SIMULATION AND ANALYSIS OF THE PROCESS CONTROL

FOR A

SOLAR GRIDIRON POWER SYSTEM

by

ENAYET ALY JIWANI, B.S. IN E.E.

A THESIS

IN

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

ELECTRICAL ENGINEERING

Approved

December, 1981

/?e "l/y^--

mi ^^ C op" » '

ACKNOWLEDGEMENTS

I am deeply indebted to Dr. John D. Reichert for his patience,

superb direction and guidance during the preparation of this thesis.

I am M^ry grateful to Dr. John P. Craig and Dr. Donald L. Gustafson

on my research committee. Also I am grateful for the help Karan

Watson has given me in the preparation of this thesis.

A special thanks is expressed to Sandi Willingham and the other

CSPP secretarial staff for the hours contributed in the typing of

the text.

n

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii

LIST OF TABLES v

LIST OF FIGURES vi

SECTION I CONTROL OF A SOLAR BOILER 1

SECTION II THE SOLAR GRIDRION CONCEPT 7

2.1 The Analog Design Verification System (ADVS). . 10

2.2 Bristol Processor Controller 16

2.2.1 ADVS Tracking 17

2.2.2 ADVS Process Control 21

2.2.3 Emergency Control 23

2.3 Data Acquisition, Storage, and Handling . . . . 24

SECTION III PROCESS CONTROL ALGORITHM 32

3.1 Control Strategy 32

3.2 Control Algorithm for the Feedwater Valve . . . 32

3.3 Time Averaging for the Controller 37

SECTION IV SIMULATION OF THE CONTROL SYSTEM 45

4.1 The Control Algorithm 45

4.2 Strategy for Simulator Development 47

4.3 Computer Simulation Model I 48

4.4 Computer Simulation Model II 52

4.4.1 Mass Flow Rate (M) Curve Fit 61

4.4.2 Calculation of Pp 62

4.4.3 Calculation of Tr 66

4.5 Simulation Model 66

iii

SECTION V TESTING AND EVALUATION OF THE SIMULATION 69

5.1 Simulation Without Using G, 77

5.2 Testing and Evaluation of the Controller. ... 79

5.3 Future Use of the Simulation 84

REFERENCES 86

APPENDIX A PROGRAM AND OUTPUT OF THE M CURVE FIT 87

APPENDIX B TMR CURVE FIT 97

APPENDIX C RESULTS OF STEAM TABLE CURVE FIT 99

APPENDIX D COMPUTER CODE FOR SIMULATION 104

IV

*

LIST OF TABLES

2-1 ALARM AND SHUTDOWN SETPOINTS 25

4-1 M CURVE FIT FOR JULY 5, 1980 63

4-2 M CURVE FIT FOR JULY 30, 1980 64

4-3 STEAM TABLE CURVE FIT FOR EXIT TEMP 67

5-1 COMPARISON OF ^^^^^ vs i|; , 85 ^meas ^calc

LIST OF FIGURES

1-1 System Block Diagram 2

1-2 Fluid Path for the ADVS 4

2-1 Spherical Reflector Ray Tracing 9

2-2 Tilt Angle vs Normalized Annual Energy Capture 11

2-3 Conical Focal Zone with a Cylindrical Receiver 12

2-4 Cantilevered Receiver Structure 14

2-5 System Schematics (Load Skid and the Receiver) for the ADVS 15

2-6 Sample of "Poor Reichert's Almanac" 19

2-7 Scan Table 28

2-8a Scan Figure "P" for July 15, 1980 29

2-8b Scan Figure "I" for July 15, 1980 30

2-8c Scan Figure "T" for July 15, 1980 31

3-1 Analog Averager Circuit 39

3-2 Implementation of Digital Averager in Bristol 41

3-3 Plots of <V> for Various G 44

4-1 Block Diagram of Control Equation Implementation 46

4-2 Plots of G vs Gj 51

4-3a Scan Figure "P" for July 5, 1980 53

4-3b Scan Figure "I" for July 5, 1980 54

4-3c Scan Figure "T" for July 5, 1980 55

4-4a Scan Figure "P" for July 30, 1980 56

4-4b Scan Figure "I" for July 30, 1980 57

4-4c Scan Figure "T" for July 30, 1980 58

VI

4-5 Results of "Test Simulation Model I" for July 5, 1980 . . . 59

4-6 Results of "Test Simulation Model I" for July 30, 1980. . . 60

4-7 Graphs of M vs V with the Corresponding o Band 65

4-8 Flow Diagram for the Simulation Model 68

5-1 Actual Controller vs Simulated Controller for July 5, 1980 71

5-2 Actual Controller vs Simulated Controller for July 30, 1980 72

5-3 Actual Controller vs Simulated Controller for

August 1, 1980 73

5-4a Scan Figure "P" for August 1, 1980 74

5-4b Scan Figure "I" for August 1, 1980 75

5-4c Scan Figure "T" for August 1, 1980 76

5-5 Actual Controller vs Simulated Controller (Interpolated

Data, Gj not used) 78

5-6 Test Simulation with Various K, Variable Gain 81

5-7 Test Simulation with Various K, Constant Gain 82

v n

SECTION I

CONTROL OF A SOLAR BOILER

One of the foremost concepts for generation of solar thermal

electric power is the "solar gridiron concept." The concept, also

known as the hemispherical bowl, the solar bowl, and the fixed mirror

distributed focus concept, has been utilized by Texas Tech University

for the construction of the Analog Design Verification System (ADVS).

The ADVS contains the largest single solar collector ever built. The

collector is in the shape of a spherical segment bowl that concentrates

sunlight along a line joining its center of curvature to the sun (the

"solar axis"). The receiver (solar boiler) is located along this axis

and tracks the sun diurnally and seasonally. The focus is "distribu­

ted" in the sense that the concentrated sunlight is distributed along

a line interval lying on the solar axis and of length one-half the

spherical radius. Figure 1-1 shows schematically the general arrange­

ment of the bowl, the receiver, and the character of the reflected

rays that enter the bowl.

The operation and evaluation of the ADVS by Texas Tech University

began in January, 1980. The ADVS constructed at the test site in

Crosbyton, Texas not only has provided quality steam for generation

of electric power, but also has generated the first commerical elec­

tricity from solar steam in the history of the nation.

When in operation, water at approximately 100°F is pumped into

the receiver at the end nearest to the bowl surface. This working

fluid moves through the focal zone in spiral wound tubing and exits

1

ui

- 2 _ u. U X

n y = ^

"

«/i

oe o >-< ee lU Z UJ o

\ *" \ ^ \ -\ SI 1 \ <r / \ 3 / \ •- /

^ UJ

5s « ^

EN

E

ST

OI

/ / »

u. O Q

/ UJ

/ s ' a. 2

O u

TR

AT

OR

^^ UJ _J

U ui 2 Z

AL

CO

V

E

PA

u — — h-* U Ui lu

-- .J iu-£ Hi 2 a: UI

E

O

o CQ

E (U

to >>

as superheated steam at the top of the receiver. Flexible couplings

and high pressure flexible hoses, located in the vicinity of the pivot

point, are used to bring the water to and remove the steam from the

receiver.

In order to achieve turbine quality steam, it is essential to

maintain relatively constant temperature and pressure. The ADVS pro­

cess controller achieves this task by controlling the feedwater and

exit steam valves. It is useful to consider the feedwater (inlet

control) valve as regulating the exit temperature and to think of the

steam exit (exit control) valve as regulating the exit pressure.

Figure 1-2 represents the fluid path for the ADVS.

The ADVS Process Control is accomplished by the Bristol Process

Controller (ref. Bristol Instruments/Systems). Manual, Emergency,

and Active modes are utilized for the Process Control. Manual mode

has the highest priority and can be accomplished either at the Bristol

console by slewing control switches or by manually turning numerous

valves at the load skid (ref. Sec. II). The Emergency control mode

has second priority (overrides anything except the system operator).

If a fault condition is detected by the Bristol in any of the continu­

ously monitored sensitive data channels, the Bristol sounds a warning

at the first threshold. If the situation is not corrected and the

condition deteriorates to the second threshold, then the Bristol

automatically takes all steps to safeguard the system. In partic­

ular, the emergency control will dictate a "stow"; and move the re­

ceiver from the focal region to a safe location. Other actions re­

lated to fluid flow control are taken simultaneously if required.

m w

Q

§

o EHEH >

x o <i wo >

CO :> o

o

4->

Q -

-o 13

CO I

Active control is accomplished by the Bristol as it receives sensory

data and uses it to compute suitable command voltages for the feed-

water and steam exit valves (Montec actuator valves). When in the

active mode, the command voltage is generated by the Bristol by

utilizing the sensory data and the algorithms selected for the inlet

and exit valves.

A completely active, memoryless control algorithm was designed

initially for the inlet and exit valve controllers. The algorithm

for the exit valve controller turned out to be quite simple when it

was considered and obligated to control only the exit pressure. The

command voltage responds only to a term like K(P - P^) where P^ is the

desired or set-point pressure, P is the measured pressure and K is a

gain factor. The inlet valve controller is considered to control only

the exit temperature. Algorithms for the inlet valve, using various

pressure (P), temperature (T), and insolation {l^^) terms of the type:

K(P - Pj). K(T - T j ) . Kdp^ - IQ^Q)

were implemented. All such controllers were subject to the following

difficulties.

1. Such controllers are biased (no correct open loop terms).

2. They tend to react too strongly to large transients.

3. They are not stable over the full range of conditions

and phenomena.

4. Nonlinearities in the system can occasionally cause such

terms to turn the valve the wrong way.

5. The hand-operated valves at the load skid are occasionally

reset (and are difficult to return to exactly the previous

position).

6. The Hardesty valve (ref. Sec. II) has idiosyncrasies in its

behavior.

In order to resolve all these problems, a controller was designed

using the concept of conservation of energy (ref. Sec. III). This

study focuses its attention on the algorithm thus developed. Analysis

and simulation of the controller algorithm is accomplished in Section

III and Section IV, while Section II discusses the ADVS in general.

Conclusions derived from the simulation of the inlet controller and

recommendations for future controller development are presented in

Section V.

SECTION II

THE SOLAR GRIDIRON CONCEPT

The Crosbyton Solar Power Project (CSPP) of Texas Tech Univer­

sity, funded by the U. S. Department of Energy, utilizes the Solar

Gridiron Concept for planned application of a 5 MW solar-fossil

fuel hybrid electric power plant for Crosbyton, Texas. The Solar

Gridiron Concept is new only in its name. Its history, under various

names, goes back at least a century. The concept in its purest form

has a collector, or mirrored bowl, with no moving mirrors, and a re­

ceiver or boiler which moves within the collector to track the sun.

The Gridiron Concept is not simply that the collector is fixed

but includes the use of a spherical segment mirror. There are two

major advantages of the spherical bowl shape:

1. the power on the receiver remains congruent throught the

day; and

2. the focal zone is well shaped for high concentration and

good heat transfer.

The basic function of the collector is to gather the incident

solar energy and concentrate it onto the receiver. The basic pattern

of the light directed into the focal region of the spherical collector

is the same throughout the day and year due to the symmetry of the

collector. This congruence of the pattern of light in the focal region

is useful, and advantage is taken when considering heat transfer and

the materials employed to build the receiver, the tracking of the

7

8

receiver, and the controllability of the fluid in the receiver.

The focal region of a spherical segment mirror, when illuminated

by a point source infinitely far away, is a line segment. This line

segment extends from the collector surface along the solar axis toward

the center of curvature of the sphere for a length equal to half the

radius of the sphere, as indicated in Figure 2-1. The focal line

segment lies on the line through the center of curvature of the sphere

and the point source. As the point source moves, the focal region

continues to be a line segment, but moves within the collector to

always lie on the line containing the center of curvature and the

source.

The actual focal region of a solar collector will deviate from a

line segment because the sun is not acutally a point source. The

finite disk of the source causes the line segment focal region to ex­

pand to be the frustrum of a cone whose vertex angle is the same as the

angular diameter of the source and whose length is the same as the line

segment described above. Deviations in the focal region occur if the

collector deviates in any way from a perfect spherical segment of the

correct curvature.

For heat transfer considerations, the design criteria for the

receiver involves matching the receiver shape to the focal region so

that it will intercept essentially all of energy flux without exces­

sive surface area. In addition, the receiver must be small enough to

obtain high temperatures. After considering economic factors, a

cylinderical shape for the receiver was found to be most beneficial.

Detailed analysis of the optical profiles on cylindrical receivers

> X I A L MAY

center of cur_y£ture

"Ik

] nerucTiNO

Figure 2 -1 . Spherical Reflector Ray Tracing

10

this can be found in B. Brock and H. S. Leung work (ref. SB and HL).

2.1 The Analog Design Verification System (ADVS)

The CSPP preliminary design for the 5 MW power plant requires

construction of ten Solar Gridirons each with 200-foot aperture dia­

meter (ref. CSPP III). In order to provide a sound basis for assess­

ment of the expected performance, cost, and economic value of the

contemplated 5 MW power plant, an Analog Design Verification System

(ADVS) was constructed.

The ADVS is a fully instrumented Solar Gridiron which was

brought to operational status on January 22, 1980, in Crosbyton, Texas.

The ADVS contains the largest primary solar collector ever built. This

collector is a quarter-sphere composed of 430 mirror panels of 12

different shapes laid out on the surface of a 75-foot diameter sphere.

The rim angle of the collector is 60°, so that the aperture diameter

is 65 feet. The collector is tilted 15° to the south. The annual

energy capture could be maximized by tilting the bowl to an angle

equal to the latitude of the collector, which is 33-5/8° for Crosbyton,

Texas. However, as shown in Figure 2-2, 85% of the maximum benefit

available from tilting the bowl is obtained with 15° tilt (ref. KW).

Figure 2-3 shows the conical focal zone (due to a spherical bowl)

and the cylinderical receiver. The receiver configuration involves

a 6 inch diameter cylinder, 18.5 feet long, wrapped with a ribbon of

two tubes (00:0.373 in., ID:0.245 in.), each 430 feet long, spiral

wound to cover the entire external surface. A feedwater line passes

11

O

CO

o"

o" >-CD LU •! •z. o

<: I— LD O •-h- O Q UJ

a: o

o—

o

Latitude = 30°

'T­

IS 60 ~\—

75 0.00 30 r

45

"T-90

TILT ANGLE

Figure 2-2. Tilt Angle vs. Normalized Annual Energy Capture

12

a is the angular radius of the solar disc.

Figjre 2-3. Conical Focal Zone with a Cylindrical Receiver

13

down the interior of the support cylinder to feed the two tubes at the

bottom of the receiver. A mid-span plenum manifolds the flow about

half-way up the receiver, and then the tube continues on up to a re­

ceiver exit manifold at the top of the receiver.

The structural support of the ADVS bowl consists of four north-

south concrete backbones supported by concrete pillars in a partial

excavation. Twenty-five east-west ribs of four inch pipe cross the

backbones to support the 430 mirror panels. The cantilever support

beam for the receiver is mounted on a pivot point supported by a

north-leaning tripod with two legs in tension and one in compression.

Footings for the tension legs are outside the aperture structure, so

that only the compression leg penetrates the bowl. These features are

illustrated in Figure 2-4, a preliminary design for a 20G-ft. bowl.

Articulation of the fluid lines at the pivot point is accomplished

by two flex-hoses: one for feedwater and one for the exit steam. A

system schematic is given in Figure 2-5. The ADVS is a closed-loop

systSfli. The water is pumped to the solar boiler by a feed pump. Steam

from the solar boiler is condensed, cooled, and returned to the system

reserviors for recirculation. Flow of feedwater to the receiver is

controlled, not by a shunt wound DC pump motor, but by a by-pass valve.

Originally, feedwater flow was regulated by a Montec actuator operating

a valve in the by-pass line. A second Montec actuator controls the

pressure in the steam exit line. Gil Hardesty, a consultant to E-Sys-

tems, suggested the new location for the feedwater actuator control

valve (CV-01) shown in Figure 2-5 with insertion of a pressure-com-

pensating-valve (also referred to as "the l-laraesty valve") 'n the

wm'

. ^ ^

14

0) s-3

4>> U 3 i .

4-> CO

&.

>

(J 01

-o i.

> 0)

I

s . 3

15

>

T—

o s-+-> d o o $- <u o >

+-> r— o m

2 : >

(U >

r ^

rO >• (U

r ^

4-> 4-> 0 S-

JC 1—

E • r— fO s-

Q

1 c 0

C_)

0 ^ c

• r -r ^

c 0

• r— CL+J E =3

CO

0 O) c

s-OJ

<u 0 $- 3 3 - 0 to to to C OJ ro S- S-

Q . 1 —

1

LU

CO :> Q

<: <u

4->

S-

o

>

o <u

(U

J 4-> -o c OS

CO

as o

u ' I —

4-)

o CO

O) +J to >»

CO

I

CM

(U

s _ 3

16

by-pass line. A static line downstream of the control valve reads the

exit pressure and communicates with the pressure-compensating-valve

(p.c.v.) to adjust flow in the by-pass line. The intent of this ar­

rangement was to try to maintain a constant pressure drop across the

control valve. Such a situation would act to reduce the tendency of

pressure surges from the receiver to shunt feedwater into the by-pass

line. The Hardesty valve in use does not maintain a constant pressure

across the control valve, but does make the system much easier for the

Bristol to control.

2.2 Bristol Process Controller

The Bristol process controller (UCS 3000) is a system that per­

forms a multitude of process operations through the use of digital

programming techniques. The device is essentially a microprocessor

computer with programming and storage facilities. Bristol process

controller is programmed with a series of software modules that ef­

fectively perform hardware functions. Bristol also has a process

operator panel (POP) which interfaces the process operation with the

Bristol process controller. The POP enables the operator to monitor

signal level, alter set-points and output levels, and change servicing

rates and priorities of the program as required. The Bristol Process

Controller serves three basic functions in the ADVS.

1. Tracking of the ADVS Receiver,

2. ADVS Process Control, and

3. Emergency Alarm and Shutdown.

17

2.2.1 ADVS Tracking

The instantaneous power capture by a fixed aperture system is

proportional to the cosine of the inclination angle, the angle between

the aperture normal and the direction of the sun. This inclination

angle, S , depends upon day of the year and time of day according

to the relation (ref. CSPP VII):

cos

where

^ = cos (A - y) cos (6) cos (x) + sin (X - y) sin (5) (2.1)

X = latitude = 33.625° at Crosbyton;

y = tilt angle = 15° for the ADVS;

6 = solar declination angle which depends upon the day of the

year; -23.5 < 5 < 23.5;

T = local apparent time (LAT) expressed in degrees and taken

to be zero at local apparent noon.

