# Matlab based Model of 40-MW Concentrating Solar Power Plant

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3 constituted by 6 series-connected collectors and each collector is 1m long and has a span of 5.76m. Then, one SCA is m long while the distance between two SCA is equal to 2 times the span of a collector. Table 1 reports the main of the CSP. variable referred to the city of Bari. It can be seen as that the curve of Bari is always below the curve of Gela. Table 1 Parameters of the CSP Number of the collectors 816 Area of each collector m 2 Total collector area 45*1 4 m 2 Distance between collectors 11.5 m Peak power of the solar field (with 321 MWt radiation of 9W/m 2 and efficiency of the collector equal to.79) Solar field area 9 ha Temperature of the hot tank 55 C Temperature of the cold tank 29 C Storage capacity 3 MWh Rated electrical power 4 MWe Thermo-electrical efficiency in rated.423 electrical Produced energy for year Load factor (ratio between produced energy and energy obtained if the CSP works in the rated conditions during the whole year) Mean collector efficiency for year (depending on the annual direct radiation) 168 GWh/year Fig. 3. Thermal cycle (a) and T-E diagram (b). Fig. 5. Comparison between GHI and DNI Fig. 4. Layout of the CSP 3. Matlab based model of the CSP Unlike a PV plant for which all the three components of solar radiation (direct one, diffuse one and reflected one) are useful for the energy production, the CSP utilizes only the direct component. For this aim it is needed to know the DNI for the installation site. In this model we consider that the CSP is plant up in Bari, a city of the South of Italy different from the installation site of the ENEA s project. The values of DNI for Bari are not available, but in mediterranean countries the values of the DNI are similar to the values of the Global Horizontal Insolation (GHI), as reported in Fig. 5; then GHI values are utilized for this paper. Fig. 6 reports a comparison between the GHI of the installation site of the ENEA s project (Gela) and the same Solar radiance [W/m 2 ] GHI BARI GELA [month] Fig. 6. Comparison between solar radiance of Gela and Bari.

4 Installation site Daily solar radiation DNI Geometric/physic Layout of the solar field Modeling of the thermodynamic system aim several input variables have been considered. In fact, the thermal performance (i.e. the final temperature of the molten salts, T U ) depends on the length of a single collector, on its flow capacity and on the radiation. As the SCA are equal each other, all the successive figures and evaluations are referred to a single SCