Category Archives: Sonar-Collecttors

Mathematical formulation

• The solar radiation field:

In the estimation of the solar radiation we used the models reported in the "Atlas solaire d’Algerie” [2]. The global solar radiation is the sum of a direct and a diffuse radiation. A critical report on the capderou work showed that if the direct radiation is underestimated the diffuse radiation for a mean day is quite surestimated compared to measured values. All the equations used to estimate the direct and diffuse radiations for any site and given day can be found in reference [1].

dT

f (i)

dt

dT

p(i)

dt

— a(p(i) Tf (i)) )(f (i) Tf (i-1))

— C(Tf (i) — Tp(i) )- dTp(i) — Ta )+ e’It

HeAs V

with a — e -, b — —

p(i)

(1)

(2)

C

f

Ax P LAcs ЬХ

,C-

HeAs, d — ^L^

C

C

and e —

FAc (та)

C

The energy balance over the flat solar collector leads to the following system of equations solved by the 4th order Runge-Kutta method.

(Tf and Tp are the fluid and the collector absorber temperatures respectively)

• The ejector flow loop:

• entrainment ratio ra :

(3)

ra—

m

m

The entrainment ratio is equal to the ratio of the secondary and the driving mass flowrates.

(4)

with m’ : driving mass flow rate and m’’ : secondary mass flow rate The optimal ratio for any working fluid is given by the following equation [2] :

( pe Л

( pc Л

ra —

3.7 •

PC

— 0.507

l PB )

0.85

SHAPE * MERGEFORMAT

The refrigerant flow loop:

Coefficients of performance :

COP = —

OQJd*eaal_________

Qbo> + Wp

T

T — T

C__ XTB TC

T — T

TH TC

B

(5)

(5) (7)

Фcool — m"(h6 — hs)

Qe

Acknowledgement

The installation of the plant and the first two years of scientific monitoring were funded by the European Commission (DG TREN) and the federal state of Baden-Wurttemberg. In 2004 the monitoring and some technical improvements are funded by the German Government as one of the demonstrations projects within the IEA Task 25 "Solar air conditioning of buildings”.

2. Literature

/1/ T. Erpenbeck, Sorptionsgestutzte solare Klimatisierung. Universitat Karlsruhe; Fakultat fur Architektur. Dissertation. 1999.

/2/ M. G. F. Motta; Thermodynamic design and optimisation of solar assisted desiccant cooling cycles for Italian climates. Doktorarbeit, Universita di Genova, 2002.

/3/ U. Schurger. Teststand fur Sorptionsrotoren — Erkenntnisse und Auswertungen. Tagungsband des 13. Symposium Thermische Solarenergie, Otti, Bad Staffelstein, S.236 — 241,2003.

/4/ A. Kodama, W. Jin, M. Goto, T. Hirose, M. Pons, Entropic analysis of adsorption open cycles for air conditioning. Part 2: interpretation of experimental data. Int. Journal of Energy Research, 24: 263 — 278, 2000.

/5/ A. Kodama, T. Hirayama, M. Goto, T. Hirose, R. E. Critoph, The use of psychrometric charts for the optimisation of a thermal swing desiccant wheel. Applied Thermal Engineering, 21: 1657 — 1674, 2001.

/6/ W. Jin, A. Kodama, M. Goto, T. Hirose, An adsorptive desiccant cooling using honeycomb rotor dehumidifier. Journal of Chemical Engineering of Japan, 31: 706 — 713, 1998.

/7/ A. Kodama, K. Andou, M. Goto, T. Hirose; Performance of an adsorptive desiccant cooling process equipped with double stage dehumidification. Proceedings of the Int. Sorption Heat Pump Conference. S.

425 — 430, Shanghai, China, September 2002.