The inclination angle serves as a guide ^ the location of the

tracking receiver. The tracking algorithm for the boiler is that the

receiver axis must lie on a line passing through the center of curva­

ture of the bowl and the center of the solar disc. The receiver is

suspended at the end of a cantilever support and balanced with a

counterweight. Motion is accomplished by two identical 1/4 hp motors

one driving a turntable for the hour angle drive, the other driving

a screwjack for the declination drive. Declination axis tracking

is very slow, because 5 changes less than one-half degree per day.

18

Hour angle tracking involves a "fast axis" because x proceeds at 15°

per hour.

Tracking control is accomplished by the Bristol process controller

and various modes are used: Clock Drive, Active Drive, Automatic Drive,

and Manual control. Though seldom used for actual tracking, the Manual

Control Mode has the highest priority. Manual is simply control ac­

complished by the system operator. He may move the recei^ver at his

discreation in either hour angle x (east-west), or declination 5 (north-

south), or both simultaneously. This is accomplished at the controller

console (POP) by slewing a potentiometer.

Clock Drive is automatically accomplished by the Bristol using

X (obtained from its real-time clock) and 6 (obtained from a memory

updated each day). An almanac is available at the site in two formats:

"Bristol operators: Each Day" and "Poor Reichert's Alamanac" (ref.

Figure 2-6). These resources are used each day to set 6 and to reset

the LAT (local apparent time) with respect to the real time civil

clock. Throughout the day the Bristol determines x and 6 and substi­

tutes these two parameters in the tracking command voltage curve fits

to determine and send out open loop command voltages to the two inland

motors. A feedback loop assures that the command is properly imple­

mented. The curve fits mentioned above are updated about once a

month, as they begin to lose accuracy. The purpose of these fitting

functions is to account for any and all nonlinearities in the elec­

tronics, offsets and biases, mechanical deflections and imperfec­

tions, gravitational effects, as well as any structural misalignments.

19

o

or > - J ID

a^

O Q_

I

— .'7

%x " ' ? ~ ?.. r? — T.r. r '^ .»• i- S « ; r I- * •-> n IM tj - fs ^ I- 7 - . 5 1.1 m

, ;2 o o ^ « <? w f i ? ° ' ^ o o <s o l o p o o o in o o < ^'^?^T r^i^ " ^ ^

5 / J T « » > » " i " - ^ — i " 5 » - . = " : - J . 6 i ^ ^ i c . i i . - - l . i r - j . = . 0 " ' ^ > i ^ a » ' «

I

' ^ ; ^ - i Q t ^ - 0 - r ' j - , o ~ r t r w i l o - - . - i 3 . w , i ~ < n . ~ i r o « 5 ' > ' ' ^ " s - - '

^ o O ~ •"• "^ '^ < •> <.» m ,., 1.1, J- ?• •>• 3- J- '•' " -•; '•« o i -J vj ;^ •-» >j. , j

• t , . , , , „ , , , , t , , . , i . , . . , . . , , Q -e O , '" ' • *• •• •" ' ' • ' • '

I

•2

^ V, : J- T 5 ' ^ ' ; ; • . . f i r . '^ *l3-3- > 1- 7- •.-,-» r firs-T'^c •>

5

^ J L ; Q O Q 2 2 - , 2 2 2 ' 2 r 2 2 2 ' 5 2 9 ^ Q ' O O Q O Q O Q O Q 5 2

^ -~.lo.•^ »• s? «^ 1 r c» .0 0^ (~ wi -.1 Q f ^ i g a - r - a . — I ^ ,Tf •» P ~ •.• o ri vi r-'CT"

r r.. I T| "I r ! >-s'<^ 0 ' o r » » ' ' " < T I » ' O T i ~ p » T PI o l i o — 0 . v» « i ;p^ . -oS . 3- n -n « , ~.o» 1 '-J-

" - 3 ' o f ^ ^ ' i 0 ' « T " 0 - r i i . i ( 3 t | 5" t n - " " T 0 4 i , n i . i O « v ' > ' " ' J ' ^ ' ^ " u "HiS . . ; •- ••1.

^ » : » n T i l n : . | i ^ i ^ • ^ n ; ^ . . . 1 T i ; , n r , o ' . o..-, r . . . . n . . ; ^ r . . . . ^ „ , .

5 °5 • I •• '

»o ;>j ••Of- v.,»-'j iro iTj>- f-.,7- —2? ^ ."^ fts*^ > «~i r-i"'" n .1 7- "^i •"=" " •• <p. r ' , * V> o - n " . r . , a V l j r , f - ) ( ^ 3- V n . R o o -• - | - r« !•. ^ a : » ; • ' • • • ^ -

^.^a ' -a- ' ' " o-••:-»- o-o Q i Q o o o O'Q r " ^ - - ' - ^ — - ~ , - - ' ^ — ~ ca -• 3- r ~ -r. T r j - >•» " i ' . , m to In u i . n i r i i „ i,, (..,(,, i-, ( , , . , i n , . . . . i wi U) w ,w. <j r, •• ••! •• •• •• •• •• I •• •• •• •• i i ' 'j.~\ " ;; lA ..'• V.» ^ „ n 1.^ !•• , n » • ..^ 1.1 < • » ( . , , » • 1.1 !.> i-">'(T>,r| ^ »> (».;•<.» ^ , r^ . . . i - l . _^ m , ^ r " __

I - • * . ; , , ;

^^r t « « Z Z ( < « J . . - % « « * 1 4 « < < < < * " i~«- i | -

Is Pi rl Ti - I — O O O " ^ j T o. •» o , r - ' r ~ v » ^ t ) l o

^ 0« OQ 0« ^ <^09 — d l o o d o d!o<S Q 6 <i C«0« &»iOi9 0QO« Qq Oo< CM ft» Oa on Oo

Q d p O < i ; O Q o<r r r

0 2 I

_ '-.> i-i n " •"* "^ <"« "^ ~ r% >^ rt r\ n 't .-t r

Ol > ; -w n:>- 'o^'p-oo- 2:: '? ' : :3: !2:: iC2?:n a fJ n - ' " ^ ^ " • ^ ' n n ft 1 Nn r\ o —

} {

vi f 1

(J

c E

t o

o o Q-

<U

CO

U3 I

CM

0)

3

20

Data for the curve fits is taken by direct visual observation of re­

ceiver alignment throughout the day as a function of the command volt­

ages.

The Bristol operator customarily updates the curve fit (by

trivially resetting a bias) throughout the day, if and as required.

When such actions become too frequent or too necessary, a new curve

fit is made. As will be explained below, the clock drive is always

used for the declination drive, but is only a default option for the

hour angle drive.

Active Tracking Drive is available for both axes, but is only

used in practice for the hour angle drive (the fast axis). Declina­

tion changes so slowly that the active tracker for this drive is just

not necessary. Each axis is fitted with a bifurcate solar detector

which generates a difference signal if the two elements of the sensor

do not receive equal illumination. This difference voltage is fed

back to the Bristol which responds to zero the signal and, thereby,

align the receiver.

Automatic Drive is hierarchal controller which automatically

selects Clock Drive or Active Drive mode depending upon solar bright­

ness. The system operator can elect Clock Drive or Active Drive or

Automatic Drive. For convenience. Automatic Drive is employed almost

all of the time. In Automatic Drive the Bristol will select Active

Drive if the insolation is above a selected threshold. Otherwise,

Automatic Drive will default to Clock Drive until the insolation

again exceeds the threshold.

21

2.2.2 ADVS Process Control

Process Control is accomplished by the Bristol in much the same

fashion as tracking control. Manual and Active are the two control

modes being utilized for process control. Although the active control

is somewhat primitive, it can definitely hold exit temperature and

pressure much steadier under transient conditions than a system oper­

ator can with Manual Control.

Manual Control is accomplished at the Bristol console in the same

fashion that Manual Drive is conducted: by slewing control switches.

There is an alternate version of Manual, however. One can work directly

at the load skid and turn numerous valves in addition to the two oper­

ated by the Bristol. These additional valves are used to adjust the

flow regime to the control range of the Montec actuators (CV-Ol and

CV-02).

Active Control is accomplished by the Bristol as it receives

sensory data and uses it to compute suitable command voltages and send

them to the Montec actuators for the feedwater valve (CV-01) and for

the steam exit valve (CV-02). It is useful to consider the feedwater

valve as regulating the exit temperature and to think of the steam

exit valve as regulating the exit pressure. In this picture, control

of the exit valve and, hence, control of the exit pressure is rea­

sonably simple. One need only establish a simple feedback control

algorithm in which the command voltage responds to terms like

K(P - P^), where P^ is the desired or set-point pressure, P is the

measured pressure, and K is a gain factor.

22

The control algorithm for the feedwater valve must be consider­

ably more sophisticated. At least three difficulties face the de­

signer of the control algorithm.

1. The Hardesty valve (ref. Sec. 2.1) has idiosyncrasies in

its behavior.

2. The hand operated valves at the load skid are occasionally

reset (and are difficult to return to exactly the previous

position).

3. Too many sensors are involved: system behavior depends

upon a great many parameters, and very few sensors are truly

reliable enough to trust with survival of the boiler.

A much more direct approach is to build a completely active

memoryless control algorithm in the sense of using various pressure

(P), temperature (T), and insolation (I j ) terms of the type:

K{P - P^). K(T - T 3 ) . Kdo^ - IQ^Q)

as was done for the steam exit valve. Although quite a few control

algorithms of this type were implemented, all were subject to the

same type of difficulties:

i) such controllers are biased (no correct open loop terms);

ii) they tend to react too strongly to large transients;

iii) they are not stable over the full range of conditions and

phenomena;

iv) nonlinearities in the system can occasionally cause such

terms to turn the valve the wrong way; and so forth.

23

Various derivative and integral terms were also investigated with re­

sults that were sometimes better and sometimes worse.

It was decided to define a controller algorithm that avoided most

of the difficulties and to try to make it work well enough that its

defects could be understood. The following algorithm was introduced:

V = <V>+ (V(, - <V>)g (2.2)

wnere V is the command voltage which will be clipped to never be sent

out larger than a maximum V which corresponds to a near zero flow

rate, M = 0, or smaller than zero, corresponding to a closed valve.

The parameter V^ is to be chosen "out of range"; i.e., V^ > V so ^ L m

that, always, V^ - <V> > 0. The average, <V> of the command voltage

is defined with a limited memory. Development, analysis, and simu­

lation of this algoritm is discussed in Section III and IV.

2.2.3 Emergency Control

The Emergency control mode overrides anything except the system

operator. Sensitive data channels are monitored e^ery 0.4 seconds by

the Bristol process controller. If a fault condition is detected by

the Bristol in any of the continuously monitored sensitive data chan­

nels, the Bristol sounds a warning at the first threshold. If the

situation is not corrected and the condition deteriorates to the

second threshold then the Bristol automatically takes all steps to

safeguard the system. In particular, the emergency control will

dictate a "stow"; and move the receiver from the focal region to a

safe location. Other actions related to fluid flow control are taken

24

simultaneously if required. Table 2.1, gives a list of data channels

monitored by the Bristol and the two threshold values for each chan­

nel .

2.3 Data Acquisition, Storage, and Handling

The ADVS was designed to collect data for test purposes. The

full sensor array of the ADVS includes:

72 thermocouples (12 not yet installed)

5 flow rate detectors (2 not yet installed)

9 pressure transducers

10 command signals for automatic control

10 weather and insolation sensors

which are available to the automatic data acquisition system (DAS). In

addition, there are about 40 gauges, meters, indicators, and displays

available for real time visual inspection plus the CRT display capa­

bility of the status and activities of the automatic system controller.

The simulation and analysis of the feedwater valve algorithm,

presented in Sections III, IV, and V, relies upon data from the following

sensors:

1. TC05: a thermocouple monitoring solar boiler (receiver)

feedwater temperature.

2. TCll: a thermocouple monitoring the steam temperature

in the receiver exit manifold.

3. FOl: a mass flowrate detector monitoring the boiler feed.

25

Table 2-1

ALARM AND SHUTDOWN SETPOINTS

ALARM SHUTDOWN CONDITION SETPOINT SETPOINT

High Receiver Skin Temperature 1575°F 1750°F

High Steam Exit Temperature 1200°F 1300°F

Low Feedwater Flow 0.07 gpm 0.05 gpm

High Receiver Exit Pressure 1250 psi 1400 psi

High Receiver Inlet Pressure 1400 psi 1600 psi

Low Receiver Inlet Pressure 100 psi

Sustained High Wind Speed 20 mph

Ousting Wind Speed 30 mph 45 mph

Maximum East-West or North-South Travel alarm

Automatic Stow Actuated alarm

26

4. F02: a second mass flowrate detector monitoring the boiler

feed.

5. PT06: a pressure transducer monitoring the steam in the

receiver exit manifold.

6. R02: a tracking pyrheliometer monitoring the direct

normal insolation.

7. R04: a second tracking pyrheliometer monitoring the direct

normal insolation.

8. WSOl: a horizontal-wind-speed detector.

9. WD: a horizontal-wind-direction detector.

10. AMB: an ambient temperature detector.

11. CVCl: command voltage sent by the Bristol controller to

the feedwater valve.

12. PSDT: presence detector (insolation) voltage from a de­

tector mounted on the tracking boom.

The various data channels are brought to the Hewlett-Packard

Model 3052A Automatic Data Acquisition System (DAS), built around the

HP 9845S computer. Acquired data is termporarily stored on diskettes

(floppy disks) and later transferred to nine track tape.

The tapes are transported to TTU for computer processing. The

raw data is transferred to the Raw Data Tape for permanent storage.

All channels in service are called back and the recorded voltages are

converted to physical units, using the calibrations in effect when the

data was taken. This converted data is transferred to the Process Tape

for permanent storage. The data handling system is fully described

in S.Chao' thesis (ref. SC).

27

The Process Tape is used in various ways, depending upon the

requirements of the various data analysis programs. One of the uses

of the Process Tape is to make the Scan Tape, from which the Scan

Tables and Scan Figures are prepared. The Scan Tape stores data from

a few selected channels. The Scan Table records sixteen columns of

information, taken on the date of the table, which serve to give a

general picture of the nature of the system operation and performance

on that date. An example page from a Scan Table is shown in Figure

2-7.

The Scan Figures are set of eleven computer-drawn curves given

on three pages:

"P": exit pressure, exit temperature, mass flow rate, and

projection of insolation onto the aperture normal.

"I": direct normal insolation, wind speed, wind direction,

and ambient temperature.

"T": TEMPO, inlet temperature, and inclination angle.

for each day. An example of the Scan Figures is given on the three

sheets of Figure 2-8. In order to reduce plotter times by a factor

of five, the data plotted is successive averages of five consecutive

time sample points. Thus, some smoothing (digital filtering) is pre­

sent in the Scan Figures.

By convention, the value zero is plotted in the Scan Figures

over any period for which data is not available. During such periods,

either the system was not operated or the DAS failed, typically be­

cause of some diskette recording problem.

28

a o

./I

o 3 a

3 3 3 O 0 3 3 0 0 3 3 O * •* * -r ^ T -t -t •* * -t ~r o o o X JC <r

o • . « r 0 »«- - « »• s r> «

•» -r * a t

N — > ••3

• r

3 — O 'A

< .f •o

J T f » a r-

a. r S A o

c •r

•o f o J> "*

rf> .A a^

* i n ^ • 0 - f . r • -r.

- f «v • * > rsi N • -<r iA <o ^ •r

« . d o ^ OO a * - f *

o 3 O

S - 4

>rt 3

IS* .-V J

•*» ^ . -r .*• <*>

^ z a "• -n > s « ^ « - • <M

-- o o »*» 0> 4' ^ O

rvi -" f-^ > -* • ^ * A l A - o

— o '^ 3 O •r 9- iTi

• «> « l A I N s a •r •*.

•o . 0 > ^r ' " m ^ (M O ^ -r o A . 4 O l A f ^ a>

. r ^ l A ^ i A ' ^ . # ^ 4 ' « ' ! < A I A } I A I A I ' ^ ^ ^ > ^ GO

a.

-J of a.

a

A o r»

- • a

0 •r « • -"n — 0

•o r- . f* 'O iA .» lA « <0 -O 'O -O

3

(*1

J^

o

* o #..

«

• *

3

—

O

. 4

f".

JO

- f

. .

o

• J»

o

o

t

^

-

s M

p .

•r

•r

••^

o

r»

4

.^

•A

•r.

•0

^*

•r' krt

1

o

• *

•r

I N

•r 3

A

<M

*

•0

o

s

'« • 0

>

•r

•

—

3>

. 4

^

*>

«*

•r

o

^ r» •a

(M

n

J

J

> ^ 0

lA

*1

V

• i .

, . -r ^ •

^

m

a

N

• f ~

•) •o

r»

1*S

•O

r^

• 0

« 4

I S

r»

-r

A

.<>

. A

-. S

«

*

>r • * >

p .

0 3)

•f

.•»

4

-

O

. ^

o

•r.

• ^

. M

<M

<

1

I M

-

X

«<

> ^4 a

o-

1 •a

»S|

a IM S

1

I f *

. I * *

3

N

A

^

*

m.

1 «A

-

c <*•

1

* 4

•>r

/ N

N

a

s

f "

-r

^ <M

» 4

l>«

e

«

*

• •n

> 0

e

lO

(

•* .«»

iA

4 a

lA

*

r»

0-M

r"

.•> r-

X

X <

4 1^ >'\ fv i*\ -t r4 * • * » o n A 2 a i a o 4 > < o

M O l A -rf •r -r O US CO S A A

lA .•X

•r a

<»» >r «

<»< * «

«A

•r X

-r A a

o I A S

r >A A

mm

r^i

s * •n a

1.4

•< .XI

0)

C/1

I CSJ

(1) &. 3

o — •a -* ^ ^ — o J> 9-f- r» 4 o

0 . ' ' r . ' I M I < 4 » » « 4 O < M A f ^ > 1 0 » * — • • ^ < M | W t ^ r M 9 > ^ - r f l M «

or o a of a

-*• • T

•A «M

« •—

a

^ 3 O z

y

n i/\ •X

m •*

• N

o

d

•• i

l A I N

«n o

^ 4

rvj

«N <X

i*» O

.^ r^

m C I

<M O

•* »W

« 4

•r

rs« O

?>•

o

v 4

•*

04

o

S '

(*»

•»> i n

• N

o

• *

l A

^ 0 ^

• 4

o

r-

o

•0 -1

• N

o

r-^

4 «f

fM

o

r»

O

<«% •o

f>^ O

•f

«M

lA •0

l>i

o

> ^

^ A

N

o

f\

•o

o m

«M O

(A

-0

* M M

t>i

o

r.

r-

l A • N

r>i O

IA

p .

