired in the DM

and 72.1% in the 700°F AM-

128

3 . 3 - 2 C o m p a r i s o n of S t r a t e g i e s

B e f o r e t h e c o m p a r i s o n of t h e s t r a t e g i e s was made i t had

t o b e shown t h a t t h e c o m p a r i s o n was v a l i d even when

d i f f e r e n t B r i g h t Eye T a b l e s , BETs , w e r e u s e d . I n o t h e r

words , would t h e s t r a t e g i e s s t i l l c o m p a r e i n t h e same way i f

t h e I^., a n d ^j2_ c h a r a c t e r i s t i c s were s i g n i f i c a n t l y ON

d i f f e r e n t f rom t h o s e o f M a r c h , 1 9 8 0 - M a r c h , 1 9 8 1 . T h e r e f o r e ,

t h e s t r a t e g i e s w e r e a n a l y z e d u s i n g BETs w i t h s i g n i f i c a n t l y

d i f f e r e n t c h a r a c t e r i s t i c s t h a n s e e n i n t h e Annua l T a b l e

(Table 3 . 7 ) . T a b l e s 3 . 8 and 3 . 9 were u s e d . The r e s u l t s

i l l u s t r a t e d i n F i g u r e s 3 . 1 1 - 3 . 1 3 ^ o w t h a t t h e o v e r a l l

s c a l i n g o f t h e o p e r a t i o n a l r e s u l t s c h a n g e w i t h d i f f e r e n t

BETs b u t t h e r e l a t i o n s h i p s b e t w e e n s t r a t e g i e s s t a y b a s i c a l l y

t h e s ame .

The s o l a r p e n e t r a t i o n s f rom t h e s t r a t e g i e s a r e shown i n

Table 3 . 1 1 . T a b l e 3 - 1 2 s h o w s o t h e r i n t e r e s t i n g s t r a t e g y

c o m p a r i s o n s . The s i g n i f i c a n t r e s u l t i s t h a t t h e D

s t r a t e g i e s p r o v i d e t h e b e s t s o l a r p e n e t r a t i o n . I t i s a l s o

i m p o r t a n t t o r e c o g n i z e t h a t a p l a n t d e s i g n e d f o r a D

s t r a t e g y c a n be o p e r a t e d w i t h a Q s t r a t e g y w i t h t h e same

nodes . T h i s r e q u i r e s o n l y a s o f t w a r e c h a n g e i n t h e

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con t ro l l e r . If t he bes t s t r a t e g y , DAQ, in terms of so lar

penetrat ion i s chosen so the p lan t can a l s o operate with the

QAD s t r a t e g y .

Before leaving the d i scuss ion of s t r a t e g i e s i t should

be mentioned tha t one more highly s i g n i f i c a n t study was

made. This s tudy, however, analyzed the r e s u l t s of the CAQ

strategy when var ious number of so l a r bowls were used in the

plant. The r e s u l t s are given in Appendix D- This study was

made for the DAQ s t r a t e g y because i t was the s t r a t egy wnich

indicated the most favorable pene t ra t ion r e s u l t s .

CHAPTER IV

TACTICS FOB SOLAR BOILER CONTROL

The previous chapter demonstrated the importance of

control l ing the f l u id ex i t ing the so la r bo i l e r s in a ce r ta in

mode. The annual s o l a r pene t ra t ion of the plant depends

upon the s o l a r b o i l e r operat ion s t ra tegy and tne solar

condit ions. A s t r a t e g y i s chosen for operat ing the plant

based on how ituch s o l a r pene t ra t ion can be increased. Ihe

calculat ion of s o l a r pene t ra t ion for each s t ra tegy assumed

perfect c o n t r o l of the so l a r b o i l e r modes. That i s , if the

strategy c a l l s for a c e r t a i n output mode, tha t mode i s

produced i n s t a n t l y and s t ead i l y u n t i l the s t ra tegy c a l l s for

a mode change. Such per fec t con t ro l i s not r e a l i z ab l e in an

actual plant due to response t imes involved in the systera.

A control system i s required which wi l l bring the output

laode to the des i red mode as rapidly as possible without

damage to t h e b o i l e r . The b o i l e r can be damaged by large

overshoots in temperature or pressure .

135

136

In the proposed plant the fossil boiler controls the

output pressure of the solar boiler whenever superheated

steam is produced by the solar boiler- The ability to

regulate large pressure pulses from the solar boiler must be

incorporated in the pressure control system since large

pulses can occur due to abrupt insolation changes. This

control system utilizes a steam storage tank to buffer

against pressure variations and surges. Control of the

pressure i s an important concern in the plant and must be

studied in order to see if the fossil boiler control system

can respond appropriately to large pressure variations.

However, experience has shown that when the output mode

temperature is controlled in order to eliminate large

overshoots the overshoots in pressure are also greatly

reduced. In this study the control of the solar boiler

output temperature is investigated: adequate control of

pressure is assumed for this study.

The control system for solar boiler temperature

involves the positioning of a valve in order to regulate the

mass flow rate to the solar boiler. This Xind of control

can be obtained in numerous ways. Figure 4.1 gives examples

^

A 137

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138

of a few of the c o n t r o l schemes which a re f e a s i b l e . The

open loop con t ro l system in Figure 4.1a i s des i rab le but not

p r a c t i c a l . This i s because the valve and the plant do not

operate in exac t ly the same way a l l year : A manual valve

may be turned which wi l l change the plant response; the

valves themselves may erode and change c h a r a c t e r i s t i c s ; the

valve ac tua to r may change s l i g h t l y due to aging in the

e l ec t ron ic s . All of these lead t o the conclusion tha t a

system with feedback i s des i red . In t h i s study, both of tne

feeback c o n t r o l l e r s i n Figure 4.1 are analyzed. F i r s t ,

however, the exact system con t ro l philosophy and process

loop are reviewed.

i*-l Basic Control Philosophy

The b a s i c c o n t r o l philosophy of the process loop of the

solar b o i l e r s in the proposed plant i s the same as the

philosophy which has been applied to process control for the

ADVS boi le r - The process loop a t the ADVS i s i l l u s t r a t e d in

block diagram form in Figure 4 . 2 . The corresponding loop

for the proposed p lan t i s shown in Figure 4 .3 . The only

difference between the two, other than the number of solar

139

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141

bo i l e r s , i s the absence of a bypass path in the la rge

system.

The bypass path i s necessary in the ADVS oecause a

constant speed pump i s u t i l i z e d . Since the pump pressur izes

the feedwater to a r e l a t i v e l y constant mass flow r a t e , and

since a constant mass flow r a t e i s not desired a t the

boi ler , pa r t cf the pressur ized feedwater i s sent back to

the r e s e r v o i r - The con t ro l of the amount of water bypassed

is accomplished by the i n l e t valve and the bypass valve.