/8/ U. Eicker. Solare Technologien fur Gebaude, B. G. Teubner Verlag, Stuttgart/ Leipzig/ Wiesbaden, 2001. /9/ U. Franzke, G. Heinrich (Hrsg.). Sorptionsgestutzte Klimatisierung: Entfeuchtung und DEC in der Klima — Kalte — Technik. C. F. Muller Verlag, Heidelberg, 1997.

/10/ Hans-Martin Henning (Ed.). Solar — Assisted Air — Conditioning in Buildings. Springer Wien New York 2004.

/11/ C. Hindenburg, H.-M. Henning, G. Schmitz. Einsatz von Solarluftkollektoren in sorptionsgestutzten Klimatisierungssystemen, Achtes Symposium thermische Solarenergie; OTTI, Staffelstein; Mai 1998.

/12/ C. Hindenburg, L. Schnabel, T. Geucke, M. Motta. First thermally solar autonomous air conditioning system in Germany — Simulations, operation experience and economic aspects. Proceedings of the ISES Conference, Gothenborg/Sweden, June 2003.

/13/ Deutsches Institut fur Normung DIN 1946 Teil 2: Raumlufttechnik/ Gesundheitstechnische Anforderungen (VDI-Luftungsregeln), Beuth — Verlag 1994.

/14/ J. Pfafferott, S. Herkel, A. Wagner. Sommer 2003: Mussen unsere Burogebaude klimatisiert werden? HLH 55 (2004)

/15/ L. Schnabel. Betriebsanalyse und Simulation einer offenen sorptionsgestutzten Klimatisierungsanlage. Diplomarbeit. Technische Universitat Berlin. 12/ 2003.

Descrip of the variants

No special window frame was applied for these measurements, other than explained in the variants below, see table 2. The reference opening was not covered with a glass plane; this facilitated the experimental set-up and would still give interreflection problems when a coloured glass or translucent glass plane was inserted. When the transition zone consists is situated in or directly on the glass, only absorption and diffraction are possible methods to reduce the luminance ratios. Diffraction is not so suitable as it has the same absorptive effect for a direct view through the window, and the diffracted rays next to the left and right side of the window can be very irritating. Diffraction is in general used for highly positioned windows where the diffracted rays give extra light deeper into the office room.

Position Method

transition zone : absorption on or in the glass plane

Realisation

empty

coloured glass

patterns in transparent glass

(dots, stripes, etc.)

reflection

diffraction

reflection

X

X

not possible

same effect as absorption lamellas

transition zone in front of the window opening

translucent glass

b

SHAPE * MERGEFORMAT

Building integration

The presence of the hybrid PV/T system inside a window makes it highly visible from the exterior as well as the interior. One of the basic ideas behind the design was to express the building integrated solar energy system architecturally in an attractive, maximally exposed way. Conceptually, the window is the traditional solar collector, hence an interesting starting point for integrating other solar technologies.

Figure 3: Illustration of the initial design of the Solar Window building integrated

Other aesthetical considerations are mainly due to the reflectors. The curved concentrating geometry is decorative and expresses the capturing nature of a solar energy system. The backside facing the interior could be covered with any surface material suitable for the interior context. The modular nature of the reflectors, with no connection to the energy distribution, makes it possible to exchange them for alternative surface, thickness or reflecting geometry. The concave front facing the window will be highly visible from the exterior, and the mirror like surface might be the most critical aesthetical property for a wider acceptance. However, the curved mirror can generate interesting optical expressions in the fagade.

The extruded picture of the PV/T absorber is visible when the spectator is within the optical acceptance angle range, which means that the impression of the individual modules will differ much in height on a short distance. The overall impression of the fagade will hence change when approaching it. The mobility of the reflectors also contributes to a dynamic fagade expression.

The system is initially intended for experimental integration into a low energy, single family house, designed simultaneously with the concept for the solar window, see figure 2. This house has an 18 m2 south facing window structure prepared for the integration of the Solar Window system. The house is constructed with an EPS module system with integrated load-bearing wooden beams, with no thermal bridges. A central brick wall and a ceramic clad concrete floor absorb passive gains. The solar heating system is complemented by a pellet burner, and the PV system is grid — connected while also carrying a local DC circuit for reducing magnetic fields and eliminating losses in battery eliminators, used for DC powered devices.

