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a

• Solar Electric Generating System IIFinite Element Analysis

Jeffrey L. Dolmer and John R. AndersonSandia National Laboratories

Albuquerque, NM 87185

ABSTRACT

On June 2 1992, Landers' earthquake struck the Solar Electric Generating System IT,located in Daggett, California. The 30 megawatt power station, operated by the DaggettLeasing Corporation (DLC), suffered substantial damage due to structural failures in thesolar farm. These failures consisted of the separation of sliding joints supporting adistribution of parabolic glass mirrors. At separation, the mirrors fell to the ground andbroke. It was the desire of the DLC and the Solar Thermal Design Assistance Center(STDAC) of Sandia National Laboratories (SNL) to redesign these joints so that, in theevent of future quakes, costly breakage will be avoided.

To accomplish this task, drawings of collector components were developed by the STDAC,from which a detailed finite element computer model of a solar collector was produced.This nonlinear dynamic model, which consisted of over 8560 degrees of freedom,underwent model reduction to form a low order nonlinear dynamic model containing only40 degrees of freedom. This model was then used as a design tool to estimate jointdynamics. Using this design tool, joint configurations were modified, and an acceptablejoint redesign determined.

The results of this analysis showed that the implementation of metal stops welded tosupport shafts for the purpose of preventing joint separation is a suitable joint redesign.Moreover, it was found that, for quakes of Landers' magnitude, mirror breakage due toenhanced vibration in the trough assembly is unlikely.

O(.,K.,UM_4T I_._.

1. BACKGROUND

This section describes the Solar Electric Generating System II (SEGS II) facility, the

Landers' Earthquake, and the technical problem at hand.

It

1.1 The SEGS II Facility

The SEGS II facility consists of a farm of glass mirrored, single axis, parabolic trough

solar collectors (see Figure 1). These collectors use solar energy to heat oil; which is used

to produce steam; which, in turn, drives a turbine-generator to produce electricity.

A collector, shown in Figure 1, consists of a flexible truss structure supporting adistribution of mirrors. This flexible truss structure can b* defined in terms of a number of

substructures. In this report, the following terminology will be used to define these

substructures. The tubular substructure which runs the length of the collector will be called

the torque tube. The truss substructures between the mirrors and the torque tube will becalled mirror supports. The flat plates attached at each end of the torque tube will be called

end plates, and the tubular shafts projecting from these end plates will be called support

shafts. The support shafts fit into journals which are attached to another set of substructureswhich will be called the support trusses. The support trusses transfer the weight of theentire collector to a concrete foundation. Vibration at this foundation can be transmitted

through the support trusses, the journals, the support shafts, the end plates, the torque tube,

and mirror supports to produce vibration in the minors. The end plates, torque tube, mirror

supports, and mirrors will collectively comprise anGther substructure called the trough

assembly.

In SEGS II, collectors are attached end to end to form rows which rotate about a north-

south axis. The assembly of all collectors in all rows is referred to as the solar farm.

Parabolic I_Trough AssemblyV

Support S!

-* t ......

Torque tube

End Plate Mirror Supports

Support Truss Support Truss

FRONT VIEW Foundation

Motion of TrussStructure due to Parabolic Mirrors

Earth motion I __-x._With the Journal disconnected from

the Support Shaft, the trough I 'assembly is allowed to fall to the

ground. ___

Mirror Supports "_ d PlateRectangular Cross _ tl \

Section _ 1/ xJournal

_ _-- Support Truss_ _ Foundation

SIDE VIEW

The parabolic collectors areconnected in series to formrows in the solar farm.Only those collectors andthe end of a row failed during +the Landers' Earthquake.

ON-SITE PHOTO

Figure 1. Drawing and Photo of Solar Collector.

1.2 The Landers' Earthquake

On June 2 of 1992, the Landers' earthquake struck the SEGS II facility in Dagget,

California. The displacement of the quake was large enough such that some troughs• separated from their support trusses allowing oneend of the trough assembly to fall to the

ground and shattex,_dseveral mirrors of each fallen collector.

As shown in Figure 2,1 the epicenter of this quake was locate near Landers, California

- a small town approximated 50 miles south east of SEGS II. The magnitude of the quake

was M7.5 (on the Richter scale). Thus, making it the largest quake to strike southern

California in the last 40 years. 2 Approximately three and one half hours later, a second

quake of magnitude M6.5 also struck SEGS II. Although its epicenter was closer, the

2_

Figure 2. Map of Daggett, California Area.

1. Rand McNally Road Atlas, 65th Edition, 1989

2. Ad Hoc Working Group, Future Seismic Hazards in Southern California, Phase I" Implications of

the 1992 Landers' Earthquake Sequence, report by the California Division of Mines and Geology,P.O. Box 2980, Sacramento, CA 95812-2980

effects of this quake were minimal compared to the effects of the Landers' quake. The

epicenter of this quake was near the small town of Big Bear Lake City - only 45 miles south

of Daggett.

There are two ground-response stations 3 within 10 miles of Doggett. The first station,

at Barstow, is located approximately eight miles to the west, and the second station, at

Yermo, is located approximately four miles miles to the east. Due to their close proximity,

it was assumed that earth motion at Dagget and Yermo was similar to earth motion at

Barstow. Therefore, recorded Barstow data could be used as input to numericalsimulations.

The Barstow data was limited in both frequency and direction. This data was band

passed filtered to frequencies below 23Hz and above 0.07Hz. Three channels recorded

acceleration in two perpendicular directions parallel to ground and in one direction

perpendicular to ground. Rotations in these three directions where not measured, andtherefore, without alternative, were assumed zero. From the acceleration data,

displacement data was deduced. Figures 3a and 3b show recorded Barstow acceleration and

deduced displacement for one channel.

As is shown in this data, the frequency response of acceleration is very high; however,

the frequency response of displacement is low. Since both acceleration and displacementare excitations to the numerical problem (discussed below), and since the problem

contained non-linear components (also discussed below), the frequency response in the

mirrors could not be bounded without the use of a simulation. High frequencies creeping

into mirror dynamics could break the mirrors.

1.3 Objective

After the Landers' earthquake, the Dagget Leasing Corporations (DLC), which

operates SEGS II, contacted the Solar The_maal Design Assistance Center (STDAC) ofSandia National Laboratories (SNL) for assistance in determining a low cost solution to the

journal separation problem. Personnel of DLC suggested welding stops at the end of each

journal to prohibit the journals from separating from the support structure. STDAC

engineers concurred that the stops would indeed prohibit separation but cautioned that thesolution should be analyzed to ensure that this remedy would not cause subsequent failures.

STDAC then contacted SNL's structural dynamics department and asked for their

assistance in performing a Finite Element Analysis to determine the acceptability of the

proposed solution.

3. A ground-response station is a location where seismic activity is recorded.

4

: : : : ! .' : --

_::-(_....i...........!.........I ow_00010_._,t,o._l........i.........."_ so .......... :.".......... _-........... -:............. _-........... "_........... _............ _-..........tn

" _ =o .......... ._ ....... _-........... _............ ::-........... _........... ._............ i ..........

(_ ,o ......... ' .... ._............ _-.-B 0 ..... . ; ;

-tlo

"_ "_'° "7

if:--'i i f t _............!._..........I-'° .......... .................................. "tiiii6"sec'6i_d_" 0 0 1 0 _ 0 _0 I _ 0 _ 0 _0 7 0 _0

'_"_ i[::!b'): : i :::: :::_i:::I Barstow Displacement Dat 4 [: : :::::i: : : : :::_ o

" _ _..........._............i......:....ii i> ::!:.....:i ii'o[-IllO 10 2_0 mO diO 60 (SO

IIIII II II

• Figure 3. Barstow Data.

The following section describes the Finite Element (FE) model used in assessing

acceptability.

2. FINITE ELEMENT (FE) MODEL DEVELOPMENT

There is a 60% probability that within the next thirty years an earthquake as large as

or larger than the Landers' earthquake will strike southern California. 4 Therefore, the solar

collectors, which failed in the Landers' earthquake, must be redesigned to survive this

imminent geological threat.

The redesign process can be experimental, analytical or both. The disadvantage of

using an experimental process is that experiments are relatively costly, whereas the

' advantage of an analytical process is that redesign costs are lower and design flexibility

higher. Nevertheless, the disadvantage of using an analytical process is that when dynamics• are complex, the accuracy of results unsupported by experiment is questionable. Therefore,

4. see Ref. 2 on page 5,

a process which uses both experiment and analysis is preferred. In this report, only an

analytical approach is discussed.

The following section describes the Finite Element (FE) model used in assessingacceptability.