The bypass valve i s regula ted by a s t a t i c pressure l i ne from

the i n l e t valve , so t h a t the two valves operate in tandem.

As the i n l e t valve i s adjusted, the bypass valve

automatically ad jus t s in an at tempt to hold the pressure

drop across the i n l e t valve cons tan t . The r e s u l t of the

tandem adjustment of va lves i s an almost l inear r e l a t i o n s h i p

between i n l e t valve pos i t i on and mass flow rate to the so lar

boiler.

In the la rge system there i s a bypass loop for the

solar bo i l e r s in t he form of the f o s s i l boi ler path. The

fossil bo i l e r has i t s own i n l e t valve which r egu la t e s i t s

142

mass flow r a t e . In a d d i t i o n , the pump speed can be varied

so t h a t , when l e s s flow i s needed due to lower generator

loads, the punps slow down. This e l imina tes any need for

bypassing water back t o the deaera tor r e se rvo i r .

In the proposed p lant each so l a r bo i l e r i s indiv idual ly

controlled with i t s own i n l e t valve and sensors . The mass

flow r a t e through t h e b o i l e r i s varied by manipulation of

the i n l e t va lve . The con t ro l system diagrammed in

Figure 4.4 shows the c o n t r o l system u t i l i z e d for each solar

boiler- Here a l l computational operat ions , tae error

detector and the s i g n a l processor shown in Figure 4 . 1 , are

incorporated into the s ing l e d i g i t a l computer of Figure 4 .4 .

This system diagram i s i d e n t i c a l to the one used for the

ADVS. Each block i n the diagram was modeled and the model

was compared with a c t u a l performance recorded a t the ACVS.

H'Z The Control System Model

In the con t ro l system shown i n Figure 4.4 the solar

boiler i s t h e component which i s the most d i f f i c u l t to

model. As nentioned in sec t ion 2 . 1 , the TMR equations

provide a good model for the s o l a r b o i l e r . This model was

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used by Enayet J iwani i n a system model which wi l l be

referred to as the TMR System Model. This system model

included no time delay f a c t o r s ; t he re fo re , an improved

system model was made which included time delays and which

shall be r e fe r r ed to a s the TMRW System Model.

i - 2 . 1 The TMj System Model

Enayet Jiwani developed the Simulation Model shown in

Figure 4 . 5 . This model included the TMR equations to model

the bo i le r performance. These equations had been tested

against a c tua l ADVS performance and were superb for modeling

boiler performance, e spec i a l l y under condi t ions of steam

output from the b o i l e r . Jiwani made curve f i t s for the

performance record ings of the boi le r i n l e t valve for the

ADVS. The c o n t r o l a lgor i thms Jiwani used were i den t i ca l to

the ones used at the ADVS. These algori thms (discussed in

section 4.3) vary the voltage s ignal sent to pos i t ion the

valve, based on an e r ro r between actual and desired

temperatures a t the b o i l e r e x i t . Since the IMB eyuaticns

determine the f l u id power ex i t ing the rece iver , not the

fluid temperature, a curve f i t from steam tab les was made so

145

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that temperatures could be found. With exception of the TMfi

equations a l l other system component models were formulated

from data collected at the ADVS. Examples of tne algorithms

used to simulate the valve performance are shown in

Appendix E. Appendix F l i s t s various curve f i ts for tne

steam tables- Jiwani used this model to see if i t could

simulate the control of the fluid state in the same way the

actual system controls the fluid.

4.2.1a Model Performance - Small Perturbations

The TMR System Model shown in Figure 4.5 was given the

same solar information measured as i t occured at the ADVS

system- The simulated temperature of the steam exiting the

boiler and the actual temperature recorded at the ADVS are

plotted in Figure 4-6 (EJ) - In addition to temperature the

simulated and actual voltage signals sent to the valve

actuator are shown in the figure- The simulated and actual

performance are in very close agreement, observation

indicating that the simulated temperature slightly leads the

actual temperature. This i s not an unexpected result since

there are no time delays in the model.

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a .2- lb Model Performance - Large P e r t u r b a t i o n s

F igures 4-7 - 4-10 show the performance of t he TMR

system model in comparison with a c t u a l system performance.

Large s t e p s i n mass flow r a t e , up and down, were forced on

the system while s o l a r i n s o l a t i o n remained s t eady in

Figures 4 .7 and 4 - 8 . In F i g u r e s 4-9 and 4.10 l a r g e s t eps

in d i r e c t normal i n s o l a t i o n were s imula ted by t ak ing the

solar b o i l e r out of t h e f o c a l r eg ion and by p lac ing i t back

into the f o c a l r e g i o n . Even though t h e a c t u a l performance

and s imula ted performance converge a f t e r some t ime, the re

are l a r g e d i s c r e p a n c i e s in the two, p e r s i s t i n g from one to

almost four n i n u t e s . Such d i s c r e p a n c i e s were the major

reason for making an improved model.

i-2-2 The TMRJ System Model

The TMR Model g i v e s a c c u r a t e s teady s t a t e and small

per turbat ion s i m u l a t i o n s , but improvement during l a rge

t r a n s i e n t s was needed . There fore , the TMRW System Model

shown in F igu re 4.11 has been developed- Each block t h a t

d i f fers between t h e two models r e p r e s e n t s a time d e l a y . The

computational time de lay i n c l u d e s t h e process ing time for a

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d i g i t a l computer t o analyze a sensor s i g n a l and c a l c u l a t e a

new actuator s i g n a l . In most c a s e s , t h i s delay depends on

the computer used and the cyc le time reguested. For the

ADVS the delay t ime i s 0-8 seconds. For the proposed plant

the delay should a l s o be in the 1 second range.

The valve delay block inc ludes severa l delays . The

transmission time for the ac tua to r s i g n a l to reach the

actuator may be represen ted here ; however, t h i s i s a

negligible time for both the ADVS and the proposed plant .

The actuator response time i s included in th i s block. The

fflain idea i s to model a smooth, ra ther than ins tan taneous ,

change in valve p o s i t i o n . This smoothing was accomplished

by using an a lgor i thm such as :

Vy tt) = ^A^^"^^ * G^(V(t)- V;^(t-1)) (4.1)

where

VA = ac tua l vo l tage for pos i t ioning the valve

V = vol tage t ransmi t ted by the process con t ro l l e r

t = time in seconds

G = a cons tan t which r e g u l a t e s response time.

Based on ADVS ac tua to r performance, G was se lec ted to ue

155

G, = 0 .33 3-A

This causes a valve performance such as shown in Figure 4.12

when the t r a n s m i t t e d vo l t age to the a c t u a t o r changes by

100%-

The two remaining t ime de lay b locks s imula te response

times of the s o l a r b o i l e r . The models £ u i l t for these

blocks are e m p i r i c a l and a t t empt only t o s imula te measured

performance. While some -physical e x p l a n a t i o n s for the

delays helped t o i n i t i a t e the models, i n depth q u a n t i t a t i v e

understanding of t h e t r a n s i e n t behavior of the u o i l e r has

not been s t u d i e d .