« ("1

rx O

^ m

I A

>r

»M

o

» IM

o I A

( M O

« r-

• I A

«M O

IM

OD

• N 0

<N

o

«* >a

p-

•r

I N

o

o> ^

<* r«»

f V O

o l A

^ rx

1 ^ 3

s

(A

• M

T

•^

o

» . * •

r-• *

m o

^ p .

rt

m •r

ir\

O

s

m IM

•o «

•a

a ] o o 9- «>

P- OX rt >f 9 M _ . ^ e » » o

^ ~- « •.» 3 o o * . .^ ^ o ^ ^ o o*

eo I.- * lA O — O O » 9- O' O-

9 f r^ -O IT- » . - < o —

c «M

o 3 X

* p . p -^ ^ ^ <M ^ IM V a p- s ^ 1 ^ ^ • ^ rt

o I S

O IM IM .M O — -< »• ^ .X •* m

O o

i « «n

IM <M ws a> o > • ^ O

O - •

rA J IM ^ «M . f

O . S » » ' > 0 0 0

A <M r x I M «M

29

12K r

too

uc

xo

DflTfl FOR JULT 15,1980

0

1300 r

900 -

SCM -

300

0

BOO r

£00

2X -

'^V^-^^\/VA

.^

<fi o CJ

z •—^

000

800

6 X

Mon

r x

—

10 J! It J6 17 le IS

LOCAL flPPflRENT TIME

Figure 2-8a. Scan Figure "P" for July 15, 1980

1700 r

BOO -

J^\-30C -

0 —

S O r

O US -UJ UJ a. tn X -

a

3 >s -

o«— 360 r

770 -

a 180 -

90 -

0

170

30

DflTfl FOR JULT 15,1980

V ^ ' r ^ V % , y , l i ^ . ^ V ^ ^

•'M '^A'-iA/vv^/^^N^/^

J ! I I I

LOCAL fiPPRRENT TIME

30

t 5 IC n 17 13 1« IS IE 17 It 15

Figure 2-8b. Scan Figure "I" for July 15, 1980

31

IK r

O SC Q-

UJ MO

70 -

0

700

ISO

100

so

0 " —

80 UJ

>—I MO -

70 -

CJ

DflTfl FOR JULT 15,1980

1 0 11 13 13 IM IS

LOCflL flPPRRENT TIME It 17 IB 19

Figure 2-3c. Scan Figure "T" for July 15, 1980

SECTION III

PROCESS CONTROL ALGORITHM

3.1 Control Strategy

The ADVS process control is accomplished by the Bristol process

controller by regulating the feedwater (CV-01) and exit steam (CV-02)

valves. The Bristol, using the algorithms for each valve, sends analog

signals to the Montec actuator valves (CV-01 and CV-02) to maintain

relatively constant exit temperature and pressure. The exit steam

valve tries to maintain constant exit pressure, while the feedwater

valve regulates the flow in a manner to maintain constant exit temper­

ature. This section deals with the development of algorithms for the

feedwater valve.

3.2 Control Algorithm for the Feedwater Valve

In order to avoid the problems encountered in implementing various

control algorithm (ref. Sec. 2.2), it was necessary to take an in depth

look at the factors effecting exit temperature. Exit temperature is

directly related to the energy captured by the fluid, which in turn

depends upon the available energy captured by the bowl and the loss

of energy due to radiation and convection. There are numerous factors

involved here. For example, the direct normal insolation (IQ»^) is the

factor related to energy capture. The available input power (P.j ) is

determined from the direct normal insolation (Ipj ) on the aperture area

(A) of the bowl:

32

33

^•n = ^DN ^ ^ ° ^ ^ (3.1)

The Ty. in this equation is the inclination angle as defined by equation

2.1. The cos 4- factor takes into consideration the angle between the

sun and the normal to the fixed aperture (the symmetry axis). P. is in

the total power available to the boiler if there were no loses. In

real life, however, loses occur due to many factors which are ever

changing. Wind speed and wind direction cause loss of energy due to

convection. Ambient temperature also affects these losses. Clean­

liness of the mirror also plays an important role, because the re­

flectivity of the mirror is affected. In order to avoid dealing with

these factors, which are ever changing, it was deemed useful to

define some kind of current average efficiency (e). If the power Pp

absorbed by the working fluid is known, then an instantaneous ef­

ficiency (e) can be defined:

P - • (3.2)

The power absorbed by the fluid can be determined from the following

expression:

p p ' " ^^ut - '"J (3.3)

where

M = the mass flowrate of the water entering the receiver [This

measurement is obtained by an optical flow meter (FOl or

F02) in the fluid line between the pump and the receiver.]

34

^out ^ ^^^ enthalpy per pound of the fluid exiting the receiver.

h.j^ = the enthalpy per pound of the water entering the receiver.

Now, in order to define a current average efficiency <e>, the

current average input power (P,-..) and the current average power absorbed

by the fiuid (Pp) may be used. The current average input power (P,--.)

can be defined as follows:

^in = <^DN> ^ ^ ° ' ^ ^ - ^

where

<Ipjl > = some kind of average of I j over a small

time period.

The current average power absorbed by the fluid (Pp) can be defined as:

Pp = <A> [h(T„„^) - h(T.„)] (3.5)

where

<M> = average flow rate over a small time period

T ^ = time average of T ., . over a small time period out ^ out

h(T) = specific enthalpy. [The pressure is considered constant

for simplicity.]

The current average efficiency is defined to be:

<"> [ 1 ( W - ' ( in) (3.6)

<IDN^ACOS^

35

This current average efficiency accounts for factors such as wind speed,

wind direction, ambient temperature, cleanliness of the mirror, and

many others. The flowrate M required to obtain the desired temperature

T^ can then be estimated:

^DN ^ ° ^ ^ = Ml,) - h(T.„)J ^ • (3.7)

Substituting the current average efficiency into this equation and re­

arranging, one gets:

<M> ^DN "^'S' "^'in

The right side of this equation identifies a useful variable combina­

tion which can be used to define an "error":

JpN ^(^out^ - ' < in) = 1 - S . (3.9) <l0N> h(Ts) - h(T.„)

where the quantity so defined will be called the "error".

Now, if V, CVCl, is the command voltage to the inlet valve, one

might presume a linear relationship between V and M, and proceed as if

M = e (V^ - V) (3.10)

where Vp is an (out of range, V < V^) "cut off command" at which M = 0,

and 3 is a constant (slope of the line). It would then follow that

36

<f^ = 6 (V^ - <V>) (3.11)

and, consequently.

; ; ^ - V ^ w =1 - ^ (3.12)

Solving for command voltage V, one gets the fo rm

V = <V> + [V(. - < V > ] ^ (3.13)

This equation is no more than a peculiar, approximate statement

of conservation of energy, but it is suitable for trial as the con­

troller algorithm. The command voltage V is clipped to never be sent

out negative or larger than a maximum value V which corresponds to a

near-zero flow rate, M * 0. The parameter V is chosen "out of

range" ; i.e., V , > V ^ so that V^ - <V> > 0. [In practice, V^ can be

made a function of V related to the slope of an M vs V curve.] The

average, <V>, of the value of the command voltage is defined with

a limited memory (further discussion in next section). The term

is such that it vanishes at steady-state set-point conditions.

The controller was given a "hand-latching" characteristic in that

the averaging operation does not function when the controller is in

Manual mode, but automatically starts with an initial value of <V>

equal to the V in effect at the instant that the operator switches to

Active Mode. In other words, if the operator assumes manual control

at any time, as soon as he returns control to Active, then Active

will latch-on and start from wherever the operator left the valve.

37

If the operator happened to leave the valve in a steady state at the

desired set-point ( g = 0 ) , then the Active controller will make no

changes as long as "£ remains zero.

The controller is also free of bias in that if ^ vanishes, then

V = <V> and the valve is (and has been) at the correct setting for the

fluid set-point. This algorithm is adaptive in that it will still

perform properly even if a hand-valve set-point is changed at the load

skid. Also, since conservation of energy was used, this controller

should not ever turn the valve the wrong way, even in the presence

of the nonlinearities. The expression for ^ can be simplified by

approximating a steam table at 1000 psia: (3.14)

t =!-< I... \ DN

^ D N "

| ^ ( W - ^'i.A . . [ DN iTout ' 1636°F\ jpr(Tirn^lT7;T - 1 -i < V r s "1636°F

The average <InM> of the direct normal insolation, is defined in the

same fashion as <V>. The set-point temperature is T^; output or exit

temperature is T .; and T. is the feedwater inlet temperature. The

active term shown in the expression above is bilinear in l^^ and T,

but under steady insolation is equivalent to K(T - T ^ ) .

3.3 Time -Averaging for the Controller

The control algorithm motivated in the preceeding subsection is

V = <V> + [V. - <V>] Z » (3-15)

where V is the command voltage for the inlet valve (V =0% gives wide

open valve, V = ]Q0% give minimum flow) and is the error:

38

t =1 -/ Inf.. \ /T..... + 1636°F \ "DN 'out

\

^DN> r S "• ^^36°F (3.16)

The command voltage is automatically clipped by the Bristol to always

lie in the range 0 - 100%, and the hand-latching procedure requires

that it be possible to reinitialize the averages <\i> and <lr,K,> quickly

and easily. The responsiveness and adaptability characteristics of the

controller are dependent upon the method of averaging, a type of ex­

ponential memory loss is desirable for the averages.

Due to calculator limitations in the Bristol computer, averaging

with an exponential weight is most easily accomplished by using an

analog approach. Considering the analog averaging circuit shown in

Figure 3-1, one gets by inspection:

d <V> dt

The solution of this differential equation.

= A = G (V - <V>) . (3.17)

IS

^ <V> + G <V> = GV , (3.18) at

t

<V>= e- (t - V <V> . G I e-S(t-t')V(f)dt"''-'''

^0

where t is the time of initialization (or of the most recent reini-0

tialization). The gain G in the analog circuit defines the reciprocal

of the "exponentional memory loss time" or "forgetting time":

E

u o II

<

4-> < ]

J O

A > « V

Q .

+J

3

A

V

I

39

' \ \ \ \ \ \ \ \ \ \ ^

s-<_)

01 a» <o s . O)

>

en o <o c <

I en

i-3

40

^M • ^

1 G * (3.20)

The nature of the <V> defined above as an averager can be re­

cognized by considering <V> for the special case that V(t) is constant:

<V>

V = V.

-_e-G(^- ^o) < V > . [ 1 - e-^(^ -^oh V^ . (3.21)

One notices that the average develops smoothly from the initialization

value, <V>Q, to the long-time average, V , with an exponential time

scale of TM- Thus the past is damped out and the "average" is de-

fined with a limited memory depending upon the analog gain factor G.

The Bristol is a digital computer, and the command servicing

cycle time used is At = 0.8 sec. Thus, the actual implementation of

the analog averaging equation

^ ^ = G [V - <V>] (3.22)

proceeds recursivsly as indicated in Figure 3-2:

(3.23)

= GV^ + (1 - G) <V>^

where

G E GAt = G (0.8 sec) , (3-24)

and the subscript indicates the time step. The hand-latching feature

41

A

V

o h—

— I «=c < : Qi I— o I—I LU •—' ^Z Q •—I

A

V

I

>

(Si

ex: o

_ J

CJ

o to

•p—

CQ

&-(U

> «3:

•t->

•r" cn o

c o

•r-4J «TJ

-t-> C <u E (U

Q . E

CM I

CO

i-3 cn

CJ A

V

42

for reinitialization is easily accomplished by setti ng

< % = Vo '

so that

<v>^ = <v>, = v^ ,

<V>2 = GV^ + (1 - G) <V^> = GV^ + (1 - G) V^

<V>3 = GV2 + (1 - G) GV^ + (1 - G)^ VQ ,

and so forth:

n - 1

<V>, , T = G 2 (1 - G)^ V^ . M l - G)" V^ . (3.25) r = 0

The sum of the weights is one, so that an average is obtained with

recent values of V weighted more heavily, provided only that

G <i 1 ; i.e., T| > At = 0.8 sec.

The role of G is wery important. If G = 1, then

T . E - E ~ = t = 0.8 sec, and • G G

<V>n . 1 = ^ '

so that the averager would act with zero averaging interval and no

memory. At the other extreme, if G = 0, then "iv; = °° » "

43

SO that the average would be pinned at the initial signal value.

Intermediate values of G, corresponding to T^ = 26.7 sec, 53.3 sec,

and 80*.0 sec are illustrated in Figure 3-3. For these examples the

average was initialized at <V>Q = 0% and the signal value was given

as step change (rise time < 0.8 sec) to a constant value of 100%.

Notice that the average rises from 0% to closely approximate

100 (1 - ^) = 63.2%

in the time T^..

The controller algorithm developed in this section has been suc­

cessfully employed for the ADVS and has been in service for nineteen

months. Although the service has been satisfactory for the most part,

improvements are definitely possible. Simulation of this controller

is considered in the next section.

44

i i

woot

SECTION IV

SIMULATION OF THE CONTROL SYSTEM

4.1 The Control Algorithm

The control algorithm developed in Section III for regulating the

feedwater valve is implemented by the Bristol process controller. As

mentioned in Section II, the Bristol performs processing operations

through the use of digital logic. The data needed for the controller

is acquired by the Bristol, and the command voltage is sent to the

valves e^ery 0.8 seconds. Since the algorithm itself is implemented

by the use of digital programming, digital simulation is the best

option.

Figure 4-1 is a block diagram showing how the Bristol implements

the control equation:

V = <v> + [V. - < V > ] ^ (4.1)

where

<V>n . 1 = <'\ * StV„ - <V>„] (4.2)

and

-£ = 1 -/ I DN

\

<^DN>'

T . + 1636°F\ out T^ + 1636°F

(4.3)

The controller action can be adjusted by varying its parameters, V . and

G. When choosing V^, it was temporarily assumed that there is a linear

relationship between mass flowraie M and the command voltage V. This

45

46

c o

<u E o.

3

O

o

ItJ & -O l <T3

9

o o

CO

I * ^

0) s . 3

Y V

47

is only approximately true. Also, since there are numerous hand-

operated valves on the load skid which are occasionally reset, and

since the pressure compensating valve is erratic, the relationship

between M and V . changes from day to day. The value of V^ was chosen • L

out-of-range, such that V , is greater than V . [The range of V is

from 0 to 100%, where V = 0 means the valve is completely open and

V = 100% gives minimum flow; M - 0.] In practice, a value between

101 and 115 was usually assigned for V^. The memory time for aver­

aging |v| = (0.8 sec)/G, was selected by trial and error. In practice,

a value of G between .01 and .03 was used, depending on the type of

insolation pattern observed for the day. One should also note that

the term [V . - <V>] in the control equation (4.1) is merely a variable

gain factor. If the system is in steady state, (V . - <V>) is simply

a constant.

4.2 Strategy for Simulator Development

In order to explore the control equation, it was decided to simu­

late the control system and then vary parameters (in the simulation

model) to see the impact on the system behavior. There are two major

obstacles in accomplishing this task. One of the problems is related

to the data storage system. As mentioned in Section II the data

acquisition system (DAS) stores data for later use. Although the

data is conveniently stored, it is only sampled every 20 seconds

during the ADVS operation. On the other hand, the Bristol process

controller receives data and computes the command voltages every 0.8

seconds.

48

The second problem deals with the prediction of exit temperature.

In the actual control system, when a command voltage is sent out, it

regulates the flow in the receiver, producing an exit temperature

which is sensed by a thermocouple. The exit temperature is then

utilized in the next calculation of command voltage. In order to ac­

complish this feature in the simulation, it is essential to establish

a mathematical model to predict exit temperature for any command volt­

age.

The task of simulation is divided into two phases. Phase one of

the simulation consists in building a test computer model which can

predict command voltage from the same information available to the

Bristol process controller. If the command voltage produced by the

computer model can be made to agree with the actual command voltage

sent out by the Bristol for a reasonable period of time, one can con­

clude that the computer model is capable of simulating the control

system.

The second phase constitutes of building a model that can predict

exit temperature given a command voltage. This model can then be

combined with the first computer model to provide a completely in­

dependent simulation model. Once an independent model is built, it

can be used for general testing and development purposes.

4.3 Computer Simulation Model I

The function of the Computer Simulation Model I is to predict the

command voltage based on the information available every 20 seconds.

Essentially, this model receives the same type of input data as the

49

Bristol process controller. The frequency of data received is dif­

ferent, though. The Bristol receives data every 0.8 seconds and com­

putes the command voltage. On the other hand, the model receives data

every 20 seconds (i.e., 25 times less often than the Bristol). Since

the TQ^.J. is dependent on when the command voltage is sent out, it is

difficult for this model to predict command voltages similar to that

predicted by the Bristol. Therefore, it is considered reasonable if

this model can follow the actual commands for one hour. [The averaging

circuit has memory of a few minutes.]

In order to accomplish this task, it is important that the aver­

aging circuit model follow the actual averaging circuit. A modified G,

denoted as Gj, must be defined for the simulation such that

<V> = <V> + G(V - <V>) for calculation iteration every 0.8 seconds

(4.4a)

and

<V> = <V> + G,(V - <V>) for calculation iteration (4.4b) " every 20 seconds

follow the same path. Curves for several values of G are shown in

Section III. It was necessary to develop a relationship between G and

G, such that they follow essentially the same curve, in spite of the J

time step size difference in the calculations. From the above equation

one can directly deduce that when G = 0, then Gj is also zero.

As a first approximation, one can relate the two gains by re­

quiring that the same memory time be observed:

^ At _ 0.3 sec z 20 sec (4.5) ' M - G G G.i

50

This requirement gives

^J ' ^ O ' = 25G . (4.6)

In order to easily improve this approximation, a program called Test

was designed to determine the best value of Gj for a given value of G.

Basically, the program consisted of using a step change in V and using

Eq. (4.4a) to generate <V> for a given value of G (similar to plots of

<V> in Section III). Then various values of G. were tried in Eq. (4.4b)

in order to obtain agreement of the <V> curves. The following values

of G and G, were found to be equivalent.

G = 0

G = .01 ^

G = 0.015-

G = .02 "

G = .025 ^

G = .03 ^

GJ = 0

GJ = 0.22

GJ = 0.31

GJ = 0.39

GJ = 0.46

GJ = 0.53

(4.7)

Figure 4-2 shows a graph of Gj vs G. These results are well fit by an

equation of the form

G = 1 - e"^^ with a = 25 . (4.8) J

This curve is shown on Figure 4-2 along with the f i rs t approximation

given in Eq. (4 .6) . Therefore, the relationship between G and Gj is

well approximated by

51

CO - I o

CVJ o

• o

CD

— o

• o

^ C3

CO >

CI5

<4-O

to +J o r—

a.

• CsJ

1 ^ (U s. 3 cn

•r— Lu

p

I

2i

U A

/I

52

July 5, 1980 and July 30, 1980 were the days picked for simula­

tion tests. On these dates the operators at the ADVS site used single

values of V . and G throughout the entire operating day, so no compli­

cations are introduced into the comparison. Figures 4-3 and 4-4 show

the Scan Figures for the two operation days selected.