VALUE OF m FOR SIMPLE SOLAR COLLECTOR MODEL

Consider steady state operation of a solar chimney power plant. The solar collector consists of a transparent deck over a floor that receives solar energy. The collector floor

transfers energy to the air flowing over it at the same rate at which it receives energy from the sun, namely at a G Acoll, where a is the effective absorption coefficient of the collector. The air in the collector loses heat through the collector deck at the same rate that the collector deck loses heat to the environment, namely at pATAcoll, where p is an adjusted heat transfer coefficient that allows for radiation and convection losses and the fact that the temperature difference between deck and environment increases from 0 at the outer edge of the collector to AT at the chimney entrance. The real situation is more complex, but this simple model employed by Schlaich (1995) may be used to derive an approximate expression for the collector temperature rise and the exponent m of the analysis above. Find the air temperature rise by equating energy entering and leaving the collector:

Qfloor — Qdeck — Qcfe

a G Acoll PAT Acoll V pcollcpAT

(11)

AT —___ a G Acoll____

V pcollcp + P Acoll

If the ambient temperature at ground height is T0, the collector exit (chimney inlet) density is pcoll and assuming parallel temperature profiles inside and outside the chimney a chimney of height Hc will generate a hydrostatic pressure potential, pp:

AT

pp — pcoll g Hc

1 0

pcoll g Hc____ a G Acoll (12)

T0 V pcollcp + в Acoll

This equation is of the form:

pp —

C1

C2 V + C3

(13)

It can be shown that for a relationship of the form p = A Vm, m depends only on the local value of the function and the local value of its gradient, and is given by:

m —-

dpp pp

“dV V (14)

For a function of another form, for example Eq. (13), an equivalent m can be calculated at any point, since m depends only on the coordinates of the point and its local gradient:

— dpp V

dV pp

‘ C1C2

(2 V + C3 )2

V(c2 V + C3)

C2V

(2 V + C3;

Back substitute for C2 and C3 and multiply the denominator and numerator by AT:

V p collc p AT

m = _

(V p coiicp AT + p Aeon AT) = _ V pcollCpAT a G A coll

Qfloor Q

deck

Q

ncfe

floor

(16)

= _ a G A coll _ в A coll AT a G Acoll

Here ncfe is the net rate at which heat is absorbed by the air between the inlet and exit of the collector, expressed as fraction of the rate of heat transfer from the floor to the air. We shall call it the collector floor-to-exit efficiency since it is a measure of how efficiently the collector transfers heat from its floor to the air leaving the collector. Schlaich (1995) writes the standard collector efficiency for his collector model as:

PAT (17)

ncoll =«_ g

The collector transfer efficiency can be written similarly by dividing out aGAcoll in Eq. (16):

ncfe 1

PAT

aG

= n coll (18)

a

It is remarkable that in the case of the simplified solar chimney collector model, the exponent m turns out to be simply the negative of the collector floor-to-exit efficiency. The immediate implications are the following:

• m must have a value between 0 and -1

• for n = 2, the optimum pt/pp is between 2/3 and 1

• the optimal pt/pp ratio is 2/3 only if the collector efficiency equals zero.

System Optimization

Two models have been designed: one system includes evacuated tube solar collector and the other includes double-glazed flat plate solar collector. Each model is simulated with different insulation thickness and size of overhang and wing walls. The simulation has been performed to select the optimum collector area and slope, generator temperature so that the maximum possible solar heat is gained, and to select the suitable insulation thickness and overhang and wing walls so that minimum possible cooling load is obtained. As seen from figure 2, Nicosia needs air conditioning for 9 months from March to November. Figure 3 shows cooling load of the building in Assab and from the figure it can be seen that air conditioning is needed all year round.