The b lock l a b e l e d "water l i n e de lay" models t h e lack of

any b o i l e r response t o i n s o l a t i o n or flow caanges for a

f i n i t e t ime, a deadband. In p a r t , t h i s delay time can be

a t t r i bu t ed t o a d i f f e r e n t mass flow r a t e occuring at the

in le t and t h e e x i t ends of the b o i l e r . This i s due to the

vast d i f f e r e n c e i n v e l o c i t i e s of s t eaa and water in tae

tubes and t h e c o m p r e s s i b i l i t y of steam. To approximate tue

delay, c rude assumpt ions were made to s impl i fy a c t u a l f lu id

performance.

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The f l u i d i n t h e b o i l e r was assumed t o be water a t the

i n l e t t e m p e r a t u r e or s t e a m . T h e r e f o r e , t h e r e i s a water

l i n e r a t h e r t h a n a two p h a s e r e g i o n i n t h e D o i l e r . T h i s

l i n e moves a t a v e l o c i t y based on the i n l e t t e m p e r a t u r e and

the b o i l e r t u b e d i a m e t e r a s w e l l a s t h e mass flow r a t e of

f e e d w a t e r . T h i s v e l o c i t y can be app rox ima ted by

v e l =JP A/(3600*M.,) (4.2) it

where

jf = w a t e r d e n s i t y a t t h e i n l e t t e m p e r a t u r e

( Ibm/ f t )

A = c r o s s s e c t i o n a l a r e a of b o i l e r t u b e s ( f t )

and

M = mass flow r a t e p e r b o i l e r tube ( I b m / h r ) , t

3600 c o n v e r t s h o u r s t o s econds .

The p o s i t i o n of t h e wa te r l i n e depends on t h e s o l a r

i n s o l a t i o n , t h e c o n c e n t r a t i o n p r o f i l e on the b o i l e r , and the

mass flow r a t e . The c o n c e n t r a t i o n p r o f i l e for a o o i i e r a t

^ = 0° i s shown i n F i g u r e 2 . 3 . T h i s p r o f i l e was used for

modeling p u r p o s e . The p r o f i l e a t o t h e r i n c l i n a t i o n a n g l e s

158

differ from this one as can be seen by the profile for

Ji =30° shown in Figure 4.13. To account for these

differences the model assumes a symmetrically illuminated

boiler { v*^ =C°), but an insolation of:

I^^ cos V^ , (4.3)

A piecewise linear approximation of the profile in

Figure 2-3 was made and is shown in Figure 4-14. with this

approximated profile and an insolation and inclination

reading the solar energy along the boiler tubes can be

simulated- Based on another assumption—that 80% of the

energy reaching the boiler wall i s absorbed and transmitted

to the liquid water in the boiler—the location of the

boilinq line for the model can be calculated. This i s done

by finding the enthalpic energy required by the fluid to

bring i t from the inlet temperature to lOO/i steam at the

saturation temperature. For water at 219° F and 900 psia the

enthalpy i s approximately 188 Btu/lbm (ST). For 100% steam

at the saturation temperature with 900 psia the enthalpy is

1195 Btu/lbm (£T). Therefore, the fluid must gain:

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OUT " ^IN " 1195 - 188 = 1007 B t u / l b m . (u.14)

The t o t a l power r e q u i r e d t o b o i l t he i n l e t water would be

M (1007 Btu / lbm) j4_ 5j

where M i s f e e d w a t e r mass flow r a t e p e r b o i l e r t u b e i n

pounds pe r h o u r . The s o l a r power t r a n s m i t t e d to t h e f l u i d

can be found ty

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where

"^ = the assumed efficiency for the water end of

the boiler ( = 0.8)

Ipjl = direct normal insolation (Btu/hr-ft /sun)

>JL = solar inclination angle (degrees)

^(L) = profile along the receiver (suns)

V = width of sclar boiler tubes

L = distance from solar boiler tube inlet to

the water line.

162

The distance is found from the boiler inlet to the place

where sufficient energy has been transmitted to the fluid in

order to boi l . This i s done by integrating Equation 4.6

from 0 to L, where L ranges from 0 to 430 f t . , until the

power found from Equation 4.6 equals the power found in

Equation 4.5, or L = 430, whichever is smaller. The water

line is positioned at the distance d from the boiler inlet .

This whole procedure leads to the modeling of a water

line position based on I , \Jl. , and M. Any changes in

l^.,, ^ , and M a l te rs d- In the water line delay model,

d can only move at the velocity of the feedwater found in

Equation 4.2- The solar boiler model, TMR Equations, sees

no change in I^ or M until the water line is allowed enough

time to reach i t s proper position.

This computation results in a deaduand which

approximates the observed system deadband. It must be noted

again that th i s water line delay is not believed to be the

only cause of the deadband. Many other factors are involved

such as the conduction time of energy through the boiler

wail. Even though the delay factor was simulated r y

163

e q u a t i o n s from a c t u a l c o n d i t i o n s which can occur i n t he

b o i l e r t h e r e s u l t i n g d e l a y e q u a t i o n s s h o u l d be c o n s i d e r e d

only a s m a t h e m a t i c a l e q u a t i o n s model ing an observed

per fo rmance , and n o t a s e x p l a n a t i o n s f o r t h e pe r fo rmance .

The f i n a l d e l a y b l o c k i n t h e TMRW model a c c o u n t s fo r

the f a c t t h a t t h e b o i l e r w a l l h a s a c e r t a i n c a p a c i t a n c e for

s o l a r e n e r g y . Also^ t ime i s i n v o l v e d b e f o r e energy can be

t r a n s m i t t e d from t h e b o i l e r i n n e r w a l l t o t h e f l u i d . Th i s

a c t i v i t y i s a very d i f f i c u l t b e h a v i o r t o model. The o lock

l a b e l e d t e m p e r a t u r e d e l a y r e c e i v e s a s i n p u t s t n e TMR based

c a l c u l a t i o n s of power i n t h e f l u i d , P , t h e mass flow r a t e

of the b o i l e r f l u i d , M, t h e i n l e t t e m p e r a t u r e of t h e f l u i d

to the b o i l e r , T , t h e p r e s s u r e of t h e f l u i d e x i t i n g the IN

b o i l e r , P , and t h e t e m p e r a t u r e of f l u i d e x i t i n g the OUT

b o i l e r one second a g o , T ( t - 1 ) . The s p e c i f i c e n t h a l p y of

the f l u i d e n t e r i n g t h e b o i l e r , h^^., and e x i t i n g the b o i l e r , IN

h , i s c a l c u l a t e d

" I N = ^ I N - 32 '^-^»

^ OUTC = ^ P / " * '' IN ( 4 . 8 )

164

However, the assumption i s made tha t the enthalpy of the

exi t ing f lu id goes through smooth, not discontinuous, changes.