The values of G and x^ = 0.8 sec/G, the corresponding values of

GJ (from Eq. (4.9)), anci the values of V^ and T^ used for the two dates

are:

Q

0.010

0.015

^ _ /0.8 sec\ M ^ G ^

80 sec

53.3 sec

!J

0.221

0.313

!c

107%

101%

Is 1000°F

800° F

July 5, 1980

July 30, 1980

Using the actual (20 second sampling interval) data for 1 , and T

for these two days, Eq. (4.1) was used to calculate V in simulation.

The simulated command voltage (V^r^) is plotted, along with the actual

voltage V p-j- sent out by the Bristol (from the recorded data at 20

second sampling interval), in Figures 4-5 and 4-6. The ability to

simulate the command voltage using the recorded tape sampling interval

is well confirmed. After a period of time, one sees an accumulation

of error, but reasonably accurate tracking is seen in the simulation

for several hours of data.

4.4 Computer Simulation Model U_

This phase of simulation deals with the developement of a mathe­

matical model to predict exit temperature from a given command voltage.

mwwz

53

1700

•00 -

uo -

arc -

0

170C

SOO -

* B O o l -

300 -

0

MOOr

30D

TOOr

JOO -

DflTfl FOR JULT 5.1980

IC II 1! 13 IM IS

LOCflL APPARENT TIME 19

Figure 4-3a. Scan Figure "P" for July 5, 1980

liOCr

»oc -

too

JOC -

u

a MS

lO

IS -

c

K O r

270

a a IBS -

X -

0 1 —

i r o r

i ST-

30 -

DflTfl FOR JULT 5,1990

'' .AMMrt^^^^^W iV

/ ^ *Y -^ \

• I I

E 7 t 9 IC 1 ! i ; IJ ]M 15 }S 17 IE IS

LOCflL APPARENT TIME

54

Figure 4-3b. Scan Figure "I" for July 5, 1980

55

IOC

a. UJ

Mr

JC -

0

roc r

:se -

w-T " * •

SC -

DflTfl FOR JULT 5,1980

LOCflL APPARENT TIME

Figure 4-3c. Scan Figure "T" for July 5, 1980

56

17S0 DflTfl FOR JULT 30,1980

BX

bOC

3K -

"AT 1 ^

*'>^^'v/\^\/A/\/

B

<

LOCAL APPARENT TIME

Figure 4-4a. Scan Figure "P" for July 30, 1980

17K

soc

600

XX -

D I—

UJ UJ

cn 3,

IS -

0

35C

rTo

a o 2

9C -

c

120

90 -

i

DflTfl FOR JULT 30,1980

-'^'''^'•'''tMi^

- ^ . - . ^ v . . . « V . , , U

W

m'^^hf^'^^

IC

LOCflL APPARENT TIME

f ^ ^

1 I ' 1

1

i 1 1

) ( 1

\

1 ( t

!

1

II* IS IE 17 «

57

Figure 4-4b. Scan Figure "I" for July 30, 1980

58

DflTfl FOR JULT 30,1980

10 11 i : 13 IK I S

LOCflL APPARENT TIME

Figure 4-4c. Scan Figure "T" for July 30, 1980

59

V

o o

k8

o o

o 00 CD

LO O

OO 3 - ^ ( ^

O

O

CE

o o o

o a

s o

o 00

in

3

S-O

CO

s d «^<n

UJ t—

i •

« a Z "^ UJ s:

S. d in

8 •

o 9

8 d

£ O (n

«>i«

I I UI S •—1

^-

z •-<

cc h-W)

(1) • a o z: c o

•^

ula

t

E •^ OO

4-> «/»

1— ~ M-. O

10 •M ^ • *

3 R

es

• i n

1

gure

4

o o . • II

CM C\J

o II

o

a o o o

cu c: <_} 00

I— '001

— I — 05*68 00'S^.

—r 1 r r-OS'33 00*05 OS'a 00 "52

33tii10A QNdWWOO

OS'Zt

o

a a

8 00*0°

S • • i

J

60

o 00

o cn

CE _J 3

i n CO

o < <— o . o o

o o »— CO

II II

- 3 O CD

II II

o OO

0Q*0O[ 0 5 ' ^ oa*S£ T — I r—

os'za 00*15 os' s 3 3 b : i O A QNdWW03

T 00'sz

— T " 05*21

a CM

8

S 8

3

o 00

O CO

o at

o o d 09

O

• « <n

Ui i—

§ 0 « - i

ox: d S z

*"•

Ui x:

8 ^ • o

8 d 9

8 •

o

o o

71 (X

tn 3 * •-.-^

II UI

z: •—1

K -

o z

a: 1—

-^ 3

O t -

t—1

o s c o •r-

(O

3 E

OO

0) 1—

O in

^ • ^

3 CO 0)

CI

1

3

cn o

!30*Q

61

The power absorbed by the fluid (Pp) is defined by (ref. Section III):

Pp = M l^^ut - N'n^ (4.10)

^ ^out ^^" ^^ determined, then steam tables and values of the exit

pressure P^^^ can be used to find the exit temperature T^. In order

to find h^^^ from Eq. (4.10), h.^, M, and Pp must be known. Calcula­

tion of h . is very simple. The inlet temperature and pressure are

known. Therefore, h^^ can be found from steam tables. Thus, the main

task consists of finding M and Pp.

4.4.1 Mass Flowrate (M) Curve Fit

Since the mass flow and the Bristol command voltage are both re­

corded data, it is possible to determine the relationship between the

two. The Statistical Analysis System (SAS) package was used for the

curve fit (ref. SAS language). SAS's statistical capabilities are

highlighted by its versatile least squares procedures, which produces

a wide variety of linear and non-linear regression analysis, analysis

of variance and covariance, and multivariate analysis of variance.

The GLM procedure, which uses the principal of least squares to fit

a fixed-effects linear model to virtually any type of data, was used

for the curve fit. Appendix A shows the program used for this curve

fit. It also shows the output of the curve fit. Equations of the

form:

M = a + bV + cV^ + dV^ + eP + fP^ + gT + hT^ +iVP + jVT + kPT

were tried, where a, b, c, d, e, f, g, h, i, j, k are constant and

62

M = mass flow rate, in Ib/hr

V = command voltage, in %

T = inlet temperature, in °F

P = inlet pressure, in psi.

Table 4-1 shows the combinations of these parameters with their re­

spective standard deviations for July 5th. Since there are numerous

other variables (e.g., hand valves at the load skid), these curve fits

for M are only valid for that day. Table 4-2 shows the parameters of

the curve fits for July 5th. As can be seen from these two tables,

the coefficients are quite different from day to day.

The curve fits marked with asterisks in Tables 4-1 and 4-2 are

those actually used for the simulations. Figure 4-6 shows graphs of

the curve fits used for the two dates, along with the corresponding

"one a" bands; i.e., M ± a, where a is the RMS deviation of the curve

from the data. The different curves used for the two days are seen

to be similar enough that their differences are not s^vy significant

statistically.

4.4.2 Calculation of Pp

A computer model TFAP was developed in 1977-78 by Dr. Clements

and H. Shankar to predict Pp given M, \^^^ V , and Q> . In 1978 Dr.

John D. Reichert developed a curve fit to results from the computer

model TFAP. The curve fit is known as TMR and is quite suitable for

use in computing Pp. The curve fit TMR is presented in Appendix B

(ref. SC).

r— 1

«!:^

OJ r—

.a <T3

o 00 <y\ '—

0t

i n

> ) 1 — •

3 "-o Q :

o u.

a:

s:

STD DEV

.2^

•>-}

•r—

. C

cn

M-

OJ

-a

o

J 3

(T3

EQ NO

15.113

- 7.317

811.969

-

10.135

-0.124

11.7

80

93.091

CM

9.532

-0.005

1.033

-75.958

2284.56

CO

9.155

0.003

-0.244

-0.1

19

8.21

1 384.910

^

9.554

-0.023

-0.150

15.346

- 4.506

i n

11.392

0.007

-0.574

-13.510

1362.214

vo

7.774

-0.0002

0.038

0.002

0.089

-21.769

.00002

-0.136

-0.085

0.469

1725

.327

r>.

63

64

CM I

CU

.a

o 00 cn

o CO

cti o

C_>

STD DEV

.KJ

""-

• r -

sz

cn

M-

OJ

-o

<J

- Q

<T3

EQ NO

21.337

1

-7.945

866.686

-

13.7

22

i

1

-0.1

11

8.17

2 307.057

CM

10.7

16

-.005

1.005

-70.406

2110

.301

*

20.083

0.003

-0.226

-10.443

1041.049

^r

10.860

10.863

-0.003

0.004

-0.318

-0.126

7.480

489.481

L D

0.004

0.195

-0.317

-0.127

7.869

462.947

vT)

10.205

-0.001

0.083

.002

• o

-30.416

0.0002

-0.265

-0.105

-4.185

2604.442

r-»

4-> in

65

> S-3

C_)

I _

i

cn

c o o. to

&.

o

di

- I -)-»

S: 10 ^ >

=~ O

m a.

S t 3

o 10

o o

p** I

3

cn

' J

'CCf-I

• - - ^ :c:s; ^ ^ ' o ' : Ow"^

66

4.4.3 Calculation of T^

With M = M (V, P, T) and Pp = Pp (M, I ^ , v^, ^ ) ,,,,,,,,^^

one can find h . from

P = M [h . - h. 1 F •- out in-'

p (4.11)

Now, h^^^ and the pressure, P^^^, can be used, with a steam table,

to find Tp. A curve fit of T^ = Tp (h ^ ^ , P^^^) using GLM was made.

Appendix C shows this curve fit. A equation of the form:

T^ = a + bP + cP^ + dH + eH^ + fPH + gPH^ + hP" + iH^

was tried, where a, b, c, d, e, f, g, h, and i are constants and

P = exit pressure = P^ . » in psi • out

H = exit enthalpy per unit mass = h ,.» in Btu/lb out

Table 4-3 shows the best values of these parameters with their respec­

tive standard deviations. The values of Tp are in °F.

4.5 Simulation Model

The final simulation model is a combination of test computer

Model I with the mathmatical model for Tp. A flow diagram for the

entire simulation is given in Figure 4-8. Appendix D shows the

complete computer code for the simulation. Tests of this simulation

model are described in the next section.

67

CO 1

"id-

0) r^ .£3 m 1—

X UJ

a: o u 1— 1—1

U-

LlJ > r) CJ

UJ -J ca < h-

IS: < UJ

OO

> LL.1

c cn H-OO

O"

<+-

O)

-o

o

-O

.-a

O 2:

cr lU

CM CO cn • ^ •"*

1

t

1 t

1

00 Ln vo •

>—

in o 0 •

0

00 00 vo •

CO LO

1

,_

in in 00 • «;r ^—

i

00 in vo •

•~

CM CM VO • CM 1

CO CO r-

CD

CM

<--

CD 0 VO

1

CM

CO

VO •

r—

1 1^ 1

0 1 ' • 0

LO 1— 1

X

00 1 CM 0

X

r CM 10

LO X

CM

.00

0

CM

0.0

0

LO p>» .

1 ^

1

0 ^ CO •

in 1

cn CO vo •—

in CO vo vo CO

1

CO

u, i CO 1 r^ "•v» CM

,.

CO 0

.00

0 1

r 0

0.0

0

r>. 0 CM • 1

' 0 t—~

T^

r-*. m

CM 1

00 0 vo • 0

«^ 0 CO • LO

^ p*-

1

•K "C-

68

U l l

I— 4-> .O (d

1— E (O <u + j 1/7

• r -U-

OJ > s. 3

CJ

jr~fi T

s .

O

L to IA <0

-M iQ CU

Q : > 4->

5 3 Li-O O

— 1

CU CO CU

a: CD

CO

^ J —

T

CU

o

o

3 E

• I —

OO

Oi

o « • -

E

cn ro

3 o

CO

(U

3

i 4 i i

SECTION V

TESTING AND EVALUATION OF THE SIMULATION

The complete simulation model developed in Section IV (ref. Appen-

dix D) consists of several mathematical models. The overall model uti-

lizes curve fits '.or mass flowrate (function of command voltage) and

exit temperature (function of enthalpy and pressure). It also uses

the TMR curve fit, developed by Dr. Reichert, for prediction of P ,

the power into the fluid. For the control algorithm, an important

factor is the parameter G. A new value of G, known as Gj, developed

in Section IV, compensates for differences in the time steps avail­

able in the recorded data from those actually used by the Bristol.

The simulation model has been equipped with the latch-on capability

of the actual controller. Thus, it can accept initial conditions from

the current status of the actual system. The model includes the

clipping feature (0% ^ V ^ 100%) of the acutal controller. Thus, the

command voltages sent by the actual controller and by the simulated

controller are newer more than 100% (equivalent to 10 volts, minimum

flow) or less than 0% (equivalent to 0 volts, valve completely open).

The simulation model has been tested by simulating the controller

and comparing the response of the simulated controller with the actual

controller. The function of the controller is to control the exit

temperature by controlling the command voltage for the feedwater valve.

In order to compare the two controllers, the command voltage and exit

temperature were plotted for the actual and the simulated controller.

The simulation was tested July 5, and July 30, and August 1, 1980.

69

70

[The test of Gj was previously accomplished by testing the Simulation

Model 1 (ref. Section IV).] Figures 5-1, 5-2 and 5-3 display the re­

sults of the simulation model compared to the actual controller. The

actual command voltage and exit temperature (from ADVS data) are de­

noted by V^^j and T^^j in the graph. The simulated command voltage

and exit temperature are labeled V^rw and T^j».

The graphs in Figures 5-1, 5-2 and 5-3 exhibit remarkable resem­

blance between the actual command voltage and the simulated command

voltage. [Scan Figures for August 1, 1980 are given in Figure 5-4.

Scan Figures for the other two days were given in Figures 4-3 and 4-4.]

The model predicts the V^j^^ quite accurately. A comparison between

Tn^j and T^.^. shows the typical phenomena of the TMR. The T^^j is

comparitively smoother than the T^^^. This phenomena can be attributed

to smoothing effects due to the physical delays in the system. [TMR is

a sequence-of-steady-states model.] In the actual system, when the

valve command is changed, the flowrate is changed very quickly. The

change in flowrate effects the exit temperature, but only after a

finite delay, because the fluid has to travel some distance before

"steady state" is re-established. This time delay has a tendency to

smooth the measured exit temperature. The TMR equations presume

steady state is instantly established, so that they are more sensitive

to changes in flowrate and exhibit a spurious high frequency ripple.

A careful examination of 1^^^ shows that it follows the T^^^ quite

accurately except with excessive vigor.

71

00£ L_

as I L_

' 8

fi zr mm

s 9 ^m

1^ n -*

n ".UJ rt3Z

»—

• -Z

OUJ o ^ r i f f —Q_

^

_J

S c j

2-J

r» » i

O 0 0 cn '~~

A

i n

>>

3 - 3

S> O

v»-

CU ^~ — o S-

4->

c o CJ

"O <u 4-> fO — 3 F

• ^ •

OO

CO >

O) '

o &.

4->

c o CJ

c«

o — o

•

II

CD

r ^ CM CM

. O

II

' ^ CD

r o '—

II

CJ >

o O O O • "

II

OO 1—

o •

CO

cn II

< 3

I— 00*001

— I — 05*19

T 00 'S I

— I 1 1 1 r— 05*23 00'OS OS*LS 00'S2 0S*2t

3f3di10A QNUWWOa

8

(O

8

12.

!^ —

(J «=c

f —

i n

3 cn

00*0

72

0031 I

OS 01 _ 1

006 1

(do) dW31 iIX3 OS^ 009 OS*T OOS —J 1 1 L_

OS t _J

O OO CD •—1 N

o CO

LJL.

I — cr -J

t— oo'oor T"

05'^ T T T T

Ln f M

o • o II

CD

CO * • • "

ro •

o II

'n CD

o 1— O ° s II II

CJ Cn > 1— <

CO

cn

< a

00'SI os-za 00*05 os'u 33«nOA ONtfWWOO

0 0 ' S 2 OS'21

°8 M

.UJ

8CD

0 . GC

8

C

r*

8

00*0

s cn

o CO

8 ^ 3

&. O

4 -

S. (U

' o s-

+-> c o

CJ -o CU

<o

3 E

CO

CO

>

CU

o

o o

rT3 3

O

CM I

i n

CU

s. 3

73

dW31 11X3 0 0 9 OS n

r" O0*00(

— I — os*:fl 00*51

— I 1 ' r -05-29 00'OS OS'a

33«i10A QNbWWOG

0.01

5

II

CD

0.3

13

II

- 2 CD

108

800°

II II

CJ OO > H - <

r—

o cn

U l C4

00*S2 OS'21 l=

00*0

o 00 cn

4-> CO 3

cn

o ^-

s-(U

o •M c o

-a a> + j (C

3 E

00

CO

>

o &-

+J c o

CJ

3

U

CO I

in

(U s-3 C7>

74

170C

»oc

XT -

0"—

9 X

EOO -

300 -

)XZ

800

EOO

o oc

TOO

c«—

JOOC

to o CJ

2or -

DflTfl FOR flUGUST 1,1980

I

f^^V-WU-A^^.f,

X

]S : E

LOCflL fiPPhRENT TIME

Figure 5-4a. Scan Figure "P" for August 1, 1980

75

i;re

sx

.-? s *

30C -

C I ­

SC

DflTfl FOR flUGUST 1,1980

a «s UJ a. tn 3C

Q »—i

0

3SS

/('^'^

no oe. a

180 Q Z

C— 12C

90

<««**^~S/\^

I SC

30 -

Cl— - i

' K'

K

^tAi^yi'i'^^W

J !_ _1_ J I

"LOCflL fiPPflRENT TIME IE 17 ]t :s

•

I «

J

Figure 5-4b. Scan Figure "I" for August 1. 1980

76

IK

' e:

P 6C

UJ .

» -

0«—

700

JSC

JOO

UJ

50 -

e l ­

se

no

CJ

c»—

OATH FOR fiUGUST 1,1980

u

j

:c i : J : la i>i is

LOCflL flPPRRENT TIME

I I

I ' l l

Figure 5-4c. Scan Figure "T" for August 1, 1980

77

5.1 Simulation Without Using G,

The simulation model discussed was designed to accept data every

20 seconds for its computation of command voltage. This was necessary

because the data was only available at 20 second intervals. The actual

system, on the other hand, was provided data by the sensors every 0.8

seconds. In order to confirm the simulation model, as well as to make

it compatible with the actual system, it was desirable to test the

model when data is provided at the same frequency. Since the data was

available at 20 second intervals, linear interpolation was utilized to

provide "data" every 0.8 seconds. The simulation model thus operated

should give results similar to those attained by the model when using

data every 20 seconds. If successful, the test not only reconfirms

the model, but establishes the direct relationship between the para­

meters of the model and those of the actual system. The "sampling

frequency" parameter match-ups would be shown to be unnecessary. The

data for July 5, 1980 was linearly interpolated to create input at

0.8 second intervals. This data was then fed into the simulation model,

and the actual value of G was used, instead of Gj. The results of the

simulated command voltage and exit temperature {^^^^ and T^^^) are

depicted with the actual command voltage and exit temperature (V ,

and T ) in Figure 5-5. The results are almost exactly the same as ML/ I

those shown in Figure 5-1.

