Off-design performance modelling of a Solar Organic Rankine Cycle integrated 1 with pressurized hot water storage unit for community level application

10 Solar organic Rankine cycle (ORC) has advantages over common PV systems in view of the 11 flexible operation even if solar radiation is unavailable. However, at present the dynamic 12 performance of solar ORC with respect to the off-design behaviour of storage unit, expander, 13 pump and heat exchanger is rarely reported. This paper investigates a medium-temperature 14 solar ORC system characterized by evacuated flat-plate collectors and pressurised water 15 storage unit. The main aim of the study is to investigate the performance of the system with 16 consideration of transient behaviour of the thermal storage unit which results in off-design 17 operation of other components. The other aim is adjusting the power output according to 18 electricity demand throughout a day. The heat storage unit is analysed using one-dimensional 19 temperature distribution model. A transient simulation model is developed including pump 20 and expander models. To meet the electrical demands of different periods, the mass flow rate 21 of heat source is adjusted for controlling the evaporation temperature. Moreover, sliding 22 pressure operation control strategy of the ORC is implemented to meet variable heat source 23 temperature. A 550 m 2 solar collector area and a 4 meters diameter and 7 meters height 24 pressurized water cylinder are used in simulation. Produced work is controlled and the results 25 are matched with the demands. Produced work from the expander under the given conditions 26 are 47.11 kWh in day time, 70.97 kWh in peak period and 31.59 kWh after midnight. 27 28 29 30 31 32

pressure operation control strategy of the ORC is implemented to meet variable heat source  storage. They presented off-design and cost analysis and findings indicate that the investment 72 cost for direct thermal energy storage systems is a 17% lower than the investment cost for 73 indirect storage system. Tzivanidis et al. [12] conducted a parametric analysis of a solar ORC 74 plant by using parabolic trough collectors to be optimize the system according to energy and 75 financial considerations. Their results suggest that increasing the total collecting area reduces 76 the solar thermal efficiency. Also flat plate collectors have been used in solar ORC systems. 77 Wang et al. [13] prepared an experimental rig to compare two collector types and they found 78 overall power generation efficiency was 4.2% for evacuated solar collectors and about 3.2%  In large scale solar thermal electricity generation systems, there are many alternative 119 materials for thermal storage, namely, molten salts, thermal oils and water. It is suggested 120 that molten salt is the best choice for thermal storage in high temperature operations (>400 ) 121 [18]. Thermal oil is also promising in the temperature range between 300 and 400 , for 122 lower operating temperature, water can be properly used because water has good thermal 123 properties and has a much lower cost compared to other fluids [19]. In the present study, the  Eq. (4) is the energy balance for the internal node ''i" and Eq. (5) for the last node.

227
The tank has a cylindrical shape with diameter and height , and the outer areas of nodes 228 are given in equations as below: and the last node: The static mode of the storage tank means there are no external forced flows entering or 231 leaving the tank. Therefore, conduction heat transfer between the nodes should be considered.

232
Heat loss to the environment also creates thermal stratification in the tank, as fluids near the 233 wall are cooled due to heat loss and these lower temperature fluids, which have lower is the pump capacity fraction, which is given by: The overall pump efficiency is therefore: The relevant parameters in Eqs. (12), (13) and (14)  and derivation of equations can be taken from the given ref. [23]. Fig. 6 gives the expander 291 efficiency variation with pressure ratio for the given conditions. It is seen that pressure ratio 292 between the expander inlet and outlet has an influence on expander isentropic efficiency. The 293 condensing pressure or temperature is related with the ambient temperature so environmental 294 changes also affect the system performance. However, in this study, it is taken as constant 295 condensing temperature at 30 , which will be explained in Section 5. Where X is the Martinelli factor which is given from vapour quality x: The T-s diagram related with variable evaporation temperature is given in Fig. 8 The related flow chart showing the procedure is given in Fig. 9. In order to evaluate the system performance, firstly, design conditions need to be determined.

379
Since condensing temperature depends on the ambient temperature in air cooled condenser, After selecting the design condensation temperature of 30 , the design evaporation 392 temperature should be corresponding to the built-in pressure ratio. However, the electricity 393 demand needs to be considered for the peak period so the expander needs to operate at higher 394 pressure ratio. Due to characteristic of the scroll expander, operation at higher pressure ratio has a slightly lower performance than operation at built-in ratio.  tank. Therefore, water mass flow rate is selected as 2 kg/s as a design parameter which leads 418 to an evaporator of 51 m. The effect of water mass flow rate on the system performance will 419 be discussed in detail in a later section. Selected design parameters are summarised in Table   420 2.