Thus the a c t u a l enthalpy of the ex i t ing f lu id n^..^ i s found

by

ÔUT^^^ = ÔUT^^-^^ * ^/^^ ^ÔUTC~ SUT^^-^^J ^''"^

where

t = time in seconds

R = v a r i a b l e based on mass flow r a t e

C = va r i ab l e based on previous exi t temperature

The value of C i s found by

T ^ ( t - I ) < TgQjL

0 .6 T £ ( t - 1 ) > TgoiL

(4 .10 )

165

where T . i s found by

^ A C T = ^ ' ' ' ' ' ^OUT ^ ' ' ' ' '

"^BOIL = ^Q"^ - lO^IPpACT ) - 37(PpACT f - (4 .11)

The v a l u e of R i s f o u n d by

R = 15 ^ 2 5 0 e-f'^/SOO) (4 .12)

These va lues were determined from da t a c o l l e c t e d a t tae

ADVS. Appendix G shows the computer l i s t i n g for t he TMRW

model.

4.2.2a Model Performance - Small P e r t u r b a t i o n s

The THR» Model of F igure 4 .11 was used with a c t u a l data

co l lec ted a t the ADVS to s i m u l a t e p r o c e s s loop behavior .

This s i m u l a t i o n i s compared to a c t u a l ADVS performance in

Figure 4 . 1 5 . The F i g u r e shows t h a t the system performance

was a c c u r a t e l y modeled by the model- The TMRW Model shows

smoother t e m p e r a t u r e r e l a t i o n s t h a t a r e more nea r ly in phase

with t h e a c t u a l da ta than the TMB Models r e s u l t s

(Figure 4-6) .

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4.2.2b Model Performance - Large Perturbations

The TMRW model was used to simulate system performance

when faced with large changes in insolation or mass flow

rate. Comparisons of simulated performance to actual

performance are seen in Figures 4.16 - 4.19. While tne

simulation i s far from perfect i t i s superior to the

simulations obtained from the TMR System model faced with

large perturbations. In particular the TMRW System Model

can simulate some of the problems faced in response times

during large transients. If these response times are

ignored, a simulated control system can look much better

than the actual control system. That is , when the

computational operations, or controller, i s developed witn

no time delays, the actual use of this controller might be

totally unacceptable. However, when time delays are

considered, a more useful controller may oe found-

ii-3 The Controllers

The reason for developing a system model is to try to

find ways to improve the system response. The easiest way

to improve the system in Figure 4.11 is to find the best

168

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172

algorithms i n the process computer. The a lgor i thms are

referred to as t he c o n t r o l l e r and two t a c t i c s for con t ro l

were i n v e s t i g a t e d . The f i r s t t a c t i c u t i l i z e s a c o n t r o l l e r

which opera te s on an e r r o r in the measured (or simulated)

solar bo i l e r output temperature and the des i red , or s e t

point, tempera ture . A c o n t r o l l e r of t h i s type i s p re sen t ly

in use a t t he ADVS- The second t a c t i c for c o n t r o l l e r s i s to

operate on an e r ro r between the measured (or simulated) mass

flow r a t e and the mass flow r a t e ca lcu la ted by the RFC

equations (Appendix B) required for a ce r t a in temperature

output from the s o l a r b o i l e r s . These two t a c t i c s are

discussed below.

i - i - 1 The T Ccn t ro i l e r

The T C o n t r o l l e r i s i l l u s t r a t e d in Figure 4 .20. This

control ler i s c u r r e n t l y being u t i l i z e d a t the ADVS. This

par t icular s e t of a lgor i thms was developed by Dr. John D.

Reichert and i t s development i s explained in J i w a n i ' s work

(EJ) . The e r ro r in the valve actuator s igna l i s determined

by

173

vJ I I

A v

CU

o 4-> E O

CJ

(U

o CM

(U

CD

174

where

I ., = direct noriral insolation DN

.> = a sliding average of I

T = neasured temperature at the boiler output

T,. = desired temperature at the boiler output,

A sliding average of a term simply means that current inputs

are weighted more heavily than previous inputs when

averaging the value. This type of averaging can be done by

an algorithm such as

<x>{t) = <x>(t-1) •G (x(t) - <x>(t-1)) (4.14)

or

t

<x>{t) = f G [x(t) - <x>(t-1)J dt / G [x(t)

J ^ to

The factor G„ determines how heavily the most resent data is

weighted. The larger G. ,the more heavily current data is

weighed so the value of <x> would approach the current value

of X more quickly. The sliding average of I is found by:

DN

< ^ D N " ^ " ^ = < ^ D N " ^ ^ - ^ ^ " ^i^^DN^^^ - ^ ^ m ^ ^ ' - ' ^ ^ ' ^'-''^

175

The ^ t e r n i n c l u d e s an l^^ comparison as wel l a s

temperature t o a i d i n p r e d i c t i n g the t empe ra tu r e r e s p o n s e .

Experience wi th t h e ADVS h a s shown t h a t c o n t r o l without IQM

c o n s i d e r a t i o n s l e a d s t o a p o t e n t i a l l y unresponsive system

during t r a n s i e n t c o n d i t i o n s , because the t ime de lays in the

system re sponse t o on ly T, and not I , i s of ten too slew t o

prevent over hea t ing i n the s o l a r b o i l e r -

The o term i s used to determine t h e a c t u a t o r v o l t a g e .

The a c t u a l v o l t a g e s e a t to t he a c t u a t o r a t the ADVS i s

0 - lOv. The a l g o r i t h m in t he T c o n t r o l l e r c a l c u l a t e s a

value i n p e r c e n t a g e r a t h e r than v o l t a g e . A s i g n a l from

0 - 100% in c a l c u l a t e d . In t h i s case 0 impl ies an open

valve. 100% i m p l i e s a c losed v a l v e , but the valve i s never

completely c l o s e d - Thus even when a s i g n a l of 100^, or

10 V, i s s e n t t o t h e a c t u a t o r the valve s t i l l a l lows

approximately 15% of t h e maximum load flow r a t e to pass the

valves- This i s done fo r s a f e t y to t h e b o i l e r w a l l s . The

actual c a l c u l a t i o n of t he a c t u a t i n g s i g n a l i s :

V(t) = <V>{t) - (V - < V > ( t ) ) ^ (t) t4. 1o)

where

176

V (t) = ac tuat ing s i g n a l in %

<V>(t) = a s l i d i n g average of V

V = a cons tant .