This test not only reconfirms the model, but also qualifies the

model to be used for improvement of the controller. Any set of data

can be created and utilized for testing the controller, without having

to make "sampling frequency" alternations in the parameters.

78

(3o) dW3i 11X3 0 0 2 1

I

o CO CD

LO O

Li_

O

CL

CO

0 0 9 I

OS+T _ i

ooe t

OS r

p*.

:T

r) - . —

O o —

C3

r i

"O (U CO 3

+J O c

•-3 CD

• M

<o •t-> ta

Q

"O CU •!-> (C — o £^ i-Q)

'.LU

OUJ C 3 ( ^

oCX - Q _

Q_ cn

GcJ

•o ex i

o o

0 O O O ,— P^ O c o o <

. I— I— 0 ^

II II II II

CJ OO

o c: o o

CU •4->

to

E 0 0

CO

>

o i-+-> c o

rt3 3

• • - >

CJ

in I

in <u i-3 cn

o o

i 03"0OI

T 05*^9

1 — 0 3 ' S i

T T T OS-29 03'OS OS'iC 03 52

— I OS'21 33 3

79

5.2 Testing and Evaluation of the Controller

The control algorithm for the feedwater valve

V = V +K[V(, - <V>]S (5.1)

was derived on the basis of conservation of energy. A gain factor K

(not used in the Bristol) has been introduced in the error term to in­

crease or decrease the contribution of the error factor. Similarly,

the variable gain factor, [V^ - <V>], might be replaced by a constant

gain factor, V^. Investigations at the ADVS, replacing [V . - <V>]

with V« = 20 seemed to give about the same results for the actual

system control.

The testing on the actual system gives results which are rather

difficult to interpret, due to uncontrolled conditions in the actual

operation. The simulation model has a distinct advantage in this

regard, because a controlled environment can be provided to the model.

A hypothetical day was created for one such test, and various cases

were explored. It was decided to run a test in which the factor K

was varied from 0.5 to 1.5. [K = 1 corresponds to the algorithm used

at the ADVS.] A test with the [V^ - <V>] term replaced by the constant

V, was also conducted, so that a comparison between the two controller

formats could be made.

Data was created for a three-hour-span for a sun at equinox (for

computation of 4 ; March 20: 6 = 0. AT = 13.04«). The insolation

Ip. was chosen to be

(5.2) I = U , [1 + ct sin 2rTtJ DN DiMO ••

80

where

IQNO "" ^^^ watts/M^ ,

t is in hours, and

a = 0.1

The function thus created is sinusoidal with a period of 1 hour.

The exit pressure (PQUJ' ^ ^ chosen to be a constant; PQ .J. = 1000 psi.

[In the final power plant, the exit pressure will be maintained constant

by a pressure reservior.] The inlet feedwater temperature was taken

to have the constant value T j = 115°F. Wind speed V., was also chosen

to be constant: V^ = 10 MPH. The controller was assigned the set-

point temperature T^ = 1000°F, and averaging parameter was G = 0.01.

For the first case, the test was conducted with K = 0.5, 1.0, and

1.5 with Vp = 107%. The second case was examined with K = 0.5, 1.0,

and 1.5, using V« = 20%. This provided values of 10, 20, and 30% for

KV„. The simulations for these two cases are exhibited in Figures 5-6

and 5-7, respectively. Each of these two figures exhibits seven curves.

The Ip) curve is placed near the bottom of the figures. This curve

provides a phase reference. The command voltage curves are denoted by

V^5 (K = 0.5), V^^ (K = 1.0) and V^^^ (K = 1.5). The temperature

curves corresponding to these command voltages are denoted by Tj^^, 1^^

and Tj^.g, respectively. Study of these curves provides some inter­

esting conclusions. In both cases, as the coupling increases; i.e.,

as the gain factor K increases, the controller becomes more effective

in maintaining constant exit temperature. The feature observed at

( io ) dW31 iIX3 OSZ. 0 0 9

81

^5

Ui

o . 1

- - •

"*

vo r

— 3' • ^

.00

— 3" "*

i n

• .UJ - c - j j ;

" ~ i - ^

*—

^-2

O U J j ^ a ^

- o ' c r —a.

a_ (X _ j

->JCJ

- c n °

S .

o +J o (O

Lu

c • r "

ro C3

(U r~»

• • S-<T3

> A

:xr

«/) 3 O

• r -

L. <T3

>

x: • M

•^ 2

o •«->

— <0

o a o —

tf>

^ r ""

o j %

OO

+J CO 0)

1—

• CO

1 i n

CU &_ 3 O )

•r—

o o

OS'^0 03 Si OS'23 03'35 OS*£.C 30bi"'0A QNtiUWOJ

33 52 QS^zr 03 3

82

o W1

— sr • ^

i n r i j

— 3-• " •

O o

- ^ ""

i n

• . U J - 0 3 I

" • • — .

»— • ^ 2

O U J - i Q t

- r^CX — C_

c_ (X

_ J

tfl?^ 1 ?>j(j

o o

— r! .-.

i n r»

— r>4

o \n

S. o

4->

u «o u. c

• f—

rtJ CD

4.^

c ( 0 + J CO

c o

C J

A

:^ CO 3 O •^ s. <o > J C 4-> • r" 5 c o

ati

— 3 E •^ 0 0

+ J

w» (U 1—

• r^

1 i n

(U &. 3 CP

•r—

J1

o o

O3'00t OS'68 03 'S i 05-29 03'OS OS'it 3-3«l"lDA aNtiWW03

03 52 0S'2I

83

the ADVS, that the controllers are very similar (for K = 1) is strongly

confirmed. It appears, however, that the "energy conservation con­

troller" (with variable gain factor) is much superior for higher K.

The average flow decreases (command voltage increases) during the

course of the day, in response to increasing values of , the in­

clination angle, as expected.

It is of interest to examine the phase shifts observed in the

figures. The command voltage (flowrate) lags the insolation curve

by a phase angle which will be called (j). The exit temperature, on the

other hand, leads the insolation curve by a phase which will be called

i). It is wery apparent in the figures that <^ approaches zero as K in­

creases; i.e., for large feedback gain, the valve command tracks the

insolation yery closely.

In order to confirm the behavior of the simulation, and to initiate

a sensitivity study (small signal analysis), the relationship between i)

and 0 was studies analytically. From a linearized-analysis of the TMR

equations, suitable for small <X and constant T^ , the relation:

sind) 8 siniJj /c^x

was obtained, where 3 is the amplitude of the M variation. The nota­

tion used is:

V = VQ [1 + 3 cos (wt - 180° -4))] (5,4)

M = MQ [1 + 3 cos (wt - cJ))]

J. = T. [1 + Y COS (wt + ij;)]

84

It is clear that the relationship between i|; and 4) is very sensi­

tive to the ratio a/3. [If a/3 = 1 then ij; -v 90° as (J) - 0. If a/3 M .

then i|; ^ 0 as 9 ^ 0.] Thus, for small (^ (large values of K), the value

of 3 must be determined accurately in order to calculate -^ accurately,

and conversely. Values of ^ measured in'the figures are compared with

calculated values (using values of <j) and 3 from the figures and the M

vs V curve fit) in Table 5-1. The results are close enough to give as­

surance that the code is behaving properly.

5.3 Future Use of the Simulation

The main purpose of this study was to develop a simulation model

for study of the ADVS process control. The simulation model has been

constructed so that direct compatibility exists between the model and

the actual controller. This provides a unique opportunity for studying

the controller under any circumstances and conditions. Hypothetical

data sets can be constructed and applied to the model for evaluation

and testing of various control algorithm. The preliminary applications

described in the present section have already produced interesting con­

clusions. It is expected that further application of this simulation

will assist greatly in the development of the control algorithms to

be used in the actual power plant to be built by the Crosbyton Solar

Power Project.

85

u

^_ 1

LO

CU

JD ta

\—

r— la o

-3-

co >

to 03 CU

E • ^ •

U -

o ~^ o CO » — 1

Of < CL.

S O CJ

-e c

•r— to

to o CJ

1

ca 3

,— 1

C (Q

1— II

O r— ro U

- z5-

REFE

RENC

E FOR GRA

PHIC

AL

MEAS

UREM

ENTS

: L.

A.T. = 12.75

CASE NO.

u

<o o

- >

to <o CU

E

to (0 CU E -e-

to <o CU

E CQ

3

•^

0.0714

23.8

31.8

39.7

0.1

0.5

-

0.0799

7.9

37.0

27.8

0.1

1.0

C\J

0.0854

-1

-

95.8

0.1

1.5

ro

REFERENCES

(Bristol Instruments/Systems) Bristol Instruments/Systems Manual, Bristol Division of Acco, American Chain and Cable Company, Inc., Waterbury Connecticut.

(CSPP III) "Crosbyton Solar Power Project Phase I, Interim Technical Report", Volume III: Appendices I-M, Texas Tech University, Lubbock, Texas, February 1977, ERDA Contract No. E(29-2)-3737.

(CSPP VII) "Crosbyton Solar Power Project", Volume VII: Performance and Cost of Solar Gridiron, Texas Tech University, Lubbock, Texas, February, 1981, USDOE Contract No. DE-AC04-76ET20255.

(BB) Brock, Billy C , "Optical Analysis of Spherical Segment Solar Collector", Ph.D. dissertation, Texas Tech University, Lubbock, Texas, May 1977.

(SC) Chao, Shih-Cheng, "Computer Based Data Processing System for the Crosbyton Solar Power Project", M.S. Thesis, Texas Tech University, Lubbock, Texas, December 1981.

(HL) Leung, HipSum, "Optical Power Concentration on Aligned and Mis­aligned Receivers in Solar Gridiron Power Systems, M.S. Thesis Texas Tech University, Lubbock, Texas, August 1978.

(KW) Watson, Karan Lea, "Performance Analysis of a Solar Gridiron De­sign Verification System", M.S. Thesis, Texas Tech University, Lubbock, Texas, May 1981.

(SAS Language) Barr, Anthony J., Goodnight, James, H., Sail, John P., and Helwig, Jame T., "A User's Guide to SAS 76", SAS Institute, Inc., Raleigh, i orth Carolina.

86

APPENDIX A

PROGRAM AND OUTPUT OF THE M CURVE FIT

87

88

:l OO

J

< •z

J

•i^ JA ir^ nvA • • • o n - j v O T )

to o on Qu

CO

to UJ _J a. < CO

n ( •> ••

'.n r^ .-4

-3 4-

"3 •^ -0 •>

,•>-> • -«vl

• «k

"Z >^ u-

a

—4 . ) •>

* o • »

- •< t o^c:^--JOOQUJCD — rt. O

O ^ '^ _

O X o n ^-00 - o u j > < " D 3

co^-n-cr: V N . \ < Z < ' v ^ K ' s n - ^ ' j

fvjo-*'Nr*-

^ > t n o - o ? » - « o ' n o ^o>l«'^JiNrj

C^OT) cor*

O O " > o o > . > > a » >

> i - r - ^ - t - N • • • • •

•

• • •

•

• •

• • •

•

•

• • •

•

• •

• • •

•

•^->r J j m . f

•—«fM vjrvi :3'r> ••^j r\x>\^\'-*^^ • - i - 1 -f ^f f r

• 0 ' 3 0 J:5 0

• " i fM"! N/' l J • ?* J* 'C'* J* (T "^

. • • ' " 0 - n o ^ 3 o^-• • • • • • • ^

. *

—4

J "> •J II ^-

. - T • >0 "n 0 o r - •«-.>-« -r ^

r^4i - . i r - i —<-^ —«a.

o<

•5 J

L J I U Q O Q a'.t: J N . a a r > s

89

fl s

•a

• f > » • J

yj -4

< —

C C

— »

r •

• . • • • • • • • J 3 3-3 3 3 0 3 3

CL

O

UJ 3

00

< f

I •

oe o

oe

^ >

o a o • a

o *-

U > a N 3 C 0 3 N 3

< 3> -S -N 3 —-*'>4 3 > "3 >4 0.0 »*>

</\ <o 3 JO 0 » » o —

Ol C 0 ^ C 0 * 3 O f i - i ^

^ l . a t . l . . .

o 00 cn

t n

a: o

UJ

CJ

U-

o CO

-a: 00

z Ui

^ 1/1

>-t / )

O l

ee 3

l/l o 111

M 0 a

1/ er a.

> * / i _ j _ i

UJ < 0

0 z r

< u; Z

<

ee M tU

Z K lU

a «/t

. 4

K

«

U i 3

< > u.

U i ft

3 3

2 < UI X

i / i UI of < 3 1 V I

•0

t

•a

•a h .

^ fM

•t •0

0

• 4

• 0

0^

• 4

'O

« 0 > * •

«

f ^

» l/^

• 4

IT • *

. 0 0

« m* t n i —

0 »>.

•irf

. 4

0-P"

* "

u. o

-.-.-.-.-.-•-•-«-• i . >r».^•n^/^".<M—«

t.X - 4 * / < « 0 3 « 0 « J

j ; . t • • Ovu M . 4 O 0 O — O 3 O 0

3 0 0 0 a o a O " ' * 3 0 0 0 —"JOO «< 3 0 0 0 30flO *

0 0 0 0 3 O 0 O 3

Ui 7 ' « O N 3 » 3 £ 0 o > i o - r 0 0 0 0 3 ^

-» • • • : ' / I : J ^ ^ o J - 0 0 0 0 0 3 3 *

0 0 0 0 0 0 0 0 3 0 ft

o » n

^->_.ny>rf« 0 - - 3

. • . . . . • • • O — (M

r - 3 »•

«

o - I

i i> - *

af>u

O T

•<.

n.

'i- ^ '^ Z X a ^ Si

o o T

' 03 >'--"'-'!::;:1 — • • • I f t — - " ^ 0 ^ • . Off . r > « ' - 0 ' ' * - o J

- , * 3 — ' - " - 0 3 ^ T . . . . 0 • • • • •

^ I I * 7 '

^ <

UI .J

4

< >

Z u 3 O -* i

•i. S 3 5 S o «/» t UI

O J 3 3 r z

• > o r o — o - V i = • • • Ui *-> ^Zs>-^ » — - " -

i >>3 3 >>0

s r 3 3 ,^^£ r * ^ • T i l l :J ;^j! io3rzXl3 2 r>>32—**?

90

I

U O

3 :; r t

•r

< O lit

u o

< *

3 O r» ^ i/t e> I •

of O

^ 3 3 3 0 3 3 ^ 3 J 3 0 3 3

3 J 3 0 J 3

a. 3 3 3 0 3 0

-U O"* S - 4 * / > 3 < f - 4 > h . O r t -J • • . I f •

-i 0 - 4 . 4

«%

• O. •< > CO

O Ui u^ A O a rn

O ^-ae • O <M * . O t - «f

1^ rg

-^•O 3 * S ' " ^ N— r-"ot>

Ui 0-* B'»9-<'\ a. n O'ft^ to V • * . . t •

— oo.raj«-o

o 00

IT)

o

OC

CJ

OO

T

U i

» •

M

> •

</t

t i l

. 4

Wt

V

^ <

z

<

J

<

u

"* ^ v»

N «

^ < K

l A

U i

oe 3 o Ui

8 oe a.

Wl

^ U i Q O Z

ae < U I Z

- i

- i

< u

z UI Id

U I 3 .J

< > a.

UI ec < 3 T Wl

Z

< UJ

Z

l/t U i ac

< 3 T i/»

' \L

o

Z 3 vf

. 4

• N f>. «0 m r

^ f « «T O « 4

« ^ f»

• lA lA (M

»

-r» (Vi IM

« O . 4

* • * i n

^ lA . 4

e

<A

.» * ^ ^ IM

« . 4

• « r»

•r m •o

». ^ t

^ r • > •0

. 4

* « 4 . 4

a

. 4

. > ^ r» • * •

1 ^

OB

. m O r» »• IM

»•

O - 4 3 ' 0 0 - * ' n » Ui •»•II»M»•^- o ^ •

a e ^ * M-'iO'Mi/'P". 0 « (^^«M4<» 3 .4 OCX ''^•ooo-t-r-t of— Q i W O i M O - O O < i iv ^ r M O O O - n o

aui ^ x O O O O O

O-* —-4 — 0 0 0 3 3 0 0 0 0 0 3 0 O O O O O O

...... J 0 3 0 0 3

M > > M i / \ S > l A — . 4 ^ ^ _ ^ ^ ^ 3 ?•^-.O^^A •- O O O O O O O J . . . . . . _ O O O O O O O < » ' 0 r - » » ^ O O O O O O O > J> S 0 O •V.N A . » « . . . •

( ^ • ^ x ) ( ^ - 4 O O O O O O O u. ^ — ae

^ a.

Ul « 0 * « " i > r > ^ O i»>OV> — 0 > 3 0 Irt • • I M O ' S ^ . f • . H '0'Ma>'M*>l/\>4

s - - - « > a " < Oaf • • . . . • . .4 r-..-Ofn» xui •TOie\r'-^0''

«^/^ lMl /^»> — 1 .4 | ^ i - . ^ Ui ^ , f r . 4 ^ p . a e i i I I a —^y>- a'*> o x

n - 4 f ^ o o . . . . . . ^ * 0 " > 4 » 0 ^ O f f ) * ^ < 0

if« .4

U. <

a.

U. « O 'O

° 5? S o Q r

l i . * » ^ a 3 f . * ^ o *o

>» O « » O . 0 ' » l M

T • » « • / > • O O f M

*» . - ^ * * o * ^ ^ O i/» (^•oo^ln^r>^ Ui •oao." — B S . . . . . . .

^^000-^3 «r.4 I I I

<

oe

>

Z Ui UI ^ 3 u U 7 U ^ « Ui Ui or Ui 3 ^ a 3 O tf ae Ui o 3 or O Q </l X Ui U

3

o a •

<j z

> — Ui

nr - • — — •4 — 3 O V J 3 0 Z O

O - f c > 0 > — > I/l (.ioao^o

Ui a 3 o z - .u o > — Ui o a u ^ r ae • • •

X » - t - > 0 3 0 Z v J « Z > > 3 > — >

^ .40oao^o

91

CO

oe a, <

< o UJ 3

• > • \J

Ui

ae < 3 3 l/»

1 ae

•M O 3 r» • •*

9

i m 9

• O

z < u z

s z

> . 4

3 0

> > m

t IS •t

I k

A

ae a

j i

3 < > UL

• 4 ' ^ ^ 3 J 3 3 3 3 3 3 3 I • .