The redesign process consist of constructing a model of collector dynamics, simulatingthat model with recorded input data (the Barstow data), and varying modeled joint

parameters to determine a set of viable joint configurations. The complexity and detail of

the model is dependent on the characteristics of the excitation, and the capacity of the

computational implementation relative to the complexity of dynamics.

In this redesign process, a FE model of a single solar collector was produced. This

model was nonlinear and of high order. The difficulty with assimilating a high order

nonlinear model into the joint redesign process is that such models require excessive central

processing unit run times. Nevertheless, for redesign, the model must run quickly. This

high order, nonlinear model was massaged into workable form via substructure modeling,model reduction, and substructure assembly. This resulted in a low order nonlinear model

sufficient as a design tool.

2.1 Substructure Modeling

Substructure modeling is the dynamic modeling of an individual or a group of

substructures. If a substructure model is linear, model reduction can be performed, and thereduced order substructure model can be combined with other substructure models to form

a reduced order model of the total system. The process of recombining all substructure

models will be called substructure assembly.

Collector dynamics were modeled using five separate substructure models. Thesemodels were:

Left Support Truss Model - a linear FE model representing left support trussdynamics,

Left Joint Model - a constraint model representing the dynamics of thejoint between the left support truss and the trough,tssembly,

Trough Assembly Model - a i!near FE model representing trough assemblydynamics,

Right Joint Model - a constraint model representing the dynamics of the ,joint between the right support truss and the troughassembly, and

Right Support Truss Model - a linear FE model representing right support trussdynamics.

A concise discussion of the production of each of these models is given below.

2.1.1 Left and Right Support Truss Models

Support trusses, composed of a distribution of welded angle iron, were modeled in

PATRAN 3 as a collection of beams. Figure 4 shows a drawing of a support truss. Notice' that this model does not include a journal. This is because journal dynamics are included

into the left and right joint models. The left and right support trusses where identical in• geometry and construction and therefore did not have to be modeled separately. Each

support truss weighs about 200 lbm, and each support truss model contained 378 Degrees

of Freedom (DOF).

2.1.2 Trough Assembly Model

The trough assembly contains the end plates, the torque tube, the mirror supports, and

the mirrors. This assembly was also modeled in PATRAN 3. The end plates and mirrors °

were modeled using thin shell elements, and the torque tube and mirror supports were

modeled using beam elements. Two problems evolved from this modeling. First, since thin

shell elements carry no normal angular rotation, it was not possible to model the

transmission of normal torsional loads into the end plates via shell elements alone.Therefore, a collection of rigid bar constraints were attached to the plate elements to allow

for torsional loading. Second, since the finite diameter torque tube was represented by a

bar element of equivalent stiffness and mass but of infinitesimal diameter, massless rigid

bar constraints had to be applied to couple torque tube dynamics to support truss dynamics.

Trough component dimensions are shown in Figure 5. The total mass of the _ough

assembly was 2160 lbm. The trough assembly model consisted of 7812 DOF.

,t 5".

9'

0.44" thick

--- --_ l 0" Mirror Support DimensionsI_'_ _-I

12.5" bars are 1.125"X 1.125"rectangular

End Plate Dimensions tubes, 0.094" thick 61.8" Mirror DimensionsA

7.0", 0.125" thick ,_

25.3 _ upper mirror

/J 27.5 ,,_ all mirrors are 1/8"r thick

•Torque Tube Dimensions 29.0" lower mirror

This was modeled as an equivalent 1

bar with no diameter. Therefore 26.0,,I "to attach it to the mirror supports,constraint elements had to be used•

91'1

Figure 5. Geometry of Trough Assembly Components.

A NASTRAN modal analysis of the trough assembly model produced six rigid body

modes and a closely spaced distribution of structural modes. The natural frequencies of thefirst seven structural modes were 9.94, 11.53, 12.01,16.39,16.41,16.53, and 16.81Hz. Due

to high modal density, the accuracy of the model above 16Hz was questionable. This isbecause model accuracy is inversely ielated to modal density. As modal density increases,

the ability for a deterministic FE model to represent reality accurately is questionable.Nevertheless, since the lower order modes were well spaced, and since these are the modes

O

which were significant in determining joint dynamics, the model was deemed sufficient as

a design tool.

Figure 6 shows the mode shape of the first structural mode at 9.94Hz. For sufficiently

large amplitude excitations, this mode produces mirror collisions. If the mirrors collide,

they will break. This mode represents a dominate mechanism of mirror collision.

__ _ mirrors

_ __"_ lowersm, rror supporm \_// //_ rmrror

collision of rm_rrors __-"'/_--torque tube.......... I I II III IIJ I

- - Figure 6. First Structural Model of Trough Assembly.

2.1.3 Left and Right Joint Models

Joints were modeled as mathematical constraints. Figure 7 shows the DOF and loads

, needed to define these constraints. The journal, modeled as a single point at the apex of the

support truss, can rotate and displace in all directions. The DOF and the loads at the journal• can be related to the DOF and the loads at the end plate attachment point. The attachment

point is the location where the support shaft is connected to the end plate. Themathematical constraints between DOF and loads at the journal, ;and DOF and loads at the

attachment point, comprise the joint model.

Rotation at Journal of Displacement atSupport Truss Journal of Support

Truss deL= Ed,,.'d,L,'d,L] r

;rL = ?r, , OTL'O,,3T:drL= [drL,'dr',' drL]r at Attachment

Point of End PlateForce at Journal of

Support Truss _'eL= Efe_.feL,fl,,] r

Fr_= Efr_,fr_,fr_] r 'Y

Toque at Attachmentx Point of End Plate

7"t,L= Etet,tt,t,tt, L3rTorque at Journal of

Support Truss Rotation Attachment

_r_ [ iT 0eLPoint of End Platek 0e','

9 _ T

= tTq tr,. v' 'T L .. VOpL, O Pl.q_.j• .'

EndON-SITE PHOTO

Journal

The journal is located at the

Support apex of the support truss.It's construction consists of

a steel housing enclosing aplastic sleeve.

Figure 7. Joint Constraint Conditions for Left Joint. "

10

Since rotations in the x and y directions are not significantly large, it was assumed that

support shafts were always parallel to the z axis. Therefore, a joint can be modeled by

equating displacements and rotations in the x and y directions, allowing rotations in z. direction to be free, and relating displacements in the z direction via a nonlinear constraint

equation representing joumaYstop interactions. If the rotation, displacement, force, and

* = O Ttorque at and on the journal of the left support truss is given by OrL EOrL, Or,, rJ,

= d T , t T_tTL EdrL,drL, rJ FrL= EfrL,frL,frL3r, and TL= Etr_,trL, rJ respectively, and if

the rotation, displacement, force, and torque at and on the attachment point of tile left end

plate is given by ;eL= EOeL,eel,, ee,3', _6,L= Edet, dpL,, deJ r

FpL= Efe_,fes, fe,3 r, and 7"pL= Ire, te_,, teJ r, and if the variable YL is the z-displacement

between the journal of the support truss and its attachment point, then the mathematical

constraints describing the left joint are given by

Xr,, : X., , Fr_L:-F., , (Eq.1)where

=' T

XT, L = EOTL' OTL' dTL,'dTL3 ,

Xm, = EOp ,ePt,dPL,dPL3 T ,

FTaL = EtTL.ITL)fTL,)fTL3 T 'It .

a, T

O t PLY' 3 'Fro, = pLZ fpL,,fpL

FT, L "== EfTL3 =- --EfpL3 -= -Fro,-" "L (YL) J(- 8L (YL, 'L )" (Eqo 2)

The nonlinear functions _L (YL) and 8L (Y_QYL)areforceldisplacement relationships which

will be discussed below. The variables Fro,, F,.,,FT,, FT,L, XT,, and Xm, are also definedabove for later use. Again, since the left and right joints are dynamically identical, the

constraint equations for the right joint are the same as those for the leftjoint except that the

• subscript L is replaced by the subscript R.

11

oL(y,) ,,.

yoL - dma x

YoL yoL 4"dma x

YL *

II I I IIIIII I II

Figure 8. Nonlinear Joint Model.

The function oL(YL) is the force/displacement relationship for a journal sliding on a

frictionless shaft whose motion is limited by stops at YoL-dmoxand yo+ dmox where Yo_is themean distance between stops. When the journal is not in contact with a stop, no force is

produced. When the journal is in contact with a stop, the support shaft elongates by 81.The

force produced by this elongation is/c!81 or K2LSIwhere K,Lis the contact stiffness for the

stop at yoL+ d o_and K2_is the contact stiffness for the stop at YoL- dsox"These two stiffnessare given by IE/A where I is the length of the support shaft in stress, E is Young's Modulus,

and A is the cross sectional area of the support shaft. Strictly speaking, two stiffnesses arc

required since different lengths of the support shaft arc stressed relative to which stop is in

contact with the journal. Nevertheless, since these stiffnesses were similar, their values

were assumed equal. A graphical representation of this force/displacement relationship is

shown in Figure 8.