Figure2. Cooling load (kJ) (Nicosia).

Figure 3. Cooling load (kJ) (Assab)

80 82 84 86 88 90 92 94

hot water inlet temperature (C)

Figure 4. Effect of hot water temperature on solar fraction.

For Assab the maximum solar fraction is obtained at the optimum generator hot water inlet temperature of 86°C for the system with evacuated tube solar collector. The corresponding figure for double-glazed flat plate solar collector is 85°C [10]. The cooling water temperature is assumed low enough so that the system works at low generator temperature. Figure 4 shows the generator hot water temperature for Nicosia and the result shows that the optimum temperatures are 86°C and 83°C respectively. The solar fraction is defined as the percentage of the solar energy supplied to the absorption chiller over the total energy supplied (from solar energy and auxiliary heater) to the chiller. When the hot water temperature increases the additional energy is delivered from the heater, which reduces the solar fraction.

Solar heat gain from the collector varies with slope of the collector and latitude. It is proportional to the angle between the collector surface and the incident ray from the sun. For Assab the maximum is obtained at a collector slope of 13° for both types of collectors

[10]

Figure 5. Effect of collector slope on solar fraction

-SLFR EVC — SLFR DGC — SYEFF EVC SYEFFDGC

. For Nicosia a maximum heat is gained when the evacuated tube collector slope is 25° and the double-glazed flat plate collector slope is 24° (Figure 5).

The effect of both collector area and storage tank volume on solar fraction (SLFR) and system efficiency (SYEFF) for evacuated tube and double-glazed collectors are shown in
figures 6 and 7 respectively. System efficiency is defined as the percentage of the incident solar energy converted into cooling effect. For the case of Assab it is given in [10]. As seen from the figures the solar fraction always increases with solar collector size and storage tank volume. In the case of collector area the increase is higher at the smaller collector area, but decreases its increment as the area increases. For the case of storage tank the variation is high at high volume.

Figure 6. Effect of evacuated tube solar collector (ESC) area on solar fraction and system efficiency (Nicosia).

collector area

Figure 7. Effect of double-glazed flat plate solar collector (DGC) area on solar fraction and system efficiency (Nicosia).

-1 SLFR -1 SYEFF -2SLFR 2 SYEFF -3SLFR 3SYEFF 4 SLFR

4 SYEFF

5 SLFR 5 SYEFF

-1 SLFR -1 SYEFF -1.5 SLFR -1.5 SYEFF -2SLFR

2 SYEFF

3 SLFR 3 SYEFF

Figures 6-10 show the effect of collector area and storage tank volume on solar fraction and system efficiency for the insulated building.

The effect of solar collector area on solar fraction and system efficiency for the 2.0m3 hot water storage tank is shown for Nicosia (Figure 8) and for Assab (Figure 9). From the figure it can be seen that the solar fraction of Assab is smaller than that of Nicosia, but the system efficiency is higher. In all cases solar fraction increases with collector area. The maximum system efficiency of the evacuated tube solar collector for both locations is obtained when the collector area is 20m2. For Nicosia the maximum system efficiency is obtained when the double-glazed collector is 20 m2 while for Assab when it is 30 m2.

The effect of thermal storage tank to the solar fraction and system efficiency is very small comparing to that of the solar collector (Figure 10).

20 10 0

3

storage tank volume (m3)

Figure 10. Effect of storage tank on solar fraction and system efficiency (Nicosia).

Figure 11. Effect of insulation thickness on cooling load.

Figure 11 shows the effect of insulation thickness on cooling load for both locations. The highest cooling load is obtained when the building is not insulated and the lowest is obtained when the insulation thickness is 0.20 m. The maximum cooling load for Assab is 265 MJ while for Nicosia it is 78.6MJ. The reduction of cooling load in the first 0.05m insulation thickness is 34% for Assab and 25% for Nicosia. For the second 0.05m insulation thickness the reduction drops to 6.2% for Assab and 2% for Nicosia. As the thickness increases the effect of reduction decreases and is insignificant for insulation thickness greater than 0.2m.

overhang and wing wall (m)

Figure 12. Effect of overhang and wing wall on cooling load.