3 3 3

- f-r / • ao

i>Ma> 3 ^ - < 3 » 0 » •f

o CO cn

U. .4 > IM O Ui M

A O 3 -0 O li^

oe • Q ^ a. o >> N

lA IT

Z Ui

1/1 • n > ' « . •/I M O 3

N i / I —

Ui o o / > a -40 r >> • . • »- * t 3

O i i ^ «

— •M-4 <A.4.4

CO

a: o

UJ :> ZD

lit

> IA

Ui ee 3

lit O i UI

•4 I J o

IA ae a V

lA - I .J

Ui < o

o Z X < oe

<

u < oe

M Ui z

k. Ui

1/1

Ui ^

3 »

> m

o

Ui ^ in ae n *^ < o -o 3 "« ir 3 - O ^ s o

ft CO Z . 4 P-

< • • UI <# »

' j; 2

o o o A o o o

0 3 0 ae t . •

a o o o

3 '^iJ^O _i . . . < g e o ^ > ON.4

u. >

O ^-^•f»# 'ii • • ^ s ^

ae*» n-tOf^ 0< O-liMM* aex —-no«8 ae— • 0 . 4 O 4 4 Al>- ^ « M O O

UI • I • • Ooi > 0 0 0 ^ •4 I/l

N. o o o o — o o o o

o o o o A • t • • o o o o ae a

1/1 m « .4 Ui o o -4 ae .4 a ^ < 1^ •c T 3 — O » 3 * O * I/l B -f 1

r» * B Ik • • • O IM .d 41

m •" o X < o *• 3 * rfl » I/l m ^ IM

» — »•

I / l flOfx M M O

» —— . 4 ^ . 4 i »

UI P * ^ ^

a —.*./> > 0 " 4 t ^ . . .

« . ^ o * O C J lA .4

o

Ooe l U i

aeui o r u.«

* ^ • O r i

. • • • > 4 1 » 4 0 O Oi*»m

I I

h>

o o X

„ Ui - i o < . 4

ee < > w z U i 3 Z Ui

a Ui 3

U.

o

UI

o O '

B wt

n

^ U i O

o X

4 1

? # 4

Z

a OC U i

•o % m4

- i

< h .

o b .

O U i to.

o UI

ae ae O u

u. O

U i

o or 3 o I / l

. ^ - r f » 4

k a

3 O a • ^ • ^ ^

•i g O O *

' I i .1^1/141 b. d ^ > > 0 « •OfM-f-4 •• o r — o * . ^ .^1^*4 — • ' l O * ^ I/l . i a > . 0 ^ Ul -J n o 1*1

. . . . i M m o p <— T •O l

ae k- «-Ul a 3 w lu o u o a T -,- • < U J — " ae h>oo3 4 Z > > 0

a —ooa

92

IM • -o

> . 4 • ^ U i

U ^ X

z ^ — o o o O A ooo •o O o o ^ oe . . .

t 0" OL O O O O r» O n i X .

IM

Ui ^ r ^ ^ . 3 l A c O ' T .J • • . < ^-^^ > « « «

e - o - . U. IM

o </« Ui

3

U i - • ee o < in

O to I / l ^ I I

oe o

I / l e o « 1/1 •0(MC^

> 9 - - i < o — « V i « r

^ • a ' - . Ik — > e Ui ^ c m

o Ui a a . O i ~ — A o o in > • . .

o • * • - — * ce » o ^ -4<ro> a O ^ 1*1 r sofM

l i l S « > 4

O CO cn

in

o

UJ

ct: I D CJ

Lu

o LU

a. <c 00

I / l

ee 3

I/l o U l

— o o

• 8E >• ^ -J

Ul • O

o

ae

Ui

o < ee

_ U l

r

Ui -f 3 « ^ • > «

O

u. o

Ui « ^

oe »^ «M < « o 3 <^ ^ r» h» o I/l o -r

Z >0 "M

Ui

X

l»»

«A li> -O -< Ui — O* - • CC 9 ^ O-« O <9 <>

S IM m f -

IM IM < I/t 1^ 94 m

9 0> O I L . . . O e <r m

- . ao o X i n — ^ 3 iM ^ 0> V * ^ ^ ' M

h - — *

I k C — * 0 < J O

A C O O O O O

ae . . . a o o o

Ui OIM^-3 e-*"^ _ i . « . < ^ i » i » > ^»*«s

» o — I k 0>/M

I / l * » ! <

— ^ ' - « 5 | . N < ^ ^

a . - * - » n > e o ^ . 4 ^ . . .

C M I M

e r e - 4 l f>-4

I t r\i.C'^-' O . « « ) M r >

Ui i / v m ^ i 4 |

aeto r^^—« S Z O ' ^ m - 4

a e — W C ' O O U i ^ m * o o

t/l . . . . Oui ^ • o o O ^ . 4 I / l

• ^ i n • . . 4 ^ k- m o o o — » o c o

^ o o o A • • • .

o o o o ee a

• * • ( M « 4 A 4 ^ * O C . . . . xu i o — i n «

k . I f . 1 ^ — aeui I I

ox u.<

ee

1*1 -O I k

o o o

O o Z

Ui ^ i n ^ ^

< m.*;ro Z Oo^o — . — r g O J ^ •— < 0 ^ 0 > f M I / l O ^ - ^ f M Ui i n ^ i . « o . . . .

• T t f l O O I - • I I

> O

z U l

o z

o > O o

^ OC Ui O • _ _ u/ C ae oe ——'^ a. 3 o oe « 3 0 0 3 Ui u o a, o O > > 0 O I/l X Ui o x^ o o a

a o Ui > o o ec • U l > ' - * ^ • - 0 0 3 z > > o — o o a .

93 'M

(9

ee

< o <A Ui 3

• ^ vJ

U i t < 3 car i/» 1

ae

3 ^ ta n

9

9

> « <

o

z < • I i

i Z

> • 4

2 > > <n

• • r

O i

A

I i 3

< > I k

• . - 4 — ^ 3 J 3 J 3 -3 3 0 3 3 3 3

• • • • 3 0 3 0

O — J N N » N . O

• f i t

— * l 0 < M

' ——a

3 Ui (.1 A G O —

O i<l ae • o o

a o >. ^

vl ?l

1/1 N — •« fM «/> 3 ' » ^ B

0 » i 4 » . 9 k

> -n^o- c — -t -f otn

•om-n — Ul a > a > > M a "-•^ fiy. V • . • . k- NO"»M

O O - f f .

— O

O 00 cyt

LO

a: o

wi

Ct:

CJ

o UJ _ J O-

<c O l

>

M

M

«4

I / l

V

^

<

z

<

^

<

o h4

»-M

* 4

H

< • i .

I / l

U i ee 3 Q U i O

o

& I / l

U l O O X

ae < U i

z

w < ee ! i i

z U i

o

w o o

Ui 3

>

t L

U i oe < 3

Sf z < u i

X

I/l U i

ae •« 3

5f u. o

X 3 ! / l

U i

o

IM

a . 4 • 4 fM m f/|

M

IM i n

9^ •0 IM (*l

t

•0 i n

^ o i n

^ N

i n OD 3 O r » iw

O

n . m

IM S3 41 o a . 4 . 4

*

m 3 i n

IM

O

• <n a

•o IM

a » o ^• IM

'«! . 9>

1 ^

S i n <M . 4

IM O

m - 4

>4

. 4 ff>

^ ^ •* f n 9

• -1

o ^• ^ IM

. 4

•e o m . 4

Ui

a

I k

A

oe a

M 3

^ < > I k

v/1 I / l

.^ •u a.

> ^

I k

o

- 4 . M _ . 4

3 ——— 0 3 0 0 o o o o 0 3 0 0 • • • •

3 0 0 0

y i i ^ " " I M r C M / }

. . . . ( 7 ' O ' O ' n 7 n r M i M ^ • n * «

o —

>

0 3 * » » M • » ^ o « Q . 4 ^ ^ J ^ - ~ - « ' * > i n ' M n " - . t * —

— — n ^ • O — J ' * . . . I

" - > f O i M - / O S » ^^ . f f M — " ' O T ' ^

i n . 4

w4

1 . mm^w^

u. 3

oex oe— 'XI —

I/l oui

I / l

^ . • «. A

or a

J " n oae TM

^ a e u i

o x U i <

« — *

a

Ui

<

^ I / l U l

i M — i n . r i n ( M < « f » 0 ' ' >

" • — - i O -i n i n o 9 . f o i ^ O — O " f ^ - O O O

. • a . t r * 0 0 0 3

(

. 4 i _ ^ M M

o o o o o 3 0 0 0 3 0 0 0 0 3

* . • • . O O O O O

• O f f ' I M B ' ^ i M i n ^ r ^ i ' ^ .

• . • . . O O — I M S ^ ^ ^ ^ 4 'M

1 1

o n j r - o - O ^ D • 0 ^ - • « > r 4 " i o - 4 i n

4» •? n o ^ 3 0 M i » i a

— o » f — » - i O ' M . 4

. . . . . ^ 1 3 0 0 -» 1 1

. 4

ae

>

<

M

z kl

3 Z Ui

a U i

O

Ui

o ee 3 o I / l

-1 Ui

o o X

X

o X OC U i

o U i

— o i i

X X

o o

U i

o oe 3 o I / l

h» ^

3 O o > a o • • . • t ^ ^

0 0 3 0

o o a o

X . . i

^ Ui

T < ee < a

^ ^ 114

n. 3 O i i O > o a o ee • • i i - 4 . . ^ — — 0 0 3 0 r > > o > — o o a o

94

• -^ Z * i — • > — < ^ 3 0 • » i i 3 A 3 3

<J -^ t -e 3 J • » X • •

•* — > a, 30

•4

.J . 4 oe & < »

> < o >/• Ui 3 «• <0

o M

•# . 4

Ui ne

< 3 9 I / l 1

X

Ik

A

ee a

. 4 A O r»

« » • o

. 4

O

o o t

o

3 X

> U i

o o I/l

4| I

IM

(M

IM 41 0-

> •0 -r —

^ 3

< > vk

I / l >/l

> m^

Ui a

> »—

M » n i »

• • > I M > . f O S

^

.441

9 ^ ^ — 41 •t-^ rsii" d O ^

t • O 'O 4 - I * • •M — »

o CO

Ul

•-3

o

u_

UJ

CJ

LL.

o U J _ l ex. 0 0

> «A

<A

. 4

1/1

>. - 1

< z <

- 1

< o . M

• B

Ul oe 3 S Ui

8 ee a

I / l

^ Ui

o o z ae

« Ui

z . 4 - 1

^ oe Ul

z Ul

Ui 3 .J

< > Ik

Ui ee

< .» 3 1/1

Z 4 JJ

z

» •

. 4 IM <*l r» in

» in IM •0 m m 9-m

• » •i4 •0

Ml

h-4 1

o "> . 4 IM . 4 r .

• M

o . 4

I k

o

Ik

A

oe a

. . . 4

0 . 4 O O O O O O • « O O

I k

o U l ee— o < eeT ae— o i f .

i/> O U I k . I / l

' O I M ^ — 9 .9 . ^ 0 » M I M ^ B 9 i « i « r<lin«M 4 i « r o C ' ^ O

• . • 4 3 0 . 4

Ui 3 . 1

< > I k

<>» > r -

• • * I M V'-t » S ^ - 4

»

— ^ . . A

« a.

• ^ . . . a 0 0 0 0 0 0 0 0 0

• • • 0 0 0

M

^ g> IM — 1/1 •O'^ O 4 i i n r t Hi — 0> — IA r-.t " « * ! • * » X ifS -fl 9- = 0 O * • • • < IM 0 . 9 . . . . ^ r . x u i m ^ i M 3 r- O r» •^'^ - ' ^ f C» O «!• •* Ul ^ * » X<1J I iS • » >r 1*1 a —' o x

r . o 9 ^ ^ o i k < I k l ' l » » • • of O <f ^ I " " f l • - ?

IM f«. O ' ^ ^

S IM -» f» " ' ^ _ in r » ^ » I/l p- m IM OS'S

Pi ^ » i n . 4

a 4' o u. 0 0 o m Ml

o 3 r

Ui

*. < X .. u WI Ui

r-ino •^<^'>i i n ^ B ^iMin inc" o o « ^ C M O r — . • • <»«—0

o>— 1

111 - I 03 < ee

>

z Ul o

'<

a Ui

lU O Ui o -< X Ui o

Ui or Ul o * * a 3 o ee ee 3 Ul 3 O oe o o O «/i Z Ui o •«

o > o •

i 4 . .

0 0

>>

ee to — Ul a o » . Ui > Ui o o T ee • < Ui — ae ^<JU < T>> a —00

95

« I M

. 4

V

»• ^ » .

U

*• ee & < • >•

< o I / l U l 3 • .

M l

o • •

• • . 4

. > . u

U i

oe 4 3 o I / l 1

oe

I k

A

ee a

w Ml 4 1 IM

a

«

m m . 4 • ^

r*

* a O

^ O O O

• o

z < U i X

• -

o o z

> U i

o a to I/l

0>

.. o •c 9 9-f . 4 1

IM •t IM

I t Ml

<« .. IM 41

I k

A

oe 0 .

U i 3 .J

< > I k

U l IA

> ^ U l

a > to

. 1 .

o o o . o

o Ml

. •4 fM r . O Ml

•C

OB

* m f . « 4

o

. pte

* 8

59

o CO

cn IT)

•-3

oe: o

UJ

Z3 CJ

OO

> I / l

WI

** Wl

> ,J

< ^ <

. 1

< o

to

Wl

.. to

•* to

I / l

U l

ae E U l

O

o QC 4k

I / l - 1 U i o o y

ee U i Z . 1 .

. 1

^ 4 oe Ul z Ul IS

to O o z

U i 3 . J

< > I k

U l

ae 3

a IA z « U i

z

Wl U l oe

« § Wl

I k O

X 3 Wl

I k O

O Ml

a * r g p . O M l

« r. 03

| 4 |

o

. >.. * 9 Ml

Ml .14

<e r>»

« •r (« i i » • ^

s

. -•* a

Ml

11

58

^

»M

» I t

"1 9 o

a St «M •M

m m O Ml • • ^ . 4

o •

« Ml

^ m

m

o Ml . 4

^ . 4

W 0>

!>. •t m eo

. I t O ^ •

S"

1 19

2

•o O Ml . 4

U i

o

t k

A

ee a

U i 3

^ < > t k

w» Wl

.. U i

a > >-

n. o

. M

o o o

a

O

« Ml a

•*•

(M 1^ O Ml

<o »«. 03 >f 4 1 p .

.. m

. p -

•* 9-Ml

Ml

^

I k

o Ui OCto

o < aez ae — Uito

Wl O U i to I / l

^ ^ A

oe ai

O •• n Ooe Z u i

h .

OCUi

o x U i <

oe to<

a i

MA

TE

to I/l Ui

0>». IMO» ft^» l w « a>«r « < M i n t M I O

. . I M O

1 •

O O O O O O

O O

IMiM I t I M

• . r . « i —tM I t I M

1

<flM <O0^ axM

—w 9-0

. . #

— » «

CO

ee <

O Ui Z O - I

3

a o C3

O Ui Ul O OC oe — oe 3 o u O > O Wl o

ee to Hi a to Ui I i i o r oe

« z >

96

X a.

o lA U i

I M

a

> a i J

i i oe < 3 3 I / l 1

ee

a i M

4 1

» • rt

N in Ml 9 a >

i O

z < i i X

HU

Uf

9

^ o « > 4 1

t

IM

I M

I k

N

X a

i i

3 .J < ^ Ik

• ^ i r f ^ 3 0 3 3 J O 3 3 3 • a a

3 3 0

n. « i3 3 3 -• a a

^ t a ^

^rto»

o CO cn

uo

o

U-

Wl J^-B^t I/l i ^ i—O

> om— — n-n a

I k — > ^ u i A I M O O U i O fti - i ^ r .

A O Q P . ^ . a a O « — t U f f .

ee • o fM O'Oo fti O ^ "M « l " g a »

w l 41 .^ ^ ^ Ml — —

CJ

IA

IA U i oe 3

Wl o Ui

M O o Wl ae a

wl . 1 - I

U l < 3

O z z < ae

.J — .1

< .1

o < ee

. 4 Ui

z

Ui «4

3 r» . i a < (M > «

(M Ui m

Ul . r « ae p- — < l b r . 3 «r »• 3 S .» I / l — ^

41 iD z « a < • • ii «f o T -t 9

O • 4

"1

I k

o

u. o

U i X t o

o< — ' — aex

9C — U i —

Wl O U i

^

— IM.41M> ^ — I t e l M

^« —« •nsr-Mi » * ^ i * » M l l t ^ O >0<oO aiMoo

. a a a 0 4 0 0 Ml

Ui o — — 0 3 ' - 3

A O O O OO'J

X • • a a ooo

Ui > ^ 0 3 i > 0 — - I t a . < ^ 4 1 ^ > * » >

O O — U. » > M

to O O O O — oooo

oooo A . a a a

3 0 0 0 ae a

o omm^ n II Ml—no Otf . . a a lUi >r^ 'N'*

<: OO

Wl "1 Ol IM ae It

I / l O ' « — k/i

n ^ M 3 m N 3 m » ^ I/l » t t

* t o Ik • . . o * »• t

( t iO o X — Ml ^ 3 41 « » Wl » 41 ^ . — »

O'" r aeoi "--ro o x X 3 r Ui <

srr-— ae - t t 3 to<

'ii — • t ^ a a —i^o ^ . . .

r > » — Ui

a 3— — M l — <

I/l U l

I I

u. o

« 4 1

8 u. — — o

99'9-r t > , f Ml o.nMi» "» O O M a»<t.r O . . • ' C f t m • O r f i t o i / ^ > 0 0 . . . .