The function 8L(_;L,Y,) is the force/displacement relationship for stick/slip frictionbetween the journal and the support shaft. This friction is not only dependent upon joint

location, but also upon relative joint velocity.

When the relative velocity between the joint and shaft is zero, friction is equal to that

required to resist slip. Numerically this can be approximated via a very stiff spring (in the

infinite limit the approximation is exact). When friction exceeds the coefficient of static

friction, ta_,times supported weight, w, its value is reduced to the coefficient of kinetic

friction, gk, times supported weight. Therefore, its magnitude is always bounded. A blockdiagram representation of these dynamics is shown in Figure 9.

Q

Friction in the left and right joints is different considering that the weight that each

support truss carries is different. If the modeled solar collector is attached at the end of a

row of collectors, the weight that the left support truss carries will be half the weight of the

modeled trough assemble, whereas the weight which the right support truss carries will be

half the weight of the modeled trough assemble plus half the weight of the trough assembleof the next collector in the row.

12

[ YL=OI

° _.sWgkW ,,

_ _ YL _

_' / YL,

_ -p.,W-_tsW

If YL= 0 and [5 (YL' YL)I = _tkW then YL = YL

III I Illllll II

Figure 9. Block Diagram of Stick/Slip Frictional Loading.

The coefficients of static and kinetic friction at the time of the Landers' quake are

unknown. Therefore, _ts and gk can only be approximated. The coefficient of static frictionwas determined from the coefficient of kinetic friction via the assumed relationship,

_ts - 1.Sgk.This relationship was made for lack of a better alternative. The coefficient of

kinetic friction was determined via numerical iteration. If _t_is large, there will be no

relative motion between the journal and the support shaft. As _t_is decreased, more motionwill occur. At the time of the Lander's quake, the relative motion between the journal and

support shaft had to be at least 4" for the joint to fail. Therefore, _tk was decreased until 4"of relative motion occurred. This represented the maximum possible amount of jointfriction under assumed conditions.

2.2 FE Model Reduction

Without model reduction, the number of DOF in the unified model would beexcessive. A non-reduced assembled model would contain over 8560 DOF. A model of this

order, using direct simulation: will require excessive cpu time. Thus, to reduce cpu run

5. Direct simulation means that all DOF are calculated during numerical integration.

13

time, model reduction was performed. The preferredmethod of model reduction is Craig-

Bampton. 7 A brief overview of this method is found in Appendix A.

Numerically, this reduction was performed in NASTRAN via D-mapping and theresults transferred into MATLAB via the NASMAT translator. Numerical simulations

were performed in MATLAB.

2.3 Substructure Assembly

Three FE substructure models underwent model reduction. These models were the left

support truss model, the right support truss model, and the trough assembly model.

The reduced second order matrix equation for the dynamics of the left support truss is

given by

mT, t mTn mT,3 mT. T,, kT,: kTi3 kT.

roT2, mTn roT23mT. XTaLI+ IkT2' kT_ kT_ kT_. XT2LI = FT2,1

mT,, mT3, mT,, mT_ XT, LI Ikr,, krn kT,, kr. ir¥ _FT,:

7T4t mT42 mT43 mT"- XT4t.i LkT4' kr42 kr" kr" XT.LI . 0 1

where

Xr,, - are DOF in the left support truss model representing displacementsand accelerations at the concrete foundation,

Xr_, - are DOF in the left support truss model to be equated to DOF in the

trough assembly model (Equation 1),

Xr,, - are DOF in the left support truss model to be coupled to DOF in thetrough assembly model via the nonlinear functional relationships

aL (YL) and ¢_L(YL,YL) (Equation 2),

Xr,, - are generalized DOF in the left support truss model which can be usedfor model reduction.

The subscript L represents the left truss. If the subscript L is replaced by the •

subscript R the equations for the dynamics of the right truss result.b

7. R.R. Craig, Jr, Structural Dynamics, An Introduction to Computer Methods, John Wiley & Sons, New

York, NY, 1981, pp. 475-478.

14

Since XT,Land are known inputs (the Barstow measurements), the above equation

can be written as

_ = - kr: (Eq. 3)

. Lm,..m,.m,.j:*'d *'j _x", _..,where all forcing functions are now on the right hand side.

The reduced second order matrix equation for the dynamics of the trough assemble is

given by

mini 4 mini s Xml[ k,% kmt 2 kin, 3 kml 4 k,% Xm_ _Fm,imini| m ml_ ram|3.5 .5

_nm2l mm,_ mm=, mm24 mma, Xmal k%l km22 kma, km24 km_ Xm 2 Fro2]

mm n mmsa mm,,smm_ m%s Xm 3 km3s Xm_

m,.,,m,.,,',,,,,m,..,m,.,,X,.,I k,.,,k,.,,k".k.'.,k',, F.Ojm"s'mms'mmssm's4mmss X._ kmslkmslkms'km"kmss- _Xm,

where

x,., - are DOF in the trough assembly model to be equated to DOF in

the left support truss model,

x., - are DOF in the trough assembly model to be equated to DOF in

the right support truss model,

x,., - are DOF in the trough assembly model to be coupled to DOF in

the left support model by the nonlinear functions o L (YL) and

OL(YDYL),

X., - ere DOF in the trough assembly model to be coupled to DOF in

the right support model by the nonlinear function o R (YR) and

% (YR,YR),

X., - are generalized DOF.

i

To couple equation (3) to equation (4), equations (1,2, 3) are used. This results in a,, combined relation as follows.

15

.ram,' mT_ mmn ram,3 ram,4 ram,' mT_ roT24 0 0

0 0 ! Xm'Iram21 mm_ + mT_ ram23mm_4mm2s mT_ roT24

0 0 0 0 X'h]ram31 ram32 ram33 mm_ mm3s .,

ram41 ram42 m%3 mmo mm4s 0 0 0 0 Xm41._

ramsI mmn mms3 mms4 ramss 0 0 0 0 Xm s "

mr_ 0 0 0 0 mr. mT_ 0 0 Xr3f

mL2 0 0 0 0 mr43mr. 0 0 _L L

0 mrn 0 0 0 0 0 mr. mr_ _r3,0 mL_ 0 0 0 0 0 mL3 mr.

" :r4s"

_ - XM I

kmu. kr. kmn kin. kin;4 kml s kr_3kru 0 0 _ma

kin2' kmz_+ krn kin, 3 kin24 kin2s 0 0 kr. kru _m 3

kin31 kms2 kms3kin34kin3s 0 0 0 0

kin4| kin4_ kin43 kin. kin4s 0 0 0 0 Xm4._

+ kin,' kms2 kms3 kms4 kmss 0 0 0 0 Xms '-

kr3" 0 0 0 0 kr3 3 kr_ 0 0 Xr3

kr42 0 0 0 0 kL3 kr. 0 0 XL

0 krn 0 0 0 0 0 kr3,kr_ _Cr30 kL2 0 0 0 0 0 kL3kr. .,

XL

--mr2 ' --kr2 , 0 0 . .0 0

0 0 --mr2'-kr_ " 1 0 00 0 0 0 XT, -i 0

oooo,,L, 10 0 0 0 .., + 0 0

--mr,,--kT_, 0 0 XT_s, i 0 :T3 J..b

--roT41 -kT4 ' 0 0 XT'_,I 0 !0 0 -m r ' 0 0 , (Eq. 5) .

•_'-kL - - 0 0

0 0 --mr, t -kT, ' ,..

16

Ity = = = QX , (Eq. 6)0010 0 0-1

"_ X = L. ! Xm_ Xm 3 Xm 4 Xm 5 XT3L XT4L XT3R

Xm3"_TXm4"_TXT3t"_TXT3s'=T_T3L' _. RlXlwhere for this problem, _'T,,1 and the 0s take appropriate

dimensions.

Written in condensed notation, equations (5) and (6) become M,Y+ KX = R_ + DE

= = This can beand y=QX where u= r,L , .XT!, XT, T3L

x

collapsed into state space form as x = Ax+Buu J-B_.F, y = Cx, and ); = C,x where

x = , a = 0 , B, = 0 ar = 0 C = Cv = and again theM-IK I ' t ' '

0s take appropriate dimensions. This state space relationship includes all the dynamics of

the _ portion of the system.