Overhang and wing wall reduce cooling load since the direct solar radiation is prevented from entering the building. As the size increases the reduction also increases (Figure 12). But the effect is very small when compared with the effect of insulation. In the first 0.5 m overhang and wing wall addition the reduction is 4% for Assab and 5% for Nicosia. When another 0.5 m is added the reduction is 2.8% and 2.6% respectively.

Figure 13. Effect of insulation thickness on solar fraction and system efficiency load (Nicosia).

Figure 13 shows that solar fraction increases with insulation. This is due to the fact that energy demand decreases with insulation. But the system efficiency more or less remains the same.

Conclusion

A TRNSYS simulation model of solar-assisted air conditioning system has been developed to simulate long-term performance of buildings in Assab, Eritrea and Nicosia, Cyprus. Two collectors types: evacuated tube collector and double­glazed flat plate collectors are used for comparison purposes. The model was used to perform a parametric study of the system to investigate the effect of collector area, storage tank size and generator temperature on solar fraction and over all system efficiency. The model was also used to analyze the possibility of reducing cooling by means of addition of insulation, overhang and wing walls to the buildings.

In both locations the highest system efficiency was obtained from the system, which used an evacuated solar collector. For Assab it is 1.85 times greater than that of the system, which used double-glazed collector and for Nicosia the figure is 1.72.

The lowest cooling load is obtained for both locations when the insulation thickness is 0.20 m and the size of the overhung is 1.5 m. Further reduction could be obtained without economic advantage. Reduction of cooling load is not enough when optimum condition is needed. In addition to the cooling load reduction analysis of the overall cost of the system is important. But for economic comparison the cost of equipment, building materials and fuel oil used in the systems are not the same in all locations.

Study on the Passive Cooling Methods by the Evaporation and Solar Reflection on the Rooftop in a Temperate Climate Region

Seonghwan YOON, Yasunobu ASHIE and Toshio ABE

Building Research Institute, 1 Tachihara, Tsukuba, Ibaragi, 305-0802 JAPAN

Introduction: There have been a number of studies on the passive cooling of the outer surface of buildings for the purpose of conserving energy without resorting to fossil fuels, and simultaneously, improving the indoor thermal comfort. In addition to this, the heat island phenomenon has been regarded as a problem (Ichinose et al., 1999). Thus, it is necessary to strive to reduce the thermal load of buildings on the urban environment. It is particularly important to examine thermal properties of finishing materials on the rooftop surface where the incoming direct solar radiation is great. For this reason, the purpose of this study is to examine the cooling effects by the evaporation and the reflection of solar radiation on the rooftop surface by conducting outdoor experiment and numerical calculation. In the outdoor experiment, various test pieces were installed on an existing rooftop to examine the change in the surface temperature on a clear, summer day. Next, numerical calculation was carried out assuming different states of insulation to clarify the influence of rooftop surface cooling on the thermal load both indoors and outdoors in summertime.

EXPERIMENTS IN THE DAYLIGHT CHAMBER

Preliminary experiments are done in the daylight chamber of the university of Delft in order to make an estimation of the size of the illuminance in underground spaces. The artificial sky simulates a CIE-overcast sky. The illuminance Ehorf in the daylight chamber is 6800 lux. Experiments are done with scale models of scale 1:20 because the height below ground level in the daylight chamber is only 0,8 m in reality (fig. 1). The dimensions of the standard underground space was taken to be 4 x 4 x 4 m3 with a tube of 1 x 1 x 3 m3 on scale.