>f<n—3 •3P» T « M l M

3 O X

. 1

U i

. J

< . 4

> to O Z Ui U l to 3 Ul o 7 o - i ae Ul i i or Ui 3 IT

• J > O

J O >>

111 O O o • • X - • — -

o > •

ae to —.4 ui a O O to U i > > Ui O IJU T X » • < UJ — — — a 3 o oe ae 3 UIJIJ X h-u\ju

Ui O 5 oe O O > > > O Wl X Ul U Wl KJ\J\J < z > > > a —ooo

APPENDIX B

TMR EQUATIONS

from

INFORMAL DESCRIPTION OF THE PERFORMANCE

OF A SOLAR GRIDIRON COLLECTOR/BOILER

M = mass flow rate of fluid (Ibs/hr)

111 = direct normal isolation (KW/m )

^ = solar inclination angle (degrees)

V^ = wind speed (MPH)

ct.. = theoretical attendance, dimensionless

= 0.686 as calculated theoretically for the ADVS

a E measured attendance, varies from day to day

a E specific attendance E (100)(a^ / a^^)

All P values = power (KBtu/hr)

A.,p = nominal gross aperture area (ft ) [For the ADVS, 'NG

^NG " "" (y-^^)^ = 33-S-3^ ^ ^

C = (0.31708) (-^^/^) ft hr / m

, 6L \ r A Ct /701 -7o\/KBtu / KWi

A = scale factor = ( ^ a ^ ^ ^NG " I W ^ '' ^^^"hT*/ T ^

[The values of 6L range from the low eighties to 99.6%.]

Power to the wall of the reciever, P^:

Po = ^ * ^DN • '''

P = P ^W 0

1 -(0.045) ( Q & / 7 5 ° )

1 + (0.972) ( C 3 / 7 5 ° ) ^ _

97

(1)

(2)

(3)

93

M ~ L'^fifri—^ » "" dimensionless [The 300 shown has units of

Ibs/hr per KW/m ].

Power lost by convection, P , :

1.75 P^L = PQ (0-0268)[1 + 6e'''-^^°^Y] [1 + (0.366)C(^) )]

V • [(0.267) + ( 0 . 7 3 3 ) ( ^ ) ]

(4)

(5)

Power lost by radiation, P RL

Z E

U =

= (2.4629) (4)^-^^^ + (2.1206) (4c)^^ 7? 75 ^

(1.374) + (0.1321) ( ) - (l.lOl) (f^y

(6)

(7)

^R^ (lMl.858)e-(Y/U) [(^)2.189. (,_ 066) (^)^° .

75<

RLl

- Z (Y - (0.1762))]

2 E PQ (0.01745) [1 + (22.831) g"'^'^^^^'^ ]

• [1 + (0.739) cos (2v9)][1.123 - (0.123)(^)] V

(8)

(9)

PRL ^R PRLI (10)

Power in the fluid, Ppi

P = P - P - P ^F W CL RL (11)

mWm

APPENDIX C

STEAM TABLE CURVE FITS

99

r » . - • — - ^ 100

1 -o ; 1

1 ;

• — ' S

. «^ ' . 4

. ' M (M 1

s ; : O '

« < , z ' • - > •

< . a

X 3 to

< Wl

I t

.r «. •>. —

• i

' z . U l

1

>' a • O

1

•

I

i I U i

1 rr < 3 . 7 Wl 1

ee

» • 1 I k 1

A

oe k a .

•

.

I t (M (M

r» • 4 4

'

n 9' 9

» a O

• o o o a O

( .

J Z :

<<. U i ' Z '

^> '

> U l

a o to Wt

-r f " i >

o ^ 4

• /

f "

> a O o

f^

IM O >r o 9 . 4 . t

a

mm

i L

S

X X

U 3 J

< > k

Wl v l

>

u a ^ ^

^ - O O 3 3

O Q a a

3 i 3

-3 — rt'M a a

n o — c ^ 91 0

•<i

0 — • * —

••• . i * \ i

r — j - o • i O

• « -r — i f r -33i-» — O « i - J — i A

«i4 * 4

nt Ui

3 / lit a

Ul M O

o VI ae

a Wl

.J . 1 ' Ul

< a o •

z z

Ul z

J — J

J u <

ne

Ui O 3 M .1 • < o > ft

. 4 IL <4

M

Ul ^ I t ae Ml ( t 4 11 'O 3 o r» r» I t in Wl o t

» o

I k

a

I k

A

X a

• . 4 . 4

3 C 0 3 O O

a . O O

I k

o i l

ae— 3 « XX ae— U i t o

Wl 3 u i

^ Wl

i t i M r -> O i n to^tt ^ O * . 4 411%! O - t f . •noo o o o

. a .

o o o . 4

z <

M iM a IM

O IM

M

a Ml

'« » — 2 — ' i J • • < -r a > o >

i n o Ik —

.n

to c o o — C * ' 3 0

O O O A a a .

O O O X

z Ul

Wl 03 IM O Ui O .4 M ae — f » < in Ml a 3 1^ - f - • Ct o a> > wt • as I t —

Ml IM s tk . . a • o -f - B

o in — z — »* ^ 3 M »• — I/l Ml m —

i/i " •— wt o —

— O ' M r-t

'U !^ — a »?> ^ r o . 4 * *

4 \ . 4

f i . i41

MIO

— m

O « i O ^ •" II r^iMi^ o.< • • • XUi O B ^

to .riMM ne'U — IM ox t Ui 4

X to<

a

U. IM Ol O Ik — a o p . 3

-.J iM

• U - « — O to n"!!*"

r ——"M — O f i i " to ^ - - tao wl a o u i Ul O O O

. . . — o — a n

I

B

X

>

J

k .

z i i

o z u a i l o

U i LJ af

3 w l

J U i

HO

O

ae O

X U l

3

CT

c

U l

- ae

o

u 1. >

a 3 3 wt a Z

ae u

to 11

< oe * a

to

i i o r '11

z - l i X

101

B 9

* : ! • * ! : oooo J ,\ Zi ti Z ' 300 30 i j <t « 0 3 0 3 0 0

. J _ " t * a a a a a

o

X

o T

•< O se 3 to

<

•r

Ul Ml ae «» < a 3 ^ or » Wl o I a

ae o

Ik o > « o Ul *

A O O O O O

ae • a » Oi O to ^

Wl a

3 > . ' ^ t»»M'a •J • a a a a < * * f * i t i ^

> ^'t—on -n .4 ' t t

Ik n r^f

wt O ^ f t ^ / ^ J 0 Wl •" — O (/I . .

» . ! « > - I M > •>•^•0^.•JV1 — » ^ ^ • i ( M n

n > OiM — i l ^ O — M « < X a - M S - r i M V a a a a a to o f » o - i n

O 0 » - o r -M - i « f . -41 a - t # — t

(M

1 3.

.* Vt

t

' Wt

' Wt

' V

. J

• <

z <

J

<

u mm

to

Wt

» 4

• "

<

w Wl

Ul oe 3 a Ul o o ae a i

1 ^ mJ U l

s z ee < U l

z w« J

- i < ae Ul z Ul 13

*

.

UJ

mj < >

Ik

U i

ae < 3 3 wt

Z < M

r

wt U i X < 3 a I / l

Vk O

z 3 wt

« O"

a

9 9' ^

O f"

i t . 4 . 4

. (M ^• ff> . 4

I t

9> ^ 03 Ml

a 0

Ml Ml

. 41 0 s » o

o »> 0 o Ml Ml

a

^•

(M ^ 9 <M t

(M

o IM

• in Ml

o " i

o N a 00 . 4

» . 4

•o .

'O m* (?

.« ^

u. 3

I k

A

X a i

U l 3 J

< > ' k

' / I wt

«— U l X > ^

. 4 W . . 4 . 4 . 4

— o — — — O O O O O o o o o o O O O O O

a a . . a O O O O O

l » » M l f M » * ^ I M if O . . . . .

5 > O i * r » ^ -'9 3 ^ i n i M < r — 9 ' i t O0> IM .f — o

f» — — M » * — f l B ' . r — ^t^. 'MPJIM OfM 0 —Ml . f t O I^Ml c ^ — > v i _ . rS^I**9^ ^ f O f ^ ^ i M a . a a «

( t . . . 4 . 4 M l » r » < t » r " ^|*^^t^r* ^ O l t < t M ^ IM I t —m

I k O

J i aeto o < XX ae — Uito

Wt Q u i

wt

. . ^ . . A

a i

3 • . N O-X Z U I

h .

arui O T I k ' *

X to.<

a

M > . 4 ( t i . 4 9 > O ^ O M l —0> O i t M l M f M ^

*«f ao—o I M . 4 . . Q O Q —anooo — O i t O O O ^ O O O O O

1 0 0 0 0 0 IM

— — — — . 4 O O O O O O 3 3 O O 0 O O O O O O O

a a a a . . O O O O O O

» 9 0OM(MO' »'««^•(a9

• a a a a a <l<rM10<OMl iMr« — i f o 1 1 1

u.

a Ml O N

Ik o

' i l . 4 ^ 1 ^ 4 1 ^ . 4 to — o — o — o < r » m . t t — ^ X O ^ t i u i ^ ' J . 4 . ^ . . f ^ >f J 1 . 1 to J ' T J O ^ - O O wl OOOOOO 'U t ^ , M . . 3 o

. a . 4 1 . .

n e o — 3 ' j

I IM I

1)

. 4 X « >

J

n T U

a i l

f )

XI ' , 1

ar 3 3 wt

_l Ul

o o r

r o iV

or Ui

1.1 U l 1<

X

-> o

u •J

r 3 a I / l

1 r r • • • 1 ra ra

u r < f • <

a

o nf u - a rr ^ • • • —a za ra

102

a

^ V 1 ^ • 4

» • t

••I

r u < < z » ^ < 3 X 3 to 4

W l

M Ml •a a . 4

X

i l

a

> t

• J

u t X 3 * . ' 1 ae

i k

A

i r

I i

t\ t

^ i «

• ^

'> 0

> r > 9

a

3

. 4

^ o 3

a

*.%

• •

( U

r ..

» i i

3

3

I / l

•r 1 ^

» a ^ r • ^ a 5 9 o

.<. t

0 . 4

» n

• t a

X

A

X a

U 3 J t

'> k

• y i

y

•>

I I !1 a .

^

-« 4 1 •» 3 t

• J 3 / I 3 1 3

9 9 •

» t'-i

— J * .

— r' * • t t ^ - t r - i

• i

' 1 n

.» 1 — "" wrs . . ^ V •1 / I fl

IM - B

or- — i l > C ^ — 1 . .

. a a 4 1 ^ . . . — < N l t n i » - t i

4

m*

> I / l

W t

ta4

W t

> . J

« Z

•<

J

< o to

^ l / »

. a .

« to

• / I

U i

• 3

a U l o a 0/

a • > i

J ' U •3 a — oe ' i i

z .. J

J

ne U l

u

' i l

3 J

<< • >

I k

l U y

« 3 r

c

< : i

^

1/1 U l

X

< 3 11

w t

k - 1

r 3 ' / I

u. ' 1

U l

I t a

. 4

o o ^ . 4

c i t

mm • ^

/ I

.. a

/ " I • t

• t

f

X t

;* • r <1

4 .

n ••1 n

I t a

o '/• ;. - 1

f l

0 mm

mm

1

n r (1

^ ,-#1

t

5 a

- T 1*1

t i

t l

( t

.f

^ ^ 0 0 r . H I

A t

l /» T n

^ 0

*".• "•I 1

IO

. f

*. -• .

* ^ % . 4

- 4

'. / 1

I k

3

•L

A

t

\

•il 1 J

< > ' i k

W l

W l

^ u

^ ^ •»

L 3

-m^^

— — I t J O t O O ' -•.>oo

a a a

3 3 3 i - -

"

M i l " * -1411*

. . . J - 1 t

t i ' ^ i •1 11

^^. . • ^ ^ i . *

" f " . 1

0 » l 0 r - t -» / ^ ^

^ - * • ^ "

>r 3 - * . . . ^ ^mm

« i ^ 4« f**". r> e. r •1 • !

• 4

. . - . i ^

I k

o 'U i T t o

3 4 XT rf— j y t o

Wl 3 u i

• / I

^ k .

mm

A

1 .

J

•. n O T f TU

.. •Y U J T •x«

V

to<

1 .

u

.. • 1 '

Ml O O O ^ f - ' M M l ( ^ O ' O ' t 9 l « « . 4 » i t i " l O

notoc M l - i l O C

'nooo a a a a

" l O O O . 4

^ . . . 4 - t

O O O t ooo.n O O 3 0

a . . a 0 0 3 U

f h - t f • • n i t ^ a a . a

^ i 3 a > . 4 i-i - 1 1 — 1 1

3 M ' « i n — O - T J C l l ' t 1

"*• T' l-f r-f^ a "

. . • t i . l . ^

. . . i j O ' . i

<1

I

u W l o Mt i t a

1 n

.1 , 1

r .1

• * to

•e

^ —axAi

103

'«

i ^

<o (^ •M t

* a r i

X u ae < X

• V < o oe 3 to • <

Wl

in i f

• • f-. 4

a >

a 1 O

,

Ul ^ < 3

wt 1

X

I

tk

A

ae a.

r* 0 ><* mm

a 3

. 4

f ^

* a O

o o o o a O

-» • <

4

X

^

> U i

a a IA

t *. • *

a mm r Pm >

a

a a 1 0

• 0 0 •r r^ •t

o

k — — - - 4 — _ . I ^ 3 0 3 0 3 0 3 0

A O J J 0 3 i n o ' 3 0 3 0 3 3 3 0

X a a a a a a a a a 0 3 0 3 0 J 3 < 3

3 0 ^ I 3 I M * » a o — J . a a . a a a a < i M O , r — O O t i t > a — — f » 3 0 O

I k

wt ^ — - k i y f l l M •A O 0 ^ — O O

O — 0 - . o o > > « n > a . r 3 j . . p . i n ^ . . . . i ^

U l O I M > f M — O a 3 ^ - i » " " n i y V a . a . • • to , / ^ TJiO t < 0

r » ^ t a j f - ' n n — ^ —

— 0 D 0 — ;il 3 - *

a * a o 3 r -

« a

3 ( 8 — Ml

o

t/t

v t

Ui 3

3 o U i o a ae a

3 o X

U i

z

> • V

I k »

Ul I Ml ^4 ae M M < o o 3 f" 0 3 o >r Wl Ml >

iO — z o o * • • Ui -r IM r o

I t

3 < « X X — U i ^

wt 3 u i

« * 0 ^ — 3 t^^9B9 n i t o o - " a . / IM Q^*^*^mfmm . ^ J D O C M O ^ i t i ^ o i o o noooo BO>r ooo . a . . a a .fOOOOO

0..t •?oo o o o O O O O O O O O O c o o O O O

... OOO

o ft.

to

Wt

a .

^ < h .

< ae U l

z U l

Wl U l X

< 3 o wt

. 4

^ 9> ? O O o (M Ml

.. IM ae f~ Ml » l

0> IM

o l"l

n on -. O mm

ffl

X —o—' — — -"- — O O O O O O — o

A OOOO'JO'nO O O O O O O O O

ae a . . B . . * a a . O O O O O O O O

Ui » ^ . f « 1 0 4 « ' M f " 3 C^ n < i 7 « 0 a — J . * . . . . « . < l » J » ^ « l t ^ 4 \ ^

> - M * — > — O O O " ' a ) » - * ^

k 0 9 CDl^i T O —

i . . a . . . 4 . 4 . . ^ . . ' r ? ' 4 — i O O O J C 3 0 J O — I / 1 3 0 0 0 ? C C 3

0 0 0 0 0 3 0 0 0 A a a . a . . . . *

ooooooooc X

a

Wl

Ul

a , ' o o' f t » —

r IM o • 3 - -W l — —

* . — — i M a ^ o o » — • s . f — o o t P » v J I M I M M I t m Q(M a..'nin>n>f f i t - O P " f\ a ^^ y _•—<•>—in Mif a^r^o—inoo r o ' • • o ' M M O ^ • . . . . . . . .

t—*.i...-noooa y ^ ^ . ^ ^ ^ . o < . 4 ' n '•tac*""^ o n o It t — •vj- i M t

—^

3 •> I I o a e Z U i

<KIU OX It.*

ee to<

a

, f i n . f n . f — o o o i f t I t a ^ u i r - T —

. . . a . . . . . — , f t « . / ^ • — 3 " t I J I I

I s; ?t

U i

I k 3

IM •o CM

o

O ^ o M i r — *-n t "• O i> -r o

< —-M,f I f n I y ^'.-f* u /* •!• " mm o>'ii/> fii." r ." to f T I C ^ ' H — * " Wl — -C Ml ^ ' ^ o o Ul 1 C " - ^ 3 T 1

. . . ^ • • •T •J — — ' ' 1 - ' l

- 1 I - t I O

O 1 I I

I n I

O 1

"J I

J T

< ar 4

>

r ViJ

T 7" u a 11

o

u o •K

3 3 wt

J U i 3 O X

i V

O a' * •

U l

J

.« ^ 3

J i j

to

o -1

I '

-* -1 o

• I I

o •e 3 a wt

C I r • • •

1. rx c-vT a za zazan

Ul

r o 0 /

• • •

a —a ra r-v za 1

APPENDIX D ^

COMPUTER CODE FOR SIMULATION

104

105

J O . J ^ O J - )

J O O O

J O O O O O O O O J

->^

>o

O J O O O O O O

-)o .->o O O

' ^ • ^

- J O J O

' J O O O O O « J O • O O

J O O O J O J O J f J ! ) t J O vJ O O

J O O J J O J J

J O O J O J J O - J O ; . > 0

o

3

3J: o

< iV

o

J J O J J O

J O J J O O J J uu J O

O O O O O J O O O O O O O i J o o r j O J •• O ' J V l O J^ ' )

uu t O O - i O ' J O J O •

uw 0 ' 0 - 4 O ' J Z O J X UUJC J J -•

O J - > O J • o o x i o o -O ' - ) •• J J — • J O .'v O J -UU-Ti O J '" J O -

uu -i j o ' n I J J ^ -j u - t

O J O J J 4 -J J ^

( J J O J J - 4

J O ^^lO i i - J

J j - ^ - o J J > f ! )

O ) -»•— JOTTT: J J - t O

J O - ) U L J J — J O o J J •OUJ J O D V

• J O " ) - u O O J O \ X

J O . si

< —

J —

• •> •3 J —

U 4 0 J - J t : * - *

^ < •t J

LU

'JJ

o

D

J

•a:

o J

I — r •• O"*- O

O. X -< .TC '^i

O O O O O O O Vi>^

'JV-—. J > - 3 < Do I— J ^J _I .V -« D -

O J 3«JL —

^ J <.u • ^ X - J

D > - 0 « - • - » -

- o - « z

UJ J - - s : -u "2

' ^ O T ' ^ ' ^ l t — -jf "XTT •——i:^ 'i-C) u — -— -."r— • 1 . — O T ^ v t ' J O •• ? t - T