Nonlinear joint dynamics,

can be implemented using joint constraint conditions given in Figures 9 and 10.

The assembled collector model can be drawn in block diagram form as shown in

Figure 11.

Displacement & AccelerationExcitation Linear

_ [ x=a+" x Buu + BFF y=C" _ Dynamico /

_"= K (y)y + R _ Nonlinear" Dynamics

III IIII I I H III I I

Figure 11. Nonlinear Collector Model in Block Diagram Form.

17

As shown in this diagram, nonlinear dynamics and linear dynamics can be separatedinto feedback and feedforward blocks. As discussed above, model reduction was used to

reduce the order of all linear dynamics. Nonlinear dyanmics were already of low order.

Thus, the assembled model was of low order. The assembled model is given by

x : (A+BrK(y)(C))x+B,,u+B . (Eq.7)

During simulations, equation (7) was updated every time step.

Also during simulations, variable time steps were used. Variability in time step was

required since journal/stop impacts produced high frequency dynamics which could throw

the numerical simulation into instability. When the journals and stops were far from

contact, long time steps were used, and when the journal and stops were in or near contact,

short time steps were used. Stability was also constrained by the stiffnesses used to impose

stop conditions. The proper selection of these stiffnesses could only be determined byiteration.

3. RESULTS

The section below presents results on model reduction errors and collector dynamics.

3.1 Model Reduction Error

The assembled model was only 40th order. The natural frequencies of each reduced

order models are given in Table 1.

Support Truss Model Trough Assembly Model

Reduced ReducedMode Full order % Error Full Order % Error

Order Order,.....

1 11.01 Hz lID1 Hz 10.08% 9.94 Hz 10.17 nz 2.32%

2 28.44 Hz 29.46Hz 3.61% 11.53 Hz 11.55 Hz 0.12%

3 60.67 Hz 63.77 Hz 5.11% 12.01 HZ 12.38 Hz 3.10% '

_1 70.80]-Iz !7112 Hz 0.46% 16.39 Hz i5.88 Hz 3.16%

111.12 Hz 444.66 _Iz 300.16% 16.41Hz 16.31HZ 0.61%

6 127.62 Hz 659.66 Hz 416.89% 16. 53 Hz 16.39 Hz 0.85%III IIII '11 IIII • I

Table 1. Model Error.

18

As shown in Table 1, Craig-Bampton matches lower order modes to within 4%,

whereas higher order modes were in substantial error. Since excitation frequencies were

low (most of the structural energy was below 1Hz), accuracy was needed only at theselower order modes.

• 3.2 Collector Dynamics

Two joint configurations were studied. The first configuration lets din,_ go to infinity(see Figure 9). This represents a Support Shaft with No Stnp.q. This was the joint

configuration during the Lander's quake. The second configuration assumes that dmo_ = 1".

This represents a Support _qhaft with Stops at 1". This is the remedy proposed and

implemented by the DLC. It was found that this was a sufficient remedy to the joint

separation problem.

3.2.1 Support Shaft with No Stops

The first configuration lets d,,o, go to infinity. This is a model of the joint as it existed

during the Lander's quake. Figures 12 (a), (b), and (c) show collector response versus time

for this joint configuration. Input excitation came from measured Barstow data.

In Figure 12(a), the distance between the center of the support shaft and the journal is

shown. If the distance between the inner end of the journal and the outer end of the support

shaft is less than 4", the journal and support shaft will separate. In this configuration,friction was not great enough to stop joint failure. Figure 12(c) shows relative displacement

between mirror corners. This relative displacement was measured at the location of the

largest relative displacement in the Figure 7 mode shape. To assure no mirror breakage,

this displacement should be less than one inch. As shown in this plot, mirror breakage dueto collision of mirrors will not occur.

3.2.2 Support Shaft with Stops at 1"

This joint configuration consists of a stop welded to the end of the support shaft which

limits its travel to a maximum of one inch. Figures 13(a), (b), and (c) show responses for

this configuration.

" As shown in Figure 13(a), the 1" maximum displacement limit results in impulse loads

occurring in the support shaft. These loadings represent the forces required to set the 1 ton

trough assembly into motion. A stop placed I" from the journal should have the ability to

survive these high impact loads. As shown in Figure 13(b), the stop must be able to

19

withstand at least a 1000 lbf load. This is a very approximate answer considering that

numerically it is difficult to produce an impulse function. Therefore, an adequate safetyfactor should be applied (-2-4).

As shown in Figure 13(c), even with impact loading, the mirrorswill not break.

'- - -i i, i i i ..... i

"1- ta) " I ..............A ! D_splacement between Center of Support i"_"........... i........... [ Shafts and Journals ..... ! ..........

._ - ........... i........... _-........... +............ i........... :_....... '..... _.._........ i..........o + ....... i ........... ! ............ i............ ! ............ i ........... _-...........

i:: -= ...... ----.!._..._ .... ,.: ...... . _i.,,,,, ..... _..........

•_" i ............ time (seconds) ....4 anosupportsnanseparate, i-m,.j "t o mo -_o ,_o mo oo 70 mc

16oo ? ; : . ,

•ooo .(b) ...................... [ Force in the Support Shafts ].........................!

o Force levels due to friction are relatively small :

-moo ........................................................................ i.......... i ...........:

: i

-1000 ........................................................................... ; ............ .- ..........

time (second_)I .... i-I so% 1'o "' _'o mo .o go eo -o ac

o.a I • , _ _ •

C Displacement between Mirrors0.2 ........................

-0,1 ........... .

.,,M

-o.2 : . ....... ::......... i.......... ':...........: : : ! : !

: :_ _ time {seconds)-.-,-, 2,-, ,,',-, -A-, M,0 _.mt ,I ........ I ! I , ,

mn1 I_1 _11"1 ,'41"1

IIIII I IIII

Figure 12. Collector Dynamics with No Stops.

20

.-. 1........... [ Displacement between Center OfSupport I........ i...........

" ,_ ...........i......[ ..........ShaftsandJournals_ I.........i.........

0 _' "_'"-,.' .....

-2 ........................ :............ _ .......... !...................... :....................

"" ............................................. ' ........ _...... time (second) .......: !

• -- • i.... i : .....

-i 500 ! ,,_ ,

(b) I Fo ei the a !,oo,,............}............-r..... rc n SupportSh ftsi...........r...........

.oo ............ i....... .'w"..--.impOIsiveloads.:............ _........... }............ i ...........

_ -800 ...................... i ............

-looo .......... i .......... " ........ ! .... i. , i ..... : ....

! i : time '(seconds)-'l 6oo/ , i i ,, ! i . ' i

o "1o oo so .so mo eo 70 8t

o. 3 • , 'Jr , •

(c) i.i. .A.-.iDisplacemenibetween'Mirr°rsio.,. / .....................

_ -0.1m

._._ -0.2

•' ; ::time(se n s.o..,,la , i .... i• o 2'o _o 40 s'o .o 70 .(--o

I I llllI II lllll Illll

Figure 13. Collector Dynamics with Stops.

21

4. CONCLUSION3

The purposeof this projectwas toredesigncollectorjoints so thatjoint separation and

costly breakage would not occur. Since a remedyto the joint separation problem hadalready been implemented,it was necessaryto determinethe sufficiency of this remedybefore furtherredesign. Forstructuralintegritypurposes,this remedyis sufficient,

Assuming the validity of assumptions madewithin this report,the implementationofmetalstopswelded to thesupportshaftis a suitablesolutionto thejoint separation problem

when the stopsare I" fromthe journal. Stops mustwithstandloadsof over 1000lb/.

Anotherconcern in this analysis was the breakageof the mirrorsdue to enhancedvibrationin the troughassembly. It was found that the additionof stops producedlittlechange in mirrordynamics. Mirrorbreakageis unlikely.

22

APPENDIX A - Model Reduction using Craig-Bampton

When performing model reduction, some DOF are eliminated from the FE model,

R_,r_l N-xlwhileothersarepreserved.Ifupe containsallDOF tobepreservedwhileu__ R '

" contains all other DOF, then the DOF of the FE model are given by [u r,u_ r . In Craig-

Bampton, a transformation matrix, T, is produced such that

P =T

LU_J LUd

where _sare a set of ordered generalizedcoordinates whosetruncation will reducemodelorder.

The generalized coordinates, us, are determined by constraining uj, = 0 and

transforming resulting system dynamics into modal coordinates. That is, if the FE model is

given by

IIMI + IIKI = "_

LM=,M2_JLU_j LK_,r_2JLU_j

then, u, = eru?, where {r2x- c0,M22}2 _, = O, and ¢ = ,, ;2, _3...;n _ R forco,s co2<c°s'" < con- •The vectors ¢, to en- are called the component modes.