The s l i d i n g average for V i s found by

< V > ( t ) = < V > ( t - 1 ) + G^ ( V ( t ) - < V > ( t - 1 ) ) . (4 -17 )

The values of V and <V> are always clipped so that they are

never greater than 100 or less than 0. If one of the limits

-0 or 100- is calculated for V the value of G is increased. V

This will bring the value of <V> closer to V.

The value of V^ in the equation must always be greater

than the value of <V>(t) if the proper command - more open

or more closed - called for by the cL^ term is to be sent to

the valve. In practice Vp is usually kept greater than 100

to assure this. The T controller, listed in Appendix G, was

used in conjunction with the rest of the TMRW System Model

for the large system in order to find the best values of G^,

G , and V to be used in the contrcller.

177

Tes t ing the T c o n t r o l l e r involved s imula t ing va r i ous

DN c o n d i t i o n s . The c o n t r o l l e r was t e s t e d while i t had a Tr

of 1000°F. This was done because overshoots i n t h i s range

must be l i m i t e d f o r t he sake of the b o i l e r . A maximum

overshoot of 1260°F i s a l lowed. Various va lues of G - GT^ V 1

and Vp were t e s t e d and the I n t e r g r a l of Time m u l t i p l i e d by

the Square of the E r r o r index , ITSE, was c a l c u l a t e d . Ihe

ITSE index p r o v i d e s a s i n g l e c a l c u l a t i o n r e l a t i n g

overshoots , u n d e r s h o o t s , and s e t t l i n g t i m e . In reducing the

ITSE index t h e s e t h r e e system responses are a l l cons idered

and usua l ly reduced- The ITSE i s found by

ITSE = / t E dt (4. 18)

where

E = 1 - T^ . (^.1^)

Table 4-1 shows t h e v a l u e s of G^, G^, and V^ which are

favorable f o r e i g h t d i f f e r e n t i n s o l a t i o n v a r i a t i o n s .

Figure 4-2 1 - 4.28 show the p r e d i c t e d temperature response

Table 4.1

Favorable Parameters for the T Controller

178

' J ^ 0.01 t 10

^ 1.0 t 10 T^= 1000

^ , _ 1.0 t 10 DN ' 0.01 t 10

T^= 1000 3

Ipf^=t/1200

T^= 1000

4 Ipf^=l-t/1200

T^= 1000

^ t Ip^=.9+.lsin(^)

1^=1000

6 t Ip^=.6+-4sin(^)

T =1000

7 t Iorj=.9+.lsin(gQ)

T^=1000

^ t Io^=.6+.4sin(gQ)

T^=1000

J 1000 t 10

^ 500 t 10

' I = 0 9 ^DN ^'^

J ^ 500 t 10 s 1000 t 10

^c

250

250

250

250

250

250

250

250

250

250

^I

0.4

0.4

0-4

0.4

0.4

0.4

0.4

0.4

0.4

0.4

S

0.015

0.015

0.05

0.05

0.05

0.015

0.05

0.05

0.05

0.05

ITSE

0-4 E9

385.4E9

40. E9

1.33 E9

60.7 E9

0.6 E9

2.0 E9

9.8 E9

0.34 E9

0-05 E9

^MAX

1000

1000

1239

1260

1113

1039

1241

1147

1069

1000

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when these values are used during the ind ica ted I

va r i a t i on . Also shown in Table 4.1 i s the response of the

system t o changes in the se t point temperature.

Figures 4.29 and 4.30 show the response curves for these

va r i a t i ons . Other f i g u r e s , in Appendix H, show the

temperature behavior for these 1^^ and T changes whenever

other values of G^, Gj , and V a re used.

4.3.2 The M C c n t r o l l e r

The H Con t ro l l e r (Figure 4.31) operates on tiie

pr inciple t h a t i t can pred ic t the mass flow r a t e necessary

for a c e r t a i n ou tput s t a t e a t the so l a r boiler if i t knows

the Ipji and N - ^ va lues- This predic t ion i s accomplished

by the use of the RFC equat ions in Appendix B. If the i n l e t

valve behavior could be modeled with 100?i ce r t a in ty then the

exact ac tua t ing s i g n a l t o cause the predicted flow r a t e

could be computed. However, experience indicated tha t the

exact behavior of the valves cannot be described with

las t ing accuracy. For one thing, other valves in the system

188

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sometiae c a u s e t h e i n l e t va lve M versus V curve to change.

Also, with t ime , va lve e r o s i o n and d r i f t in e l e c t r o n i c

elements in the a c t u a t o r cause the M versus V curve t o

change. T h e r e f o r e , feedback i s s t i l l d e s i r e d in the rt

c o n t r o l l e r .

The feedback s i g n a l in t h e M c o n t r o l l e r i s the mass

flow r a t e r e a d i n g t o a b c i l e r . The reason an rt c o n t r o l l e r

has never been u t i l i z e d a t the ADVS i s because ao r e l i a b l e

feedback s i g n a l a t t he low flow r a t e s c a l l e d fo r i s

a v a i l a b l e - However, with t he l a r g e system flow ne te r

producers have a s s u r e d much g r e a t e r r e l i a b i l i t y from the

flow meters-

The feedback flow reading i s used to de r ive an e r r o r

terra:

e = ( M Q / M ) - 1 (4 .20 )

where

fl = t h e flow r a t e des i r ed by the RFC equa t i ons

M = t h e measured flow r a t e t o the b o i l e r .

192

T h i s e r r o r t e r m i s u s e d i n much t h e same way a s t h e ^ t e r m

of t h e T c o n t r o l l e r - T h a t i s , t h e a c t u a t i n g s i g n a l i s

c a l c u l a t e d b y :

V ( t ) = < V > ( t ) - Ke ( 4 . 2 1 )

where <V> i s found by E g u a t i o n 4 . 17 . The v a l u e s of V and

<V> a r e s t i l l c l i p p e d t o r e m a i n w i t h i n 0 t o 100%. A l i s t i n g

of t h e c o m p u t e r c o d e f o r t h e M c o n t r o l l e r i s found i n

Appendix G .

The M c o n t r o l l e r was t e s t e d a g a i n s t t h e same Igt. and Tr

v a r i a t i o n s a s t h e T C o n t r o l l e r . T a b l e 4 . 2 shows t h e

f a v o r a b l e v a l u e s of K, and G f o r t h e s e c o n d i t i o n s . I h e

ITSE was a g a i n f o u n d by E g u a t i o n 4 . 1 8 , a n d t h e maximum

t e m p e r a t u r e o v e r s h o o t was a g a i n l i m i t e d t o 1260 F-

F i g u r e s 4 . 3 2 - 4 . 4 1 show t h e t e m p e r a t u r e r e s p o n s e c u r v e s f o r

each o f t h e c o n d i t i o n s i n T a b l e 4 . 2 . A l s o i n Apper .d ix H a r e

F i g u r e s s h o w i n g t h e r e s p o n s e of t h e s y s t e m wi th M c o n t r o l l e r

us ing v a r i o u s o t h e r K a n d G v a l u e s .

Table 4.2

Favorable Parameters for the M Controller

193

" J ^fo.oi t<10 ^^ l i .o t^lo

Tg= 1000

^ I =0-0 t<io ^ lo.oi t>10

T^= 1000 3

Ipj^=t/1200

T = 1000 s 4

Ip^=l-t /1200

T = 1000 s

V.9+.lsin(f^) T3=1000

\ ^ = . 6 4 - . 4 s i n ( ^ )

T =1000

7 ^ Io^^=.9+.lsin(gQ)

T =1000 s 8 ^ Ij3^=.6+.4sin(gQ)

T =1000 s

J OOOO t - ' lO

H 500 t ^ i o ' " I = 0 9 DN ^'^

J ^C500 t < 1 0 s (lOOO t > 1 0

K

100

100

20

5

20

5

5

100

5

100

Gw

0.8

0.8

0.8

0.2

0.8

0.2

0.8

0.2

0.011

0.5

ITSE

9.2 E9

385,4:E9

83.8E9

42.2E9

15.9E9

22.9E9

20.8E9

2.1 E9

•2.4 E9

22.5E9

'MAY

1000

1000

1184

1260

1260

825

1260

1077

1000

1259

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4.3.3 Comparisons Between T and M Con t ro l l e r s

A comparison of Tables 4.1 and 4.2 as well as the

f igures of the previous s e c t i o n s demonstrate acceptable

control of t he s o l a r b o i l e r s t a t e by a number of ways.

There are two reasons for favoring a T c o n t r o l l e r . The

f i r s t i s t h a t , even though Figures 4.20 and 4.31 do not make

i t obvious, the T c o n t r o l l e r requ i res l e s s memory spiace and

computational time than the M c o n t r o l l e r . The second reason

i s t ha t the M c o n t r o l l e r seems to outperform the T

con t ro l l e r i n only two cases . Both of these cases have

o s c i l l i t o r y I cond i t i ons . I t i s very hard to bui ld a DN

switching funct ion around condi t ions such as these s ince i t

cannot be known to be o s c i l l i t o r y un t i l a f te r the f a c t . I t

i s recognized tha t an M c o n t r o l l e r may reen te r the

considered c o n t r o l l e r s whenever the pressure cont ro l

guestion i s cons idered , but a t t h i s time the T c o n t r o l l e r i s

recommended.

The u t i l i z a t i o n of a switching function for the G

parameters in the T c o n t r o l l e r might be used based on large

pos i t ive values for the de r iva t i ve s in 1^^ . However, i t

does not appear to be necessary for the c o n t r o l l e r to switch

205

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This w i l l change t h e response l i s t e d i n the prev ious s e c t i o n

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these c o n d i t i o n s i s shown in F igures 4.42 - 4 . 4 4 . The

response has not s i g n i f i c a n t l y d e t e r i a t e d .

206

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CHAPTER V

BECOHHENDATIONS

The f i n a l d e s i g n of t h e S o l a r F o s s i l - Hybrid P l a n t by

t he C r o s b y t o n S o l a r Power P r o j e c t w i l l be u n d e r t a k e n in t h e

next few a o n t h s . The r e s u l t s from t h i s s t u d y p r o v i d e u s e f u l

i n f o r m a t i o n f o r t h e f i n a l d e s i g n . S e v e r a l s t r a t e g i e s f o r

o p e r a t i n g s o l a r b o i l e r s have been i n v e s t i g a t e d and two

t a c t i c s f o r c o n t r o l l i n g t h e p r o c e s s l o o p of t h e s o l a r

b o i l e r s have been a n a l y z e d .

The s t u d y of o p e r a t i n g s t r a t e g i e s i n c l u d e d f i v e m u l t i -

mode s t r a t e g i e s . The n o s t f a v o r a b l e s t r a t e g y i n t e rms of

annual s o l a r p e n e t r a t i o n and s o l a r b o i l e r l i f e t i m e was t he

DAQ s t r a t e g y . Th i s s t r a t e g y h a s t h e s o l a r b o i l e r s p roduce

500°F, 900 p s i a w a t e r t o be used by t h e f o s s i l b o i l e r . I f

too much w a t e r can be c i r c u l a t e d th rough t h e s o l a r b o i l e r s

( l i m i t s e t by maximum f low r e g u i r e d by the t u r b i n e ) , t hen

some of t h e t o i l e r s a r e s w i t c h e d to t h e 700 °F, 900 p s i a

A u x i l i a r y Mode. The number of b o i l e r s s w i t c h e d t o t h e

209

210

Auxi l i a ry Mode depends on t he s o l a r c o n d i t i o n s . The

f lowra te must not exceed t h e s e t maximum. I f a l l t en bowls

are in the AM and t h e f l o w r a t e i s s t i l l too high then some

of the bowls can be swi tched to t h e 1000° F, 900 ps ia Qua l i ty

Mode. This never became necessa ry i n the c u r r e n t p l a n t

des ign-

The s o l a r b o i l e r AM ou tpu t must pass through the

Auxi l ia ry S u p e r h e a t e r before e n t e r i n g the Steam Storage

Tank. The c u r r e n t p l a n t design (ref : Chapter I I ) does not

inc lude an A u x i l i a r y Superhea te r equipped for inpu t from

both t he f o s s i l and s o l a r b o i l e r s . A study should be made

to compare t h e c o s t of a more f l e x i b l e Auxi l i a ry Superhea ter

with t h e economic v a l u e of t he s o l a r p e n e t r a t i o n gained by a

s t r a t e g y u s i n g an AM.

A c a r e f u l s t u d y should a l s o he made of the p o s s i b l e

cos t s i n c u r r e d by us ing the s o l a r b o i l e r s as feedwater

p r e h e a t e r s . An a l t e r n a t e f o s s i l b o i l e r might be r egui red i f

t h i s i s t he predominant s t a t u s of the s o l a r b o i l e r s . F o s s i l

fuel c o s t s could r e l e g a t e whether t h e p l a n t o p e r a t e s in a D

or Q s t r a t e g y . However a p l a n t designed for the DAQ

211

strategy needs only software changes to operate with the QAD

strategy.

The study of strategies also lead to other possible

changes in the plant design. Highly significant results are

shown in Appendix D which could promote altering the number

of Solar Gridirons utilized in the plant. This study shows

important penetration per Gridiron values for the DAQ

strategy- These values in consideration with economic worth

of solar penetration and capital cost of Gridirons should be

carefully reviewed before the final plant design is done.