- D > - J - j e : i C X ' i . • I I J3'^i>— • • ' • i_ O—« ^ "J

')u.-* -Z'Z. t — r - l . ' — ^ t -X D - " ^ - • • —

- ) J 5 : — • - i T x — " c r i r - o - i - f — j < — r . « h - ~

> ^T 5 " — D CD * U ^ - r j — TD to.4 T T ' r i - ' X 3«N/ <"» -

O n o • . • U - ' O T : " - ^ I— • . - ! < ' - 3 ^ i: _ . ^ — o —

: T U y* U ! « : - 3 — > J > — — to-' - ^ u o ^ ' ^ — < x u u < • / i :Z -t 'JJ'U J O D D * ^ T •>-—I — - r — < < i j ^ - j / — < _ ^ i :

u O U . 0 — ' Z U ' U J J i J C O f T ^ O • ' j j 3 0—to:* )^ JC ': '-»_ : 2 " ? ' x

a U- O ^

^uu o o

— -J

T. i -» _J

"J

>-

-^a

—i

Wi.

o 0 : 3

—• u

OJ

•XI ^

r I—JJ

r o J . ' Y :

o •5 a .

o<y> •J- > • —

< x t -

o

.T y l -T i—

3 c; b '" o ^ J uu • w ^

j j u i . u X J " * - i ^ , ' Z ' T Z — 0 0 "5 •

Il ' L U . ' J - ' — - ^ II II II —i J ' U J ' U l l * / i o ~

o o o o

106

•o -u -" r:

» _ :3 • <

- r - . . -^ i ^

* • -/ * - -J

- ) * » - «

-u .n i:

- * • 0 _ 3 - -^ AJ f - . _)

•> .X —• — "> A • ) < J ^ X D J: X • j j j

•xT .VJ — n j o •• N i •-• t

' U O • t J — O. -1 1 h— < J < • - • / ) J J • - • " . >

Z i. 2 -. Ttrs: •• :J T. JX-

CC ' i j i - X - * -« — 'J J -S ^ - • j j i ^ ^ • — • i > O n ^ t » - t •)!——»

>• < X * J D J - ^ - ^ 4 . •J < S IK- r\LL D - « ' J «•

' T O • • • T -' '<.J'> *— "^^ 0 - < ' - « 0 "D •

x r or*— ••'VJ g -1 ^rn Z2^ u . - » K r » u D ' - o i i l . O OvTtTJ- n < - t - i

• t o n » ^ v_ - > ' * j - •

z r' o^-<o. i j ••'J • > r •

o A*\ x3 iTv ^-^j-—«a« ro.-n o:> o Oi^j "^-^^'^•~* '•'-' •—*' • • — J *—• »—'*i <*• f^C O O C'nr-->'> ^ j^^jrvL/^o j(»->o '5r^(i>-n3 r - « J — O • -^o T'— t _»

-u "Or- ' -vj r ou^A' ^Jr to^ i3 n."n-<.-^.-D-^,.^^ ^ - ' ^ - * n — ' " ^ K "J>k—L JJ I / : * - • • j : r '_ i i ' - ) Zld-^ • ( > J O — o ^ r - • - J • - n r - • • • • • • « • • • • • O — O ' i ' "^/^ T"3 -) —'u"!) II —'Ol*** J • • • • • # 0 0 •'^1 • •—*0—<r>ioo ^j ' Jf^ ' -^O-^ II O "3 ••r' ••—I -1—1-4 If •>>, j-_« X IJ O 0 . 0 v 0 - « 0 ^ II II O . ^ J - « 0 II II II II II II II II II II H II O a < - r n c t r X ' X — I I - 4 - 3 T J J 'UTT II II II If II II II II .-4 .- 11 II II II Mrg-^—* jrOxf'NJU^'^Nf^ II 0 'JJ'UT\ D O U X " ) X O Q O ciu< t : o O ' u x ' j ) x ~ 3 v r o 5 : z v i - 3 x : D T ' D D D rz)->»'siNjz»-ia 2C»-x •-rt^-«-i4-.—i _>_)_;

m O O O O J J

107

V)

.V

ti.

p- J ) ^ Z yl ft 'i Z f.nu'X XJ "3 0 h- • z a,*}" —I T -4 — UJrO »-

- - I . O

^ XI -^ -f r<"i UJ -J •oo-f . rT XI

T^ > H • y ) . o < i n D — ^ ^ v i . c T O

(V—•»• u j r * • Oi—I—-^i ir '»-<-CO Z x - J ^ - Q . •• rD -f < o E : a i - » ^ _ i > i '

z •to.sTa.H-otx.-vj • * -J > — 0 U J 5 * " D J " I - I

C/11—'U O l — O J O L I I/) • X l - r j O - J • r -K>J" ' .O .N

j -n iuo Z n - u • ' " D u j < - f • CLQ.—«-'»—-^ O •<1 ST CO

J 2 • — J D O

J • u —< Ol— Ii II AJ

rH.-t Q J O

> > . J J O O O

o

I

.3

O

o

I - ^

z •XI J O I

>r O O

To O kJ

Q J J

Da: * - t ,— iJ »-zx o o ^ ji TTUJO - • > x i / ) 0

D '-I

^ - U J toi4

z>-o O T T O O O D

- 4 0 « / » ' D o o ^ C L O H -c/1 ^ - I II II ti ! i J X I « i < 0 ^ t j - H Q > x T XI f— v l < UJ

o

o 0

^^

.n

J

r 0

X 0

- • O • N. • •XJ OUJ 0<Ni •• i i a > i j y ) Z JJUiT*

I — • — T r - X • — r s i T • T r«-»Q i^j>j -3 v9 O V - i f • — — < a . " — H — ^ ^ " ^ ^ Ot-i

• • O - f ^ r a » rH • • • .-^..^UJ t ' U O U L J > r ' i J > — : | J - « I J J 7 » ' ^ I U J O > - t r ^ — l i ' > r - a J r - 3 i — ** > — X V J > > <'-*< II Z ' - t o - r :^ >f r- o "O O O J'-« J > - a . z J"v. j> ' : _ i - ' ^ a o < ^ j - n u u x i

O II D ") II t i .3 11 D II o—H-«r or "^ cjf—ocVf- II o ^ - o ^ - o II II r II -JO J 2: D Z - I o o a o z .D—z

X X < 0 0 < l in-H < Q < . 0 < "D^XQ p i - i » - » i j a . O h -

'Voo I.DV JifJJ

JJ—

i j j *

^< •3

J <

J -3 >

Q Z

o

xo o

0 3

iJ o > o

z .3

-X o

T

Z

O

1 .

x - » x - ^ i - ^ 0 0 ' . 3 0 <

II • > o O JJOXJ<'JJUO Z ' ) II J > O C L - < > X K I < I a • JO':^xi.'>:^— ^ ^ . - ' ' ^ U O J J . O

u o

o •^•1

—4 •0

o

o

UJ JJ O O 3 l U T H - J • • • : 3 H . < 0 ' - 7 - 7 n

• D J o • 0 * O

N — O - ^ n f - <

• J » O X I - » 0 • - ! • - • \ n — 1 .

XI • - • 0 0 > > > ( / l » ^ ^ T > O t o ^ • •cOVi t - J • - » < 0 ' ^ a . t / l • v I N O D O - * ^ O J O — — 0 < J " ^ - — •c'^oJO—« * O • ' U ^ f X I > * • _ ) « • u . ^ ^ ^ X i V l < ' i J - i O X - ) X " i — * Z J : ^ c r ) N x - n o > C • •> -_D»—iJ?«^OT I to^-i-«0 0

x"/Tj? I t - t - h - + •*• • ^ - < : i c v a f * — •—a.>o ' j 5ox i -3 ' i j < u-^—"^>-••«•> ^'y^ - " — - X O x x i - • t < < ( y o < Z c ^ II I C X I ' o O " ^ I > - " O J _ » > J a . o :t X i j u v i — O ' O r r

" - • — r D ' > • • ' t o ^ O ' / I O II > > " > O H O II "D>-i—"^i— II II II < r-Y.\JOZ Z Z * OQ. ^ l U O O J J O J-f U't-~"-^ II W ^ ' " Z < O a f Z - a — II o - i : — — O ^ J O O II II ' - " D O J - I II

^ j - ^ ^ , . j - 4 _ i « * _ . - *u . i_ i O t — < X X X X I I O I I < " > C L X t i . < < < 0 0 < t t o 4 N / < 3 O ' x ( 3 t o 4 h-h-oa.osTO'^c^'^toH o i / ) o »-(to.i>—iz u > o - - - - -• - • • - • 0 " > J Q . ( j a H ^ _ » t - > - 0 J -

o

o o o o o 0 0 0 o o

108

>

— a: zn o —H mm,

V - - 4

<a Z -n '.'*> -« -r -) o — • O D>f Z O I O ' to4(JJO m^rt ^ L 0 ' / 1 — . •.U "'^

J O ^

- ^ Z D . 3 t o H O

- i . i " ? J

'2 • XI o

T V - 1 - « - t . o

J r\ • v T D l -

- * o — O II

to4<-^

o j - >

J

J *> o .» '_J

J • >

r j K

(> o

u - ->

o • ,r 1 ^ j j

o i ^ >

O J X **

X I • - 0

l - l >

'X J

• j j r y "> -^ /^ r D O O •

• H

•u * r u 1 — J

'.5 0 Z^f ^ t '.n n D A

> ( U • ^ T \

-f r*-OC 1

^ ! ! ? - • O 0 O ' n X •

v f IJ - 0

1— NJ f I M

J II

o •

o II

X

• -3 O TT

—* O

• o •

1— o

• X l _

o -3

D X U J 5 : J t—U J : T >

^^

•<r O o x os:* to4

X a.

.5 Z »-• o z — X

>-33

H - O

D t r O ' L X 1

o 'XI o • - • x

< 1 oz D - « O X J I I < l i l .

o a .

'•

-^ 4 ^

to< r^

' J

o + •

—» —4

.^ .»— z \ Q — 1—1 to^

• !<• >-*

U o • »•

Z - O ^ 'O • - • O O (-0 — a. 3 ^ 3 1

O — - o • 'JJ ^ \ i n * ^ > _ \ U . ' ^ ^ - 4

< Z * - \ o ^ O - 3 "3 toH . - * - D

n—• zawi^ 'y. O II "^ I I -tf I I o z — • II z < 0 II • - • O ' ^ o ^ > j i . a .

o J

a < o

• ^ J

-^ «

^ ^

0

•^ - H

->

»?•

•"•

If-

• — « ' - 4

• J

> •

-^ —» *

-.» >. ^ X 1

to-

.n X oJ • t

' U 4.

• toH

— j j ^ >

» - \ J <: 'r o > 3 II

* 3

a. O O II J ^ < - ?

o t . j

0 > J L

• > j

^ * • ' » •

"-» -^ -0 3 1

> >•— .k i V j

1 • ^

• 'i

—\ » «<

— J

> J

•J

1

T

->

-^ J ..« M.

• • * *

• -f

< ^ j » - i » * . ^ * J —.«.*

H-

—» 3 •

•-•» \ o -. ).r»>co — 3 * - •

m—

.•^

o ^ "5 > »

(^iJ

x: 1

i \ j - 5

"^ • *** " • *

-Vi -< J

.^ 3 •o

• •

i f

. i . k

—. ^ >

V

* "T*

\

O L

X U

•.* ' — - « * | \

• — 1 — »

O ' v J f ^ J ' V . ' V cr' 'V. 1 xx» -»»

i - i l -•XI J — "

•— <

> -» .->i J

O " ^ — 3 o

••. *

I J J — .

•«—•—1

'~ •¥

•

•—• X

o > JL 3 - J

1— - u ' J • i j »

r o J • —• r u > •^ f z

• ' X -T :>•••

•

r \ D

j -

to4':; - 5 X > — " •

N . -

• J Z O Z*-" o ^t——l

3

^ t o

,..( - t »

u l ^ » "3

3 * - » J " ^ X

y -4 x a

_ _ 4 ' - l

i f J 1

o

Z • — • ' 1

T 1—i..^Ziv—

X * 3 "vir

* O O J ^ J J O J ' ' 1 \ -^ " 3 •

» a 1 -3 -^ <

••• M Q T : O

• •^ — < 4 - . ^ II

M : i i3 '^ II ' J

O ' v / 3 I I r v j O O O

< I I II ' X T ' ^

r\ 1

r r

• . H

^ l|

^ 1 X < Z X _ i - . ^

D ^ I I J II t -

O Z 3

<-— 4

^ 1 •^

— D

Tf a : « * X « * - ' 3 0 o 3PSI TC O 'X a o a. J T ^ T -

»_ ."3 J

X I

t _

o J

1

«• a 1

* — AJ

-« -n X —«

u • "> 'NJ < 1 3 — J 3

1J 'J v r .

- J X i t - —

r. ^ ozn X < 0 -1

— - M -

^ Z '^ < 'J J "^ U • f)

— • — - v - 1 O D *

i J U Q . - ^ r •"» J

H - O . " M C ) •3 D

5- X ' • ) o 0 1

r •»— X .-^ D -)

T-^ J •——r~ r - • - T - > x ^ . J - • —

J Z ' J - ) ' 1 < > 3

X • r JJ i"\-» — ^ r J' • I to***, r i

J 1 J - ) ' - '1 T . ) - « y » -J J X X • < n j ' i j 0 w - * - *•

uu uu O O O O O O 0 0 0 0 • J O O J

o

o J

J . 1

3 M

— 3

- • J J ^ - y ) - »

< o o 3 v i r \ IJ r > " > 3 j j ' H O >—'-)ot—H- • : i

i| II M II II H--4

3 3 J 0 3 - Z >U ^U Jfr- 3

— - . — - • ' - EO

•t

u Ji

4 m.

J

Ml . - ' J

^ o o

109

1 i.' —< kJ'— V —' 'T J t . j x ^ - ^ > " : r ixi X I X ^ O O ' — ! - - •

O ^ M O O O m trun

O O o

no

o o z •* 3 3 # #

AJ vl

3 O . J

o

-5 O O < J X • i - ' O ^ r v j * _ J ' ' 3 o 3 0 - 3 . 2 2f • - " - • - ^ < -CO O I j O-* to^-« T » — • ' ••X • • . . ^ •• OUJ z Z • • "^ • 3 J -i-^jr\ • •..-o •'>fN *<Nin - - f l i j j i • s. "3-1 o — —n ' - 3 •2 3 •»• I I j .oAco • " .^ I I •'>}-.jj vjsf • i \ j * n j - ) n -)(0

'-J - > ^ > JJ -UUJ 'OO'^r^ -«»J-UJXl iur |:uon J3,-!-:>-«rO-< O — • — • 'jji-1 'jjto4> J » n^'•'I>-J'.au^ •••0'-*-Njf^4fooa»j"oor-^uj-^'aj >-x " ^ x X " i "^ -^ ^ f ' - i ' - t -c^ ' •T^'-nmr^vom o DcsjOi-nuj > j i j j r o3o • J • 3 h - 3->_o XI :3 r*0 'no-4>ro»r^ ' - i -c .o^ j ' . -H-rNtoo-r \ ;>OH-_j-> j y r I—X h- o • : « • - » -Of-i'Ojo •-«»-^i-«>f JO'jo j5^<Nj.-nin j i 34*-or- 3 x 3 x < J - t O ^ •«/ '•^ Ovr.OrO OOO^ r «3" r —•vAin n o O T \ Xi(r>-r|3T X O I L ^»— 2i— • r, *-' m—i^ j - r* JO o fco>f nc^ o-H(Mto^ o<^»-tinin .oi»'11 * . i

'JLJ — • U • J 3 1- O D r JTO-H A 0 ^ .^ r o M - r ^ - ^ J • J3 . • . - O O 0 3 a x i i n a . x j • 3 jr-i*...—,.— • • • ••JI .NJ,-<NO • • •• J • • "co • - ^ ' - • O ' ^ J t j "D > TrZ^T.Ti "i X uct^^ ov> in -^r * I r I ^ I Al.-^rvjo • r g O i N I 4" I I >/ | - . | . * iii^-i 'Xji-i • -n 1 - ^ ^ . \ I \ \ I Vi • u > 'u->-' - H - Z ' - l - ' D ^ - * Z - ? - 5 - ^ ^ 3 - 5 ^ •X' i • J • J

—.'JJ .—win •. XH-x>-x i—H- X h- X - u ^ o -< J I—-uo t—XII—inx o x o x O J X o x ••••3 • •o — • Z i : « - « Z 3 ••rsj Z Z J J Z U J Z Z U Z tl 3 ' J X O J a . X — t u X - t J O — 3 3 3 3 3 3 3 "3 3 3 Z < i l . u ^ ' l x o z u j o i . —•— to^-),_j-3!j-3-) o -5 o -^—n —a.z

i u < H- "iii J r " o _)"^(V I — o o i — o o i — : s : o o _ j o o o < < < < — O X I ^ 3 U J 3 3 0 0 3 0 0 » - t C r r 3 Z < < < < < l — H- H- >- •>i— "> H-1-0 < < r 0 < < r t : 3 Z 3 • x x i u j u j u j < < < < x l l Z O i i Z ' U a . o o a . o c J 3 : x x X ' i : . 3 : v Q C a i : 3 3 3 Q - t x x j x x v

\j.-o (NJCi -invO fvjfo <Nm >J•^r^o^-c3c^ o o >0 a:

O O lA

Ill

—. • ^

* o X i<)

m

) 3 - . 4 . . ^

> J J - < 3 J — 3 D O •v —

^ O Z O ' ! > ' ' * • 3 - « 3 - 5 v - V — •vO — 3 II Z — r^ . - ^ " D ^ ' j - - ^ ""i-ar J IJ 4i h- 4 •• 1 - ) 0 3

r — O iJ •-) II a. z / T : J

0 3 II • •<n ' U X ^ II

" J : z x -< J < U ' "> J^

u •• - i ' D • O

— O II r» j - <

3 II "> JJ

••"SJ

< • - •

- i . * ) 'xx: J J

-• a X •• • r •i -^

"0 0 i n II - )o •^o • 3 'U

< :t: 3 J • .^

i: II t .o ^ o X 3 v/1 • • • J J- D II 1 O

r> 3

•» i . — < o • O i >——H

< 3 J • ^ f ^

-^ -^ •u •

z — - » J It i .

OL II ' ^ Z - 4 , • )

"3 3 •> »

fV.-* * ^ i — j j

Z ^ ^ • • H > » _ l

•-</>T^ 1 •11 •

Z J 3 J ^ ^ ' / I D II c/> -< -n D 4-a. -z • ' ^ ' / > — i 3 n 3 II ^ O i - D

.4

z - • 3 O O X

Z ' ^ T O Z 1 - V - 5 — J l — 3 ' - * 3 H H II II 3 !l II II 'JmO^Z-^ x 3 ' > - - 5 3 > - > - - 5 t o ^ a . c r - X H-

O l A fOrO

X •

D

o

-o — w O •• 11 3 V •»«' o jt: x i - J - D r O —^3 < 0 II O ' X J J Z

•no-* - 4 < U 0 K a . > • L ^ t / l

• • 3 3 D (J)

X N W W X * ^ W W W > s V . \