P p

These modes along with constraint modes, 't',, will form a complete collection of basisfunctions for the FE model,s Constraint modes are determined by solving the n static

problems given by the solution to the following problem statement

IF up (n) is the n'h element of ue then for ue(n) = 1, Up(m_:n) = O,

FIND _ = 't', for n, m = 1,2, 3.... Np in the static case.

These Ne solutions are given by _i' = -K_:K,2 where 't' = Iq', _2 ... _t'N1 •

Therefore the transformation matrix, T, is given by

NpxN_ RNpxNe -where 0 _ R is a zero matrix, and I c is an identity matrix. Since u_ is in modal

- coordinates, model reduction may be performed by simply eliminating the highest modes

8, This means that any response can be represented by the time weighted sum of the basis functions.

23

. Rs_xt R (s, +N;)x(N,+iv,)ofu a Therefore, for the truncated matrix use ,and T¢ where N# <NT.,

the reduced order model is given by

ru'l=It]m, +'_'l_"J

where m, = Tr iI Mi T , kr = Tr II KI T mr,k,e

24

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5931 Office Blvd. NE FrancestownTurnpikeAlbuquerque NM 87109 New Boston Nil 03070

New Mexico Institute of Naval Civil Engineering Lab

Mining & Technology Kwan8 Ta HuangJoc Galen CODE L 72AssociateDirector of Engineering Pen Hueneme CA 93043PhysicalPlant DepartmentCampus Slalion NebnlskaDcpanl,cill of Eco.omic Developme.tSocorro NM 87801 Rex Manta

Universily of Nebraska-LincolnNew Mexico R&D Forum W I91 Nebraska Hall

Umvcrsily of New Mexico Lincoln NE 68588.4)535Richard Cole

Dircctor Pal MonloyaR&D Commullicalion Office Slate IssuesDirector

Albuq.crquc NM 87131-6076 625 Sih,er Ave.. SWSuilc 130

Nc_vMexico PublicServiceCommission Albuquerque,NM 87102 [

Pcler Bickle_224 E. Pahlcc A_cnuc Howard NelsonSa.ta Fc NM 875t)1-2031 1(124Lmda La.c

Charlotte NC 28211

New Mexico Manufacturing Extension ProgramKen Manicki NEOS Corporation

Mamlfiicluring Projec[ Manager Kirk SIores1()()9Bradbur3'Dr. SE 165 South Union Blvd

Albuquerque NM 87106 Suile 122Lakewood CO 80228

Nc_ Mexico MamffaclurmgProductivily Ccnter New E.ghmd Powcr Scrvice

Grah;un Bartlcll Ed Gulachcilski

11)119BradbuD Dr, SE 25 Research DriveAlbuquerque NM 87106 Weslborough MA 01581

r

NM Sohir Energy I.dustries Association New Mexico League of Women VotersTom Voick Barbara M. Rosnagle

. PO Box 9()275 Natural Resources Chair

Albuquerque NM 87199-0275 i 16 Salamanca NWAlbuquerque NM 87107

35

New Mexico StaleUniversity North Carolina Alternative Energy Corp.CooperativeExtension Service Bob WeissSkip Finley PO Box 12699PO Box 390 Research Triangle Park NC 27709Mora him 87732

Northern Research & Eng. Corp.New Mexico State University Dr. James B. Kesseli

Cooperative Extension Service 39 Olympia Avenue ,Bob Grassberger Woburn MA 01801-20739301 Indian School Rd hiE, Suite 201

Albuquerque NM 87112 Norlhwest Power Planning Council .-Tom Truelove

Nc_ Mexico State University 851 SW Sixth Ave., Suite 1100

CooperativeExtension Service Portland OR 97204Robcrl O. Coppedge,PII.D.Box 3AE NRELLas Cruces NM 88003 Meir Carasso, Ph.D.,P.E.

Manager, Thermal Science Research SectionNew Mexico State University i617 Cole BoulevardPal Melendrez Golden CO 80401

San Migu¢l County ExtensionAgentPO Box 2170. West Branch NREL

Las Vegas NM 87701 James G. Jones1617 Cole Bird

Nc_ Mexico Slale Universi .[y Golden CO 80401-3393Southwest Technology Development InstituteSlcvcDurand NREL '

, Box 30001/Dept. 3SOL Steve RubinL_tsCruces him 88003-0001 1617 Cole Blvd

Golden CO 80401

Ncw Mexico State UniversitySotllhwes[ Technology Development Institute NRELAndrcw L.Rosemhal Chuck Kutscher, P.E.

Box 3(|()()l/Dept. 3SOL SeniorEngineerL;JsCruces NM 88003-0001 1617 Cole Boulcvard

Golden CO I_()4()1

Nc_ Mexico SImileUlliversilySoulhwcsl Technology Development Institute NRELDr Rudi Schocnmackers G. David Mooney, PhD.Box 3(Itll)l/Dcpt. 3SOL Project CoordinatorL;=sCruccs NM 88003-0001 I()17 Cole Boulevard

Golden, CO 80401-3393

Ncw York Stale Energy Research and Dev. AuthorityFred Strnisa NREL2 Rockefeller Plaza FedericaZangrando,PhD.AIh_tn_ NY 12223 SeniorEngineer

1617 Cole BoulevardNc_ York Sialc Pub. Sen,'.Comm. Golden CO 804t)1Edw;ird Schrom

Emp=rcSlate Pla/_l NRELAlbany NY 12223 RogerW. Taylor

Prgject Manager "

Nippon Electric Glass Co., Ltd. 1617 Cole BoulevardBernardL. Stcierman Golden CO 80401-3393I IX(l! Rockvillc Pike Suite 1704Rockvillc MD 20852

36

Oklahoma Gasand Electric PennsylvaniaPower & Light Co.J. D. Hampton R.J. FernandezPO Box 321 North Ninth Street

Oklahoma City OK 73101 Allentown PA 18101

On Ice Philadelphia Electric CompanyHarryFraney Don Fagnan

. 3116 Pleasant Grove Rd. 2301 Market Street 510-1

Plcasanl Grove CA 95668 Philadelphia PA 19101

"" Pacific Gas and Electric Co. Photon Energy, IncStoveHester John A. JohansenBrian Farmer 9650.A Railroad Dr.

3400 Crow Canyon Road El Paso TX ?9924San Ramon CA 94583

Photovoltaic Energy Systems

Pacific Gas and Electric Company Paul MaycockJoseph J. lannucci P.O. Box 290Program Manager Casanova VA 2201734()t) Crow Canyon RoadSan Ramon CA 94583 Plains Electric Generation and Transmission

Cooperative, Inc.

Pacific Power and Light Daniel S. BalletSieve Carr PO Box 6551

9211SW 6lh Avenue Albuquerque NM 87197Ponhmd OR 97204

Plains Electric Generation and Transmission

Packerland Solar System Cooperative, Inc.Richard Lane Dwight LambcrsonPO Box 8262 Supervisor of Forecasting & Modeling

Green Bay Wl 543(18 PO Box 6551Albuquerqtle NM 87197

PAL Engineering Services, Inc.Ken Lambert, VP Platte River Power AuthorityU.S. Office: 621 Heather Knoll Carol DollardDesoto TX 75 i 15 Timberline and Horsetooth Roads

Fort Collins CO 80525

Parsons of California

D. R. Biddle Plumas - Sierra Rural Electric CooperativePO Box 6189 Paul S. BonySIocklon CA 95206 Manager of Member Services

PO Box 2000

GaD Peacock Porlola, CA 96122-2000142Sandy Oak TrailCharlotte NC 28210 Portland SlateUniversity

JeanP. Mvrray, Ph.D.Ralph R. Pence Associates PO Box 751725 S. Broadway Porlhmd OR 97207-0751

t Denver CO 81)209Power Kinetics, Inc.

• Pctms) lvania Energy Office W.E. RogersDirector 415 River Street116 Pine Slrecl Troy NY 12Ig()-2822

Harrisburg PA 17101-1227Andrew G. Proulx

!{}Kelly RoadWeslford MA 01886

37

Public ServiceCommission Real Gasand Electric Co.Allen Girdner PO Box F

Ulilily Economist Santa Rosa CA 95402224 E. PalaceSI.