Without considering the cost to build a Gridiron, the

results indicate that 18 Gridirons should be incorporated in

the Hybrid plant. This is because a good value for solar

penetration per Gridiron, 1.43, is availible with 18

Gridirons. The plant with 10 Gridirons does get a

penetration of 1.62/Gridiron; however, the total penetration

(continuous load; turbine 1) is only 16-18 compared to the

18 Gridiron total penetration of 26. 12-

Whichever strategy is chosen, the fluid exiting the

solar boilers must be controlled at certain temperature and

212

pressure l e v e l s . The f o s s i l bo i le r works to regula te

p ressure . The i n l e t va lves to the s o l a r bo i le r s regu la te

the mass flow ra te of feedwater through the bo i l e r s and thus

the temperature e x i t i n g the b o i l e r . Two t a c t i c s for

con t ro l l i ng t h e i n l e t valves were s tud ied . The f i r s t , the T

c o n t r o l l e r , which c o n t r o l l e d the e r ro r between the desired

temperature and the measured temperature seems more su i t ab l e

than t h e second which con t ro l s the e r r o r between desired

mass flow r a t e and t h e measured mass flow r a t e . I t was a lso

noted t h a t switching the parameter values in the T

con t ro l l e r scheme based on inso la t ion behavior does not

s i g n i f i c a n t l y improve the response of the so lar bo i le r ex i t

temperature. Therefore , a T c o n t r o l l e r with one set of

parameters i s recommended-

This recommendation provides information for the memory

space which the p lan t conro l l ing computer must have-

However, f l e x i b i l i t y must s t i l l be provided since the actual

plant b u i l t might s i g n i f i c a n t l y a l t e r the system model used

to analyze the c o n t r o l l e r . A change in the model might

r e su l t in t h e d e s i r e for d i f f e r en t T c o n t r o l l e r parameters

or even t h e use of the mass flow r a t e c o n t r o l l e r . Also,

213

there are other control schemes which have not been studied.

Ihe present study does indicate that either a T or «

controller can do an adequate job of controll ing the solar

boiler out let temperature-

REFERENCES

(CP 8) "The Crosbyton Solar Power Project," Volume VIII: Preliminary Design of 5 MWe Solar-Fossil Hybrid Electric Power Plant at Crosbyton, Texas, Texas Tech University, Lubbock, Texas, USDOE Contract No. DE-ACO4-76ET20255, February 1982.

(HS) Shankar, Hariharan, "Simulation of the Receiver in a Fixed-Mirror Distributed Focus Solar Power System," M.S. Thesis, Texas Tech University, Lubbock, Texas, August 1981.

(HL) Leung, Hip Sum, "Optical Power Concentrations on Aligned and Misaligned Receivers in Solar Gridiron Power Systems," M.S. Thesis, Texas Tech University, Lubbock, Texas, August 1978.

(RC) Reichert, Dr. John D. and Clements, Dr. L. Davis, "Informal Description of the Performance of a Solar Gridiron Collector/Boiler," CSP-RPS-1, Texas Tech University, Lubbock, Texas, December 1978.

(ST) Reynolds, William C , "Table B-2; Properties of Superheated Steam," Thermodynamics, second edition, McGraw-Hill Book Company, pp. 466-467, 1968.

(CP 7) "Crosbyton Solar Power Project," Volume VII: Performance and Cost of Solar Gridiron Electric Power Plant, Texas Tech University, Lubbock, Texas USDOE Contract No- DE-ACO4-76ET20255, February 1981.

(KW) Watson, Karan, "Performance Analysis of a Solar Gridiron Design Verification System," M.S. Thesis, Texas Tech University, Lubbock, Texas, May 198I.

214

APPENDIX A THE TMR EQUATIONS

Key: M = mass flow rate of the fluid through all tubes of

the solar boiler (Ibm/hr) 2

Ij = direct normal insolation (KW/M )

^ = solar inclination angle (degrees)

V„ = wind speed (MPH) W

(X = the Solar Bowl's attendance factor (\initless) 2

Ang= nominal gross aperture area (ft ) 2

' . e x . n Ol TAo KBtu M C = c o n v e r s i o n f a c t o r : 0.3170 8 KW f t^ hr

P = power (KBtu/hr)

Equat ions:

Y = M/(300 Ij^^)

Sl^ = S/15'

Power t o t h e w a l l of t h e r e c e i v e r , P^ :

PQ = C AngO<Ij^j^ cos J ?

P = P B. ! Ld) W 0 i n ^'

where B. is the multiple reflections factor m

Bi_ (i))= 1 - (0.045jp) / (1 + 0.972jp^)

Power lost by convection, P^L-

^CLM= 1 + 6 exp[-1.1705 Yl

p n 1-75

CUl= 1 + 0.366j;p

^CLW= 0.267 + 0.733 (V^ / 10) 21S

PCL= 0-0268 PQ P C L M P C L ^ ^ C L W 216

Power l o s t by r a d i a i o n , P : RL

Z = 2 .4629 J l^^-"^^^ + 2 . 1 2 0 6 j ^ - ^ ^

U = 1.374 + 0 . 1 3 2 l j l p - l . l O l J p ^

R^^ 1 .858 e x p [ ( - Y / U ) ^ ]

R = Jlp^''^^^ - 0 . 1 0 6 6 j l p - Z (Y - 0 .1762) Ril

^R " ^ " ^RM ^Ri).

^RLM= 1 + 22.831 exp[-1.3549 Y^]

Pj j = 1 + 0.739, cos (2il)

PRLW= i-.i ^ - ^-123 (V^ / 10)

PRL= 0-01745 PQ RJ V^^^ P J ^ PJ^^

Boiler efficiency, G „

Cr^ = 1 - ^CL " RL

Power into the fluid, P^:

Appendix B The TMRF EQUATIONS

The TMRF e q u a t i o n s assume a wind speed of 15 l MPH

Key:

T = Temperature of the steam exiting the solar boiler (°F)

T. = Temperature of the water entering the solar boiler (°F)

T- = Reference temperature, 100°F

M = mass flow rate of water through all tubes of the solar boiler (Ibm/hr)

2 I = direct normal insolation (KW/M )

J. = solar inclination angle (degrees)

P = pressure of the fluid exiting the solar boiler (PSIA)

PQ = reference pressure, 1000 PSIA

h = specific enthalpy (Btu/lbm)

To find the specific enthalpy for fluid with temperature, T, in °F and pressure, P , in PSIA:

1) Find the saturation temperature for P

^^ ,1400 - Px -3-7 ,1400 - P,4 ^SAT= 5^^ - ^^^ ^ 1000 ^ - ^^ ^ 1000 ^

2) If T<T3^^

h(T,P)= T - 32

3) I f T > T ^ , ^ A 1400 - P ^ _ ]50n - T D) ±T L ^ SAT, p = —yoOO ' " 1000

^ ^ ^ r.rr c f^ ' 140,^^4 h ( T , P ) = 1 7 8 5 + 1 2 . 5 p - (562 - 35p) t - 9 5 . 6 ( J^QQQ ^^