Figure 2 shows this standard space and the different variants of which the level of illuminance has been tested. The dimensions of the cylindric model (H) and the half sphere

(I) are chosen in a way that the surface of the walls is the same as in the standard model.

All scale models of the underground space are made of white foam, so that internal reflections are taken into account. The inside material of the tube was a material of high specularity in order to send as much daylight as possible to the underground space.

The effects on the illuminance in relation to the dimensions and the form of the space and the tube are investigated. The illuminance is measured at different points on the floor and the wall. On the floor the distance between the grid points was 0,5 m on scale (fig.3). On the wall there were two rows of measurement points: one row on 1,5 m and one on 3 m height, with distance of 0,6 m between the points (fig. 4).

Table 1 and 2 show the results of the measurements. On the floor almost all the models show illuminances between 150 lux and 450 lux and on the wall illuminances between 80 lux and 180 lux. Raising the height of the space or the tube reduced the illuminance in the space, but raising the height of the tube has the most impact. From the symmetries of the spaces it can be concluded that the measurement uncertainty is below 10 lux.

The measured illuminances are too low for offices and livings, but these buildings are yet forbidden below ground level by the building norms in the Netherlands. But exposition spaces can be built underground. Illuminances of 150 lux on walls are very well suited to expose paintings, and illuminances of 300 lux — 450 lux on the floor are suited to show 3D art objects like statues [2,3].

fig. 1. Measurements below ground level in the daylight chamber.

A. Standard

Ci^£aceJieic]hU5m

E. Space length 6m

F. Space length 8m (1 tube)

D. Space height 6m

Bi^£acejieic]ht_3m

SHAPE * MERGEFORMAT

fig.2. Different shapes of the scale models used in the daylight chamber.

0,5 m

fig.3. The gridpoints on the floor of the underground space, distance 0,5 m (scale 1:20).

3 m

1,5 m

0,6 m

fig.4. The gridpoints on the wall of the underground space, distance 0,6 m (scale 1:20).

table 1. Illuminances on the floor of the underground space for the different variants.

lux

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

A

260

250

225

190

252

243

219

189

229

223

200

174

197

190

172

152

B

370

358

305

235

352

337

295

228

300

291

255

204

243

242

215

182

C

200

195

183

162

197

193

181

162

190

184

173

155

179

174

161

144

D

161

157

150

141

160

156

150

141

154

152

146

139

148

144

140

128

E

222

217

195

158

219

213

193

157

203

198

178

149

180

177

159

135

F

204

198

178

141

201

196

176

140

188

183

166

133

169

166

149

123

G

221

219

243

265

219

218

240

261

210

208

232

248

193

192

205

220

H

249

241

218

188

242

233

214

178

227

219

197

169

201

197

179

162

I

436

396

290

226

426

404

309

245

350

328

260

218

279

267

230

192

J

381

370

342

293

383

369

342

296

366

357

326

293

343

335

306

279

K

196

183

155

130

181

170

149

123

151

146

127

108

134

131

117

95

L

251

245

221

189

249

240

219

186

229

211

223

176

202

198

180

157

M

259

250

226

189

255

246

223

189

234

227

208

178

212

207

187

159

N

260

251

230

195

256

247

225

194

235

228

208

183

210

206

196

168

O

265

258

229

203

259

253

229

199

239

228

212

189

213

205

197

165

table 2. Illuminances on the wall of the underground space for the different variants.

lux

1

2

3

4

5

6

A

169

167

154

132

128

116

B

185

173

151

C

150

139

123

130

129

122

D

123

123

116

107

108

104

E

137

131

116

98

97

85

F

118

112

95

86

84

75

G

160

160

169

129

132

141

H

161

123

I

163

J

196

181

162

141

135

128

K

147

141

132

132

130

121

L

165

160

144

128

125

110

M

167

165

155

130

126

116

N

168

167

154

132

125

114

O

172

170

151

143

136

128

The Skylight-Dimensioning Method

Figure 8: Notation system of the Skylight-Dimensioning Method

This existing method can be applied to determine the minimal necessary area of transparent surfaces of those skylights that are effected by the hole hemisphere (that "can see” the whole hemisphere).

