10.07.2015   Sonar-Collecttors

Thermodynamic Model

For describing the thermodynamic behavior of the collector, a semi stationary model, based on an energy balance, is used. With equation 4 the reachable massflux M of a collector segment is calculated via the absorbed radiation Iabs = r? optIb, the heat of in- and outflow.

referred to direct horizontal irradi — ance Ibh

%

losses qloss and the enthalpy-difference zih

(0opt(0zCr) lb-q!

M

) Ac

4hi

The whole collector-field can only reach the lowest massflux of the three sections:

7в = arcsin(cos(7)sin(0z))

(a) 5 x 104 rays (b) 5 x 105 rays

M = min^, M2, M3) (5)

This way matching losses between the sections are taken into account. To make sure, that the collector is in operating conditions to produce its corresponding output, a dynamic thermal node at each end of collector-stage is used as shown in equation 6.

(mcp)l dt — (Ubs^loss) Wap (6)

The thermodynamic model is implemented in the simulation environment Co/S/m[5] which was developed at the Fraunhofer ISE to simulate solar-collector systems.

Power Block

(a) flow sheet

(b) part load of a simp/e fresh water coo/ed process

Figure 6: Powerblock Cost Model

The cost model is based on a first estimation for a starting configuration with N = 34,

H = 7.5 m, D = 0.075 m and an absorber tube with a diameter of 15 cm. The specific direct cost8 of this collector would be Cc = 90 €/m2 for the mentioned configuration. This figure corresponds to cost estimations of the Solarmundo collector. The cost estimations were evaluated and seem reasonable for a third plant. All changes in cost due to mutations of the geometry are assumed to be linear. The specific direct collector-cost Cc is expressed by equation 7.

Cm N + Ch (4m + H) + Cd (N-1) D + Ca

Cc ^ NB (7)

The whole investment Бр of the solar field, power block, infrastructure, land and engineering can be calculated with:

The power b/ock is assumed to be a simple process with only the fresh water tank as a preheater (see figure 6). The condenser is cooled by fresh water. The part load behavior is integrated into simulation via look-up-table.

TE — (CcAc + TO) x (1 + «e) + C|Ac(1 + -^^-21 + 2pb The LEC is calculated via annuity «a and the annual electricity yield.

(8)

LEC =

(«a + K. + ^Mt1 + «c)TE

Ja Eeldt

Table 1: 50 MW Faro DNI = 2247 kWtlm2a

Cc

90 €/m2

specifi c direct collector-cost (N = 34, H = 7.5 m, D = 0.075 m)

Cm

30.5 €/m

specifi c cost of a primary mirror (B = 0.5 m), incl. structure, tracking etc

Ch

13.8 €/m2

specifi c cost of the absorber tower

Cd

11.5 €/m2

specifi c cost of gap

Ca

304.0 €/m

specifi c cost of the absorber

Cl

3.0 €/m2

land and preparation

To

4002 t€

others, piping steam-separator

T

640.0 t€

Infrastructure

Tpb

33600 t€

powerblock 672 €/kW

a

9.368 %

annuity 25 a rate of interest 8%

«e

22.5 %

engineering, commissioning, project managing & license

«O&M

2 %

operation and maintenance

«i

1 %

insurance

c

5 %

additional mark-on for contingencies

The assumptions of the cost model are shown in table 1.