SantaFe NM 87503 RenewableEnergy Training InstituteJeffrey S. Ross

Public Service Co. of New Mexico Assistant Director

M. Phyllis Bourque 122 C Street, NW vAlvarado Square Suite 520Albuquerque NM 87158-2822 Washington DC 20001

Public ServiceCo. of New Mexico RensselaerPolytechnicInst.Vic Silva JoseM. BorregoCR Dept (0076) EESE Dept. JEC 7020Alvarado Square Troy NY 12181Albuquerque NM 87158

Research Triangle InstitutePublic Service Co. of New Mexico Carl Parker

Becky Kilbourne PO Box 12194Rclail Electric Marketing Center ResearchTriangle Park NC 27709Alvarado SquareAlbuquerque NM 87158 Alan Richardson

BusinessLiaison

PublicServiceCo. of New Mexico New Poslal BuildingMark E. Harlan Room 3004

Technical Analysis Coordinator Santa Fe NM 87501Alva rado SquareAlbuquerque NM 87158 Rile Engineering & Mfg. Corp.

9441 Washburn Rd.

Public Service Co. of New Mexico Downey CA 90242Tom Nesmidi, P.E.

Aivarado Square - MS 0256 Roan Corporation

Albuquerque NM 87158 James L. Aboit177 Bovet Road, Suite 520

Public Service Co. of New Mexico San Maleo CA 944(}2John M. Noble, P.E.

A!_a r_,doSquare - MS 0510 Rockwell inlernational CorporationAlbuquerque NM 87158 Energy Technology Engineering Center

Robcrl K. Hoside. C.E.M.

Public Service Electric & Gas PO Box 1449

Hart,.' Roman Canoga Park CA 91304B. Radimcr

PO Box 570 The Rovac Corp.Newark NJ 07101 Raymond E Shea, Sr.

President

Purdue Universily PO Box IllOleg Wasynczuk 1030 Stafford St.School of Eiec. Engr. Rockd;,;c MA 01542Wcsl Lafil._CllCIN 479(17

SAIC

Radco Producls. Inc. Barr). L. Butler, SEIA Chairman ,

George O Radford Room 2043, MJS C2JPrcsidem 10260 Campus Point Drive2877 Industrial Parkway San Diego CA 92121Santa Maria CA 93455

38

Sandia National Laboratories Segal'sSolarSystemsMark S. Allen Barry Jay SegaiTechnologyTransfer Division Consulting EngineerPO Box 580(I 3357 Cranberry SouthAlbuquerque NM 87185-5800 Laurel, MN 20724-2419

Sandia National Laboratories Scientific Analysis, Inc.R. Hamil Jolm Allen Gunn, PED. Belasich 6012 E. Shirley LaneC. Lombawa Mon(,gomery AL 36117

,,,, Ors. 4212PO Box 581)(I Mr. Ernest Schiele

Albuquerque NM 87185 2323 Bellwood Drive #49Grand Island NE 68801

Sandia National LaboratoriesJulie Clausen. 7161 Mr. Ed SchrieberPO Box 58(1(I 3225 S. 14th St.

Albuquerque NM 87185 Lincoln NE 68502

Sandia National Laboratories Seed International, Inc.Rolf Wrons. 7816 Harold W. Nelson

PO Box 58o11 General ManagerAlbuquerque NM 8'7185 Vice President of Marketing

221 Rio Rancho Blvd

San Diego Gas & Electric Co. Rio Rancho, NM 87124Skip FralickPO Box 183 i SLEMCO

San Diego CA 92112 A.J. Slemmons19655 Redberry Dr.

San Jose State Universi(,y Los Gatos CA 95031.}Helmer Nielsen

Dept. of Mech. Engr. Sea Sun Power SystemsWashington Square George HagermanSan Jose CA 95192 124 East Rosemont Ave.

Alexandria VA 2231.11-2326Schoifield Solar

Allen Carrozza Segal's Solar Svstems2450 Chmmcl Drive, Suite A Barry Jay SegalVcmura CA 93(1(13 3357 Cranberry South

Laurel MD 2o724-2419

Science Applications International Corp.Roger L. Davenport Seldom Seen EducationDivision 448 Mary C. Stuever151}()1)Wesl 6(,h Ave., Suite 202 PO Box 474Golden CO 8(14(11 Placi(,as NM 87(143

Science Applications International Corp. Sevier County High SchoolKelly Beninga Jeremy Smith, Student

( Di_ isim_ 448 3118Caton Rd.15olJ(1West 6th Ave.. Suite 202 Scviewille TN 37862Golden CO 8(,14(11

• Siemens Solar Industries

Science and Technology Corporation Bill HowleyRonald J. Nelson PO Box 6(13212452To_nerNE Camarilio CA 93011

Albuqtlerquc NM 87112

39

Sicrra Club Rio Grande Chapter Solar Kinetics, Inc.Kcn Hughes Gus HulchisonEnergy Chair 10635 King William Drive1204 Placita Loma Dallas TX 75220Santa Fe NM 87501

Solar Power Engineering Co. Inc.Sierra Pacific Power Co. T. BtmaR. G. Richards PO Box 91

PO Box 10100 Morrison CO 80468Rcno HV 89520

Solar ReactorTechnologies "Skyline Engineering Robin ParkerDr. Robert Wills, P.E. P.O. Box 330975Route 45, PO Box 134 Miami FL 33233

Temple NH 030844_134Solar Steam

SMUD D.E. WoodDoll Osborne PO Box 32Box 15830 Fox Island WA 98333Sacramento CA 95852-1830

Solar Stirling Industries ,,SMUD Jack Stearns

David W. Rienhart 2822 Highridge Rd.Box 15831) La Crescenta CA 91214 'Sacramento CA 95852-1830

Solar Systems EconomicsSolar Dcvelopmcnt, Inc. Michael Lotker, ConsultantDavid Burrows 1646 Folkslone Terrace

.363(IReesc Avenue Westlake Village CA 91361Gardcn Industrial ParkRlvicri| Beach FL 33404 Solar Uno

EPS

Solar Energy Corporation #A-355Robcrt Aresly PO Box (12-5256Box 31)65 Miami FL 33102-5256Princeton NJ (18540

Solid Waste Bureau

Solar Energy Industries Association Barbara Hoditschek

Ann Polansky Program Manager777 Norlh Capital Street, NE Environment DeparlmentSu_(c 8()5 119(I St. Fratlcis Drive

Washt|lglo|l DC 20002-4226 Santa Fc NM 87503

Solar Energy Industries Assn Southern California Edison Co.Ken Shemkopf C. LopezLi,ldaLadas PO Box 80(I

ScottSklar Rosemead CA 91770

StHIc805

777 N. Capilol St. NE Southwest Public Affairs, Inc. '_Washington DC 201_02-4226 Fred L. O'Cheskey

PresidemQ

Solar Kincttcs. Inc. 31)1)First Interstate Plaza

Paul Schcrlz. Vice President 15()Washinglo|l Avenue

1()635 King William Drive PO Box 2187Dallas TX 7522(} Santa Fc, NM 875(14

40

Southwest Technology Development Institute State of FloridaRobert Smith Daryi O'ConnorM.E. Properly Control Division Executive Office of the GovernorGcncral Services Department The CapitolSimms Building Tallahassee FL 32399-0()01715 Alta Vista

v Sama Fe NM 87503 State of FloridaJohn B. Stark

Specialized Environmental Executive Office of the Governor"" Products, Inc. The Capitol

Arlhur J. Brooks Tallahassee FL 32399-00013325 Ali Baba, Suite 609

Las Vegas NV 89118 State of HawaiiThontas J. O'Brien

Stearns-Catalytic Corp. Department of Business and Economic DevelopmentT. E. Olson 335 Merchant St., Room 11(1Box 5888 Honolulu Hi 96813Denver CO 8(}217

State of Hawaii

State of California Maurice H. Kaya, P.E.California Energy Commission Department of Business, Economic Development, &Energy Technology Development Division TourismResearch and Development Office 335 Merchant St., Room 108Promod Kulkanfi Honolulu H! 96813Phil Misemer1516 9lh Street State of HawaiiMS-43 David A. Rezachek, Ph.D., P.E.

S=lcnimento CA 95814-5512 Dcp;irlme,I of Business and Economic Development335 Merchant St., Room !!0

SImileof California Honolulu HI 96813

Dcpanmem of CorrectionsDelano Stale Prison State of New Mexico

Tom Shanyfelt Energy, Minerals and Natural Resources DepartmentPO Box 567 James ComonDelano CA 93216-O567 Anita Lockwood

Harold TnuilloSt;ire of California Brian K. Johnson, P.E.