Ff represents the necessary transparent area of the skylight, it can be calculated with the following equation:

{2}

eaverage a • b m2

100 Tg — Ts -Td ■ ka ■ ^

Nomination of the initial coefficients and parameters:

e

average

a, b,h

r

Pc, Pw, Pf

p, q,m

Pa

a

: the average illumination coefficient [%],

: the main dimensions — width, depth, height — of the interior space [m],

: the distance between the reference plane and the floor level [m],

: the average reflection coefficients of the surfaces — ceiling, walls, floor — of the interior space [%],

: the main dimensions — width, depth, height — of the light-well [m],

: the average reflection coefficient of the internal surface of the light-well [%],

: skylight transmittance modification coefficients: rg — transmittance, rs — obstruction and rd — dirt coefficients [-].

: the efficiency of the light-well [-],

: the efficiency of the internal space [-].

Calculation and determination of values of the initial coefficients and parameters:

eaverage : the required illumination coefficient, which can be determined using

standards and tables or preliminary recommendations, or it also can be calculated using the En interior (function) specific nominal illumination:

eaverage = EE^ 100%]. {3}

Ekm

Tg, rs, rd : the Tg — transmittance, rs — obstruction and rd — dirt modification values of the

transparent surfaces of the skylight can be determined using existing standards and tables according to the type of the applied — glazing, — structure or depending on the actual environment, for instance:

Tg

As

*d

simple, clear glazing

0.9

structural glazing

1

countryside, regular cleaning

0.8

double, clear glazing

0.8

metal structure

0.9

countryside, accidental cln.

0.55

simple wire-gazing

0.77

timber structure

0.8

residential, regular cleaning

0.7

double wire-gazing

0.63

RC structure

0.8

residential, accidental clean.

0.4

plastics

0.8

industrial, regular cleaning

0.55

industrial, accidental cleaning

0.25

clean state at handover

1

Table 2: Approximate Transmittance, Obstruction and Dirt modification values

a

: the efficiency of light-well, that can be determined using the following equation, where i is the light-well index and pa is the average reflection value of the internal surface of the light-well:

i = m-(p + q)

2 • p ■ q

The value of ka can be determined using the light-well efficiency table bellow:

kr

kr

{5}

a ■ b

(a + b)-(h — r)

: the interior coefficient can be calculated using the following equation:

П

: the efficiency of the interior can be determined with the help of the following table (the kr interior coefficient values and the actual pc — ceiling, pw — wall and pf — floor average reflection coefficients shall be also substituted to the table):