217

n 2^^ To find M(T^^ P^^ ^DN,'^ ^ ^^^ steam is being produced by solar boiler:

Y = (Tg - 700) / 150

AQ = 464.5 - 41.16Y + 2.475Y^ - 0.825Y^

BQ = 460.7 - 3.867Y - 14.6502Y^ + 7.0017Y^

* C = ^DN (^ -^O]^ 75)1-8)

M = M^[h (Tg, PQ) - h (TQ, PQ)]

Lh (T _, P^) - h (T^^, P )] E' E' 'IN' E'

To find M(500°F, P^, I ^ , ) when 500°F water is being

produced by solar boiler:

M^ = Ip^ (1513 - 1169 ('/ 75) ^'^)

m

M = M^, (h (T^, Pg) - h (TQ, Pg))

(h (Tg, Pg) - h (T.^, P^))

Range of validity for RFC equations:

The TFAP model as well as experience with the ADVS identified a range of J- and M in which it is best for boiler lifetime not to operate. This range is identified by:

and

where J ^ = 117 - T^ / 150 ^ ^

and ^ „.M ^ 40 (Ibm/hr)/ tube in the boiler.

APPENDIX C

THE POWER FACTOR TABLES COMPUTER CODE

The Power Factor Tables show the expected power in the

working fluid for given ^ , I^^, and outlet temperature for

solar boiler. The following code was used to calculate the tables.

In the code the RFC equations are used to find the required flow-

rate for a given inlet and exit temperature for the solar boiler

of a 200 foot diameter Solar Gridiron. The flowrate was found for

various inclination angles and insolation values for each exit

temperature. The data generated has been stored on a tape, CSPBF3,

kept at the Texas Tech Computer Center.

219

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STUDY OF NUMBER OF GRIDIRONS TO USE IN THE PLANT

As mentioned is section 3.3.2b, the DAQ strategy is a three

mode D strategy which utilized two modes when ten solar bowls

are in the plant. A study was made to see how many bowls caused

the strategy to utilize its third mode. This is also interesting to

see the solar penetration per bowl for the plant as the number of

bowls in the plant changes. This is a particularly interesting result

when the cost analysis of the plant is done. The additional solar

penetration a bowl can supply for the plant can be compared with the

cost per bowl.

In this study, the number of solar bowls available to the plant

was varied from one to ninety. The plant was operated in order to

have the maximum flow through the solar boilers without exceeding

59,000 Ibm./hr. Only three output modes are allowed, 500°F, 700°F

and 1000°F along with 900 psia.

In the cases where there were many bowls in the system, the

average solar boiler effeciency, <ar>, was fairly low. This condition

would threaten the boiler lifetime. Therefore, one more feature

was added to the basic DAQ strategy. This feature would not allow

the boilers to be operated in a mode which cause the boiler efficiency

to be lower than 50%. This efficiency limiting strategy is referred

to as the DAQ-SNAP strategy. The following figures illustrate many of

the results seen in this study.

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THE STEAM TABLE CURVE FIT

Table G was generaged by Enayet Jiwani with the SAS program

at the Texas Tech Computer Center. The table applies to the

equation

T^ = a + bP + cP + dH + eH^ + fPH + gPH^ + hP^ + iH^

where

Tj. = temperature of fluid exiting the solar boiler (°F)

P = pressure of fluid exiting the solar boiler (psi)

H = enthalpy per unit mass of fluid exiting the solar

boiler (Btu/lbm)

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THE VALVE RESPONSE CURVES

Figure H shows the mass flowrate, M, verses actuator voltage

command, V, for the inlet valve at the ADVS. Two curves for

different days, July 5 and July 30, illustrate how the valve

characteristics drift from day to day.

Tables H-1 and H-2 were generated by Enayet Jiwani with the

SAS program at the Texas Tech Computer Center. The table applies

to the equation

M = a + bV + cV^ + dV^ + eP + fP^ + gT + hT^ + iVP + jVT + kPT

where

M = mass flow rate (Ibm/hr)

V = voltage command to actuator (V)

P = pressure of fluid through the inlet valve

T = temperature of fluid through the inlet valve

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APPENDIX G

THE CONTROLLER COMPUTER CODE

This computer used the ITMR equations to test the response of

the system to various transient conditions. The code listed is

for the M controller: however, by substituting the COMP M

subroutine with the COMP T subroutine, the same tests may be run

for the T controller.

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• o

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w.-« • g » < r A O " » « < > 0 ' < " g - « 1 * A O K 3 3 0 O O . » ' > » ' O — A I - O ^ T A O O o O O J O O O O o - H ' ^ ' H ^ - * - « — . — — — - . — — ' H - H i - i i N A i ' v ^ ' g ^ p g

V

M

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^ f - O o j o i - 4 Z O -o:». - 1 1 > > • > K K 4 K O Z K ar x ^ o u - o > x a . I > — . j o — — > — K o z o ^ j j — ^ - 1 > - X K l u i ut- 9 t » o . o * i > — — - i ^ - O X JJW0O4 - T O K X — o — ^ o > — o — > — O O — c Z J Z O O Q >-•— K O ' K . ' i ^ ^ • ~ • : . ^ a . o i _ J ^ a t O K O I ot — > . — K K Z K — 0 0 r—3-0 OOZ—-•-wo-I o » 0 4 o o o o o — 1 0 . O O . x u - O ^ »o—or4 O— > z o > • .—o——o O S U O - I Y J J U ' X O O - X Z - I N 4 3 - ' ^ - " " ^ • - J J

2 _IC:*^i/<CZ —> O <x> >p-' . > —— — 4—KK

2 — « «

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K Q UJZ oruj

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K O r^ Z, OC O C

- o 0 0 0 o

0 0 0 O o t . 0 0 — — — ^ ' ^ ' ^ . •HPSi

O O o < - D O O O O O ' J O C O O

0 0 OC-oooo o o o o o o o

APPENDIX H

RESPONSE CURVES FOR VARIOUS CONTROLLERS

The figutes that follow show the predicted temperature response of

the ITMR system to seven imput conditions with various controllers.

The input conditions are:

Input #1

Input #3

Input #4

Input #5

Input #6

Input #7

Input #8

DN

'DN

"DN

"DN

"DN

"DN

"DN

0.01 Time < 10

1.0 Time >_ 10

= Time/1200

= 1 - Time/1200

= 0.9 + 0.1 sin(7r Time/10)

= 0.6 + 0.4 sin(Tr Time/10)

= 0.9 + 0.1 sin(7T Time/60)

= 0.6 + 0.4 sin(TT Time/60)

T = 1000°F

T = 1000°F

T =

T =

T =

T =

T =

1000°F

1000°F

1000°F

1000°F

1000°F

The T controller was tested with different values of G , G^ and V I

V for these imputs. The M Controller was tested with different values

of K and G for these inputs.

244

247 • I I I

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