428
Before simulating the whole system, the reaction of the heat exchangers when the system 429 operates at off-design conditions is investigated. Firstly, the effect of water inlet temperature 430 originating from top of the tank needs to be analysed. Furthermore, its effect also depends on 431 mass flow rate. Fig. 13 shows the effect of the water inlet on evaporating temperature with The system operation is based on the following strategy: day time period starts at 08:00, the peak demand period starts. This period covers the main target of the study and ends at 24:00.

481
Only ORC works and water mass flow rate are set at 2.4 kg/s to satisfy the excessive demand 482 by reaching higher evaporation temperature. The last period is late night period from 24:00 to 483 08:00. During this period, the water mass flow rate is switched to 0.5 kg/s again as 484 production of a high amount of electricity is not required.

485
According to Fig. 13 and Fig. 14, it is expected that the tank temperature, especially the first 486 node temperature, should be higher than 100 both to provide the required production and to 487 avoid low expander performance. Otherwise, the performance of the expander will be 488 degraded significantly, as shown by the characteristic curve in Fig. 6. Therefore, initial tank 489 temperature is selected as 100 for simulations. One of the important aspect is selection of One of the most important issues for the daily simulation is the selection of the initial 502 temperature in the tank. According to previous sections, it can be concluded that temperature 503 levels have an influence on the work output. Since selecting a proper initial tank temperature 504 is significant for the results, it is required to eliminate this uncertain situation. Otherwise, it 505 results in over-or underestimation of the work output.

506
In order to determine the reasonable initial condition, a number of simulations need to be 507 conducted until initial and final temperatures reaching a stable level in the simulation. After After determination of the initial temperatures, the system is ready for the investigation. Fig.   557 20 shows the temperature distribution in the tank in hours. An interesting trend is observed 558 between 08:00 and 10:45. Although collector output is discharged into the first node, during 559 the first half hour this only affects the last node. Later, other nodes are affected and finally, it 560 gets mixed with the first node at 10:45. The reason for this trend is density difference. At the beginning, collector outlet temperature is only matched with the last node, however, later its 562 temperature increases and systems operate as usual. The same phenomenon can be seen 563 between 15:00 and 17:00 for all simulations.

564
The rest of the day has a similar trend with the Fig 16. The only difference is the period 565 between 07:00 am and 08:00 am. During the last one hour, the system is switched to the static 566 mode. It means the tank is only subjected to heat loss to the ambient.  Fig. 17 but during the first two hours, the production is higher and more stable compared 573 to the Fig. 17. One of the reasons is the temperature difference. Previously, all temperatures 574 were assumed as 100 . However, the first node temperature is determined as nearly 105 , 575 which results in a higher work output. Also, stable generation comes from the steady first 576 node temperature which is already explained in the Fig. 20. Moreover, it can be seen that 577 work production is interrupted at 07:00 am because temperature of the middle node falls to 578 100 . The stop criterion is activated at that time, the work generation is interrupted to 579 conserve the stored heat in the tank.  To evaluate the off-design performance of the system, performance of the expander during 603 the second day has been analysed and it is shown in Fig. 23a. During the daytime and late 604 night periods, the isentropic efficiency of the expander varies slightly. Referring to the Fig. 6, 605 since expander operation pressure difference range at these periods are close to expander 606 design pressure ratio (low evaporating temperature despite higher water temperature during 607 these periods), its performance is higher. However, during the peak period, it falls below 0.63 608 because evaporating temperature is forced to increase by the present model for controlling the 609 expander output. According to off-design performance of the expander, this control strategy ORC efficiency is also useful metric for evaluation of the system performance. It is related 620 with some parameters but in the present study, main factor is evaporating temperature which 621 is higher during the peak time period. Fig. 23b shows the ORC efficiency during second day.

622
In the other periods the evaporating temperature is forced to decrease by the present model.

623
The main purpose is to avoid using the heat source excessively and of course to meet the 624 demand. The efficiency variation is observed between 0.076 and 0.092.