Department of Corrections 2o40 South Pacheco StreetH_lrr3Franey S;|nla Fe NM 875(153116 Pleasant Grove Rd.Plcasam Grove CA 95668 Simileof Nc_ Mexico

Ne,,_ Mexico Slale Land Office

St;Ire of Colorado Gcoff Webb

Office of Energy Conservation PO Box 1148Howard "Andy" Walker Ph.D., M.E. Santa Fe NM 875(}4-1148Renewable Energies Coordinator1675 Broadway Stale of New Mexico

( Stfilc 131)(1 Office of Interstate Natural Gas MarketsDenver CO 8(1202-4613 Ronahd H. Merrett, Director

P.O. Box 2088o

St;Ire o1"Florida Room 2(16. Land Office Bldg.Colleen McCann Kettles Santa Fc, NM 87504David Block

Jim HuggiusFlorida Solar Energy Center_¢}()State Road 4(11

C;lpc Canaveral FL 32920-4099

41

State of Wyoming Suntec Systems, Inc.Department of Commerce J.H. DavisonJohn F. Nunlcy I11 Suite B-4FcderalGrantsSupervisor Loring Park Office Bldg.Barren Building 430 Oak GroveSt.Cheyenne WY 82002 Minneapolis MN 55403

StateUniversity of New York SustainableEnergy SystemsAtmospheric SciencesResearchCenter David N. Borton, Ph.D., PresidentR. Percy Hilltop RoadAlbany NY 12222 Troy NY 12180

StirlingTechnologyCompany Swedlow.Inc.Mr. MauriccA. White E.Nixon

2952GeorgeWashingtonWay 12122WesternAvenueRichhmd WA 99352 Garden Grove CA 92645

Stone &Webstcr Engr. Sylvestcr/BernexDave Agenta Richard P. Vento245 Summcr Street . 24700 HighpointRd.Boston MA 01921 Beachwood OH 44122

Ken Stone Technology EnterpriseDivision6882 Via Angelina Karen MartinHumingtoll Beach CA 92649 P.O. 549

Mesilla NM 88046

Strategies UnlimitedR. Winegarner Tech Reps, Inc.2()! San Antonio Circle John StikarSuite 205 5000 Marble NE, Suite 222

Mountain View CA 94(140 Albttquerque NM 87110

Stmdstrand Advanced Technology Grp. Tennessee Valley AuthorityWilliam J. Greenlee, Engineering Manager Sharon OglePO Box 7(Io2 Solar Applications BranchRockford IL 6 i 125-7(1(12 B 513 Signal Place

Chananooga TN 37401

Sun Exploration and Production Co.R. !. Benner Mac ThayerPO Box 288o 6 Byard St.D=dlas TX 75221-2880 Athens OH 45701

Sundstrand ATG The Solar LetterD Chaudoir Alhm L. FrankWilliam J. Greenlee 9124 Bradford Rd.

PO Box 70o2 Silver Spring MD 2(19(11-4918Rockford IL 61125

TESCO

Sttnqcst Fresource Linda Terrel )Grcg Baer, PE PO Box 97(IPO Box 3763 Fort Worth TX 76101-(1970 •

H_ckory. NC 28603Tetra CorporationKenell J. Touryan, PhD.Director of Energy Resources3701 Hawkins St. NE

Albuquerque NM 87109-4345

42

Texas Tech University University of Colorado, BoulderDept. of Electrical Engineering Dr. Jan F. Kreider, P.E.E. A. O'Hair Dept. of Civil Environmental and ArchitecturalPO Box 4439 EngineeringLubbock TX 79409 Boulder CO 80309

Tl_crmacorc, inc. U.S. Air ForceMr. Donald Ernst Clifford E. Richardson, III

780 Eden Road Professional EngineerLancaster PA 17601 Constntction Management

1606th Air Base Wing (DEEC)The Gas Company Kinland AFB NM 87117Shivu Desai

Market Development U.S. Air ForceProject Engineer RobertR. CooperMarketing Electrical Engineer555 W. Fifth Street 6 CES/CEEE

Los Angeles. CA 90013-101 i 7621 Hillsboroush Loop Dr.MacDill AFB, FL 33621-5207

Tierra de Sol EngineeringDarnl P. Ruchle U.S. Army Corps of EngineersE.E.. President LarryD. Lister4600-C Montgomery NE Mechanical EngineerAlbuquerqtle NM 87109 PO Box 401`)5

Champaign IL 61820-1305Trends Publishing Inc.Evelyn Didier U.S. Army Corps of Engineers1(179National Press Building Roberl S. Gorham Jr., A.I.A.Washinglon DC 20045 Chief. Technology Transfer

PO Box 9005

Tritech Incorporated Champaign IL 61826-91,)05Timothy BenedictPO Box 1429 U.S. Army Engineering and Housing Support CenterTahlequah OK 74465 Robert G. O'Brien, P.E.

Chief Utilities Engineering DivisionUnited States Environmental Protection Agency CEHSC-FUPatricia C. Plympton Fort Belvoir VA 22060-5580Special Assistant, Policy and Resources DevelopmentOffice of Administration USAF/ETAC

Salbtv. Health. and Environmental Management Hilda ShellingDivision ENGRC Meteorology Section

4111M Slreel SW (PM-273) Scott AFB IL 62225

Washiilglon. DC 21146(IUS/ECRE

Umtcd States Environmental Protection Agency Guy Be(tenPhil Wirdzck Executive Director

Chief. Building Alteration Section Renewable Energy Training InstituteFacilities Operations Branch PO Box 10095

(. Facilities Management and Services Division Arlington VA 22210-9998

Umversily of Central Florida 3M-Solar Optics Program,D Dr. Gerard G. Ventre Paul Jasler

Research Scientist Heather Kutzler

Ii|slilt|te Ibr Simulatioll and Training 3M Ceillcr12424 Research Parkway Bldg. 225-2n-06Suite 3011 St. Paul MN 55144-10(}0Orlando FL 32826

43

Tri Stole Technology Service University of ColoradoSam Aversano Dr.JanF.Kreider,P.E.

27 GovernorsHillRd. Dept.ofCivilEngr.OxfordCT (}6483 BoulderCO 80309

TRW Space& TechnologyGroup UniversityofDelaware

G. M. Rcppucci Alien BarnettOne SpacePark Depl.ofEERcdondoBeach CA 90278 Newark DE 19711

TUV Rheinland of N.A., Inc. University of Hawaii "_Paul Schuitze Patrick Takahashi

Vice President Hawaii Natural Energy Inst.3420 Execulive Center Drive 2540 Dole StreetSuite165 HonoluluHI 96822

AuslinTX 78731

UniversityofHoustonEnergyLaboratory,SPA

U.S,Army CorpsofEngineers LorinVain-HullRobcn S. Gorman Jr.. A.I.A. Houston TX 770(}4Archilcct

Chief. Technology Transfer University of LowellP.O.Box 9005 Thomas Costello

Champaign, IL 61826-9005 Fahd Wakim! University Avenue

U. S. Dept of Commerce Lowell MA (}1854Mr. Les Garden

ITA/OGIM, Rm 2805 University of Minnesota

W;Ishil)glOl)DC 20230 E.A. FlclchcrDept.ofMechanicalEngineering

U.S.Dcpanmenl ofEnergy IIIIChurchSt,SEG. Burch Minneapolis MN 55455C. Carwile

N,Haque University of New MexicoForrcstal Building M.W. WildinCode CE- !32 Department of Mechanical Engr.

I(}(}(} IndependenceAvenue SW Albuquerque NM 87131Washinglon DC 20585

University of New Mexico

U.S. Dcpanmcnt of Energy NMERIFrank (Tex) Wilkins G. Leigh

!(}(}(}Independence Ave., SW Albuquerque NM 87 !31W;Ishlnglol) DC 20585

Universily of Texas at Arlington

Univcrsil) of Arizmm Jack FilzerGcorgc V. Mignon West 6th at Speer StreetEnvironmcnlal Rcsearch Lab. Arlington TX 76019Tucson AZ 85706-6985

University of Wisconsin

Universil) of California T.A. LipoKurl Ltmd Dept. of Elcc. Engr. and Computer ScienceSECR (}31() Madison W! 52706La Jolla CA 92(}93-()310

Utility Power Group

Umvcrsity oi"California, Berkeley M. StcrnC. Hu 94 !(}DeSoto Ave., Unit G

Dcpt. of Elcc. Engr. Chalswonh CA 91311Bcrkclcy CA 94720

44

Ventures PiLls,inc. WG Associates

Frank A. Simko Vern Goldberg4123 N. Tamiami Trail 6607 Stonebrook CircleSarasota FL 34234 Dallas TX 75240

Dan Vermonl Mr. Jay Whimpley3()1()1 Wolf Rd. 2456 North Plain City

•_ Bay Village OH 44070 Farr West UT 84404

Brent Wilson, PE

_" Viking Solar Systems, Inc. Associate Direclor Engineering and ArchitectureGeorge Goranson 16(.)6ABW/DEEE1850 Earlmont Ave. Kirtland AFB hiM 87117-5496La Canada CA 91011

Wyle LaboratoriesVirginia Polylechnic Institute and State University Don McAvinSaifisr Rahman, Ph.D. 7800 Governors Drive WestAssociate Professor Huntsville AL 35807

Electrical Engineering DepartmentBlacksburg VA 24061 Yankee Environmental Systems, Inc.

