Thermo-economic evaluation of an innovative direct steam 1 generation solar power system using screw expanders in a 2 tandem configuration

: Tandem screw expander (SE) technology is a promising solution for large 15 volume ratio situations. Tandem SE driven direct steam generation (DSG) system is 16 first proposed for distributed solar thermal power generation. Steam accumulator is 17 adopted for storage due to its moderate heat source temperature. Compared with the 18 cascade steam-organic Rankine cycle (SORC) system, the novel tandem system has 19 simpler structure, easier control strategy and lower technical requirements, less 20 operating and maintenance fees, more stable power output and higher security. 21 Thermodynamic analysis and economic evaluation of the novel system are conducted 22 based on some parameters of a recently constructed tandem SE project. Steam Rankine 23 cycle (SRC) efficiency of 18.49% is achieved by employing built-in volume ratio ( P3 11 1213 PTC V1 ) 24 of 3 for the high-pressure SE (SE1) and , v b r of 7 for the low-pressure SE (SE2). The 25 cost-effectiveness of the system is improved as the power capacity and heat storage 26 time increase. Levelized electricity cost (LEC) of 0.118 $/kWh and payback period (PP) 27 of 10.48 years are obtained for 1 MW tandem plant with 6.5 h heat storage. The cost of 28 parabolic trough collectors accounts for nearly half of the total investment while the 29 accumulators occupy less than 7%. The cost of SE2 is approximately seven times that 30 of SE1 due to the larger design outlet volume flow rate and rotor diameter. 31

where T is collector inlet temperature;  is incidence angle modifier and is is incidence angle and its calculation process is shown in Section 2.1.2. 135 Thousands of collectors are usually adopted and the temperature difference between 136 neighboring collectors is supposed to be small. To calculate the overall efficiency of 137 PTC, it is reasonable to assume that the average operating temperature of the collector 138 changes continuously from one module to another. 139 For liquid water, in order to reach an outlet temperature out T with an inlet 140 temperature in T , the required collector area is obtained by where m is mass flow rate of water. 143 Heat capacity of water can be expressed by a first order approximation: (3) and (4) is calculated by  ;  is the solar hour angle (°). 168 For horizontal PTCs, s  is determined by [14] 169 sin sin sin cos cos cos where  is the geographic latitude (°), where n represents the n th day in a year, S c r e w E x p a n d e r 2 where AST is the apparent solar time (min). T he rm a l e ff icie nc y w he n T 9 is 20 0 oC T he rm a l e ff icie nc y w he n T 9 is 18 0 oC P res sur e r atio in S E 1

Efficiency (%)
Ef fi ciency of S E2 ( %) SR C ef ficie n cy wh en T 9 is 2 00 oC SR C ef ficie n cy wh en T 9 is 1 80 oC E ffic ien cy o f SE 2 whe n T 9 is 18 0 oC E ffic ien cy o f SE 2 whe n T 9 is 20 0 oC   is determined by the characteristic of SE, and it has a constant value for a specific 205 SE. By definition, the theoretical efficiency is given as:     The material cost of accumulator is  is the heat capacity of water.

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T  is the temperature drop in discharge process.
Cylinder vessel generally has two elliptical heads at the top and the bottom. The 257 standard ratio of the half long axis (a) and the half short axis (b) of an ellipse is 2:1.

258
The design thickness is expressed by where head h is the edge height of head (mm) and is regulated by the standard [28].

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The total mass of material used for the vessel is  The required aperture area of PTC not only meet the simultaneous heat collection 283 and power conversion duration ( sim t ), but also fulfill the capacity of heat storage: Cost of PTC is assumed to be 170 $/m 2 , the same as potential installed cost assessed   inlet. An over design area of approximately 10% is ensured for the condenser. All the 311 other fixed parameters are displayed in Table 5.  efficiency of SE2 with the pressure ratio in SE1 at given T1 are exhibited in Fig. 8.

347
Efficiency of SE1 can be kept constant by adjusting its pressure ratio. Efficiency curve 348 of SE2 ascends in discharge process owing to the decline of its pressure ratio. Given T1, 349 there exists an optimum pressure ratio in SE1 which makes    pros and cons, ideal number of 6 seems to be acceptable.

386
The investment proportion of each unit is shown in Fig. 12. The cost of PTCs occupies nearly half of tot C , followed by SE2. The cost of SE2 is approximately seven 388 times that of SE1 due to the larger design outlet volume flow rate and rotor diameter.

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Water storage only accounts for 6.59%. LEC of 0.118 $/kWh and PP of 10.48 years can 390 be obtained using the economic models.  The parameters of the condensers corresponding to 0.2-0.8 MW are listed in Table   411 8. The investment proportion of each unit and economic indicators are indexed in Table   412 9. LEC and PP increase as the scale turns smaller. Similar to the conventional turbine-            Pressure ratio in SE1