pf

0,3

0,1

Pc

0,8

0,5

0,8

0,5

0,3

Pw

0,8

0,5

0,3

0,5

0,3

0,3

0,5

0,3

0,3

kr

0,6

0,63

0,39

0,33

0,39

0,33

0,34

0,37

0,33

0,32

0,8

0,76

0,53

0,45

0,51

0,45

0,45

0,50

0,45

0,44

1

0,88

0,62

0,54

0,60

0,54

0,53

0,58

0,53

0,50

1,25

0,95

0,71

0,63

0,68

0,62

0,62

0,66

0,60

0,60

1,5

1,02

0,78

0,70

0,76

0,69

0,68

0,72

0,68

0,66

2

1,1

0,89

0,81

0,85

0,78

0,77

0,80

0,77

0,74

2,5

1,14

0,96

0,88

0,91

0,85

0,83

0,85

0,82

0,80

3

1,17

1,01

0,94

0,95

0,89

0,87

0,88

0,86

0,84

4

1,21

1,07

1,01

1,00

0,95

0,92

0,93

0,90

0,89

5

1,23

1,12

1,06

1,03

0,98

0,95

0,96

0,93

0,92

Comparison against coal technology

In a recent U. S. regional power plan discussion document (North West Council, 2002) the cost of a 400 MWe pulverised coal plant was found to be $1468/kWe in the North West USA. This plant is used as a coal cost baseline for comparison costings against two CLFR/cavern scenarios, one with 54% capacity factor and one with 68%. In Table 1, the coal plant is given an 80% capacity factor, within the normal range for capacity factors in the USA. David and Herzog (2003), for example, use 75% in a study of carbon sequestration. The coal plant IRR was held to 14%, assumed as a reasonable payback for solar plants in NREL (2003), by adjusting the wholesale price for electricity. premium charged for peaking sales, because as the capacity factor is reduced, there is a greater opportunity to indulge in ‘peak lopping’, giving a higher return per kWhe. The IRR for such trading can only be determined using a complex grid pricing model not available to the authors.

Annual Output MW(th)

14,038,462

3,620,800

4,526,000

Thermal to Electrical efficiency

39.0%

31.5%

31.5%

Online Status

0.98

0.98

0.98

Total Annual Equivalent MWH Output

2,522,880

1,117,741

1,397,176

Annual Gross Plant Revenue US$

111,315,773

45,291,605

56,614,506

Coal cost 0.71 MMBTU

42,

522

644

Reflector Array Cleaning

3,

587,

,143

4,

483

929

Operations and Maintenance

15,

646

080

2,

022,

,019

3,

,159

,404

Debt Payment

28,

,146,

027

20,

522,

963

24,

359

,041

Annual Gross Costs of Service US$

58,

,168,

724

26,

,132,

,125

32,

О

о

го

373

Annual Net Plant Revenue US$ 53,147,049 19,159,481 24,612,133

Net Present Revenue per MWh

$43.05

$43.05

$43.05

Net present cost per MWh

-$28.97

-$24.43

-$23.84

Net present profit per MWh

$14.07

$18.61

$19.21

CPI

2.5%

2.5%

2.5%

Debt cost

7.2%

7.2%

7.2%

Debt ratio

50%

50%

50%

25YR IRR

14.00%

13.87%

14.76%

2nd Year Example Revenue Sheet400 MWe Coal

CLFR/Cavern

CLFR/Cavern

Capacity Factor

0.80

0.54

0.68

Electricity Sale $/MWH

45.23

45.23

45.23

Environmental Support $/MWH

0.00

0.00

Total Revenue $ per MWh

45.23

45.23

45.23

Collector Area m2

0

3,188,571

3,985,714

Array related cost $/kWe

0

1435

1744

Storage Cost $/kWe

0

68

92

Power block and BOP cost $/kWe

1468

281

281

Total Cost $ per kWe

1468

1784

2117

Table 1. Costs and IRR of coal and CLFR systems

The solar plants were then evaluated on this selling price and it was found that their IRR is comparable to coal; slightly higher than coal for the 68% capacity factor plant and slightly lower for the 54% plant. The optimal capacity factor depends upon the

In Fig. 2, the capacity factor of new pulverized coal plant is now varied to produce a range of electricity wholesale prices which meet the desired IRR of 14%. This is compared to the 68% CF CLFR/cavern storage solar plant which is also held to an IRR of 14%. The graph shows that the coal fired plant is more costly up to about a CF of 82%, and even at a CF of 90% is only $5 per MWhe less expensive than the 68% CF solar plant. This suggests that minimal measures such as low priced carbon trading

Wholesale Price of Electricity for 14% IRR

Coal Plant Capacity Factor

Fig. 2. Cost of electricity in the second project year required to produce a 14% IRR in high CF Coal and Solar scenarios. The Coal CF is allowed to vary while the CLFR storage plant is held at a 68% CF, close to the higher range of solar CFs possible using daily storage in mid-latitudes such as NSW and California.

would be sufficient to provide solar competitiveness against the cheapest baselaod coal fired plant.