Mark C. Beaubien

Virginia Power Co. Senior EngineerTim Bernadowski IOi Industrial Road

Corp. Tech. Assess. PO Box 7465()()()Dominion Boulevard Turners Falls, MA 01376Glen Allen VA 23060

Dale F. Zinn & Associates

Ross R. Wagner Dale F. Zinn744 E. Samaria Architect

Eric MI 48133 212 E. Marcy St.Sanla Fc NM 875111

Wall Street JourmdEnviromncnlal Reporter William E. YoungIt) Post Office Square 380 Milford Point DriveSuite715 Merrill Island FL 32952Boston MA 02109

Zomeworks [

WestinghouseScience& Tech. Ctr. 1011 A Sawmill Rd NW lWalter J. Dollard Albuquerque NM 87104Technology Director, Energy & Utility Systems Group13 I() Buelah Rd. Ricardo Xavier Zuniga

Pittsburgh PA 15235 State Co-DirectorI I9 East Marc._. Suite I() I

Wichita State University Santa Fe NM 87501Center for Energy StudiesDr. Ward Jcwcll Dr. Gracicla LcsinoBox 44 INENCOWichita KS 672(.)8 Buenos Aires 177

( 44(I(ISaita ARGENTINA

Wisconsin Power & LightBob Terreil Australian National University222 West Washington Ave. Depanment of Engineering PhysicsMadison WI 537(11-OI92 Prof. Stephen Kaneff

PO Box 4CanbcrraACT 260(IAUSTRALIA

45

Ministry of Energy Adel Tawfik Soliman, Ph.D.lan Lewis New & Renewable Energy Authority56 Wellesley StreetWest Directorof SolarThermal Dept.Toronto, Ontario M7A 2B7 PO Box 39 EI-souk EI-TogalTCANADA Maadi 11693

Cairo, EGYPTNational Research Council of CanadaG. Rumbold Energy and Technology Associates lr

John Ayer AItn: Dr. Adel SolimonPholovoltaic Division P.O.B. 39 EI-Souk EI-TogaryMomrcal Road Maadi 11693Ottawa, CANADA KIA OR6 Cairo, EGYPT

Qucens University DLRP, C. San Institute for Technical ThermodynamicsDcpt. of Elec. Engr. R. BuckKingston, Ontario Pfaffenwaldring 38-40CANADA K7L 3N6 7000 Stuttgart 80

FEDERAL REPUBLIC OF GERMANY

Railcx Power & Energy Group (IPP)PO Box 2148 indo-American Credit Corporation Ltd.Vancouver.B.C. Dr. Amil N. Shsh

CANADA V6B 3T8 Chariman & ManagerRegd. Office: lol House, Near Swati

Rcpublic Equities Corporation Apartment, Opp. Central Bank Lane,Mr. L. P. Bradley Ambawaki Bazar, Ambawadi, AhmedabadPO Box 2874 (Guj.) INDIA-380 006Va,couvcr, B.C.

CANADA V6B3X4 The Industrial Credit & Investment Corporation ofIndia, LTD.

Umvcrsity of British Columbia Dr. P. H. VaidyaW. G. Dunford 169. Backbay ReclamationDept. of EIcc. Engr. Road No. 3Va,couvcr. BC Bombay400 020CANADA V6T IWS INDIA

University du Quebec Luz IndustriesIsraelTrois-Rivicrcs Yoel Gilon

V. Rajcgopalan PO Box 7929Dcpl. d'ingchicric - C.P. 500 Jerusalem 91079Trois-Rivieres. Quebec ISRAELCANADA G9A 5H7

PCJ Enginccring. Ltd.U niversilyof Toronto W.R. (Roddy) AshbyS. B. Dcwan ManagerDcp! of Elcc. Engr. Box 579Toromo. Ontario Kingston I(L JAMAICACANADA MSS IA4

Thcrmosol Equipments "_Solar UI|O AH-158

Ellis Perez. Atom Nagar ,Vicc-Presidcme de Mercadeoy Ventas Madras-60() 04()Axe. SarasolaNo. 54, Apto. 102SantoDomingo,DOMINICAN REPUBLIC

46

CONDUMEX

Ing Enriquc Hill B.Sojuana inesde la Cruz344020. Piso Tiaincpantia. Edo. de MexicoC.P, 54000MEXICO

Discno Solar y Arquitectura BioclimaticaDr. Everardo HemandezA-P 69-738

MEXICO, D.F.C.P. 04460

Equipos y Sislemas de Captacion SolarIng. Enrique Ramoneda CarrilloBahia de Chachalacas 42 Col. V. Anzures

II 30(} MEXICO. D.F.

Ing. Armando Nava EscobedoJcfc dc Scrvicios de Conservacion

Durango 291-80 PISOColonia Roma067()0 MEXICO, D.F.

Inslalaciones Tecnicas Especializadas, S.A.Aim: lng. Enriquc Ramoneda CarrilloOcrcnlc GeneralBahia Dc Chachalacas42

Mcxico Cily, D.F. MEXICO 11300

InslilulO de lnvestigaciones ElectricasDr. Jorge M. Huacuz Villamarinlcrior lnlernado Palmira

Apanado Poslai 47562000 Cucrnavaca. Mor., MEXICO

Saudi Arabian National Ceqter

forScienceand TechnologyAbbas A. Salim

PO Box 15164, Riyadh 11444SAUDI ARABIA

Bcrna/Bcrncx AGR. S.Boncui/M.ToblerInduslriestrassc 36

CH-461){)Oltcn. SWITZERLAND

Nalional Rural Eleclric CooperativeAssociation( Pctc Smith

Manager5a. Avenida 16-28, Zona 10, Ol010

Gti_llClllal_l. Gualcmala, C.A.

47

Internal Distribution

MS MS1380 M. Allen, 4212 0321 E. Barsis, 14001380 R. Hsmil, 4212 1111 S. Dosanjh, 14021380 D. Belasich, 4212 0821 J. Ang, 14041380 C. Lombawa, 4212 1109 J. Jortner, 1408

0724 D.L. Hartley, 6000 0318 G. Davidson, 1415 i"0735 D.E. Arvizu, 6200 1111 W. Camp, 142 I0735 A. VanArsdali, 6200 1! 10 R. Alien, 14220704 P.C. Klimas, 6201 1110 E. BHckeU, 14230753 G.J. Jones, 6202 1109 A, Hale, 14240752 T.C. Bickel, 6213 0441 J. Biffle, 14251127 C.P. Cameron, 6215 0819 J. McGlatm, 14311127 R.M. Edgar, 6215 0820 P. Yarrington, 14321127 R.A. Mehoney, 6215 0821 P. Stanton, 1433

1127 M.E. Ralph, 6215 0439 D. Martinez, 14341127 E.E. Rush, 6215 0841 D. McCIoskey, 15001127 J.W. Soachan, 6215 0836 C. Peterson, 1501

0703 C.E. Tyner, 62 !6 0827 P. Hommert, 15020703 J.R. Anderson, 6216 0827 J. Rottler, !51 I0703 C.W. Bennett, 6215 0834 A. Ratzel, 15 !20703 L.R. Evans, 6216 0835 R. Skocypec, 15130703 T.R. Mancini, 6216 0832 W. Wolfe, 15510703 D.F. Menicucci (20), 6216 0833 C. Halley, 15520753 D.E. Hasti, 6218 0833 L. Whinery, 1552-10753 R.R. Hill, 6218 0826 W. Hermina, 15530753 R.C. Pate, 6218 0825 W. Ruttledge, 15540753 J.W. Stevens, 6218 0825 Z. Mahmud, 1554-1

0899 Technical Library (5), 7141 0443 H. Morgan, 15610619 Technical Publications, 7151 0437 R. Thomas, 1562

0100 Document Processing 0557 Tom Baca, 2741for DOE/OSTI ( I0), 7613-2

0933 R. Wrons, 78169018 Central Technical Files, 8523-20617 J. Clausen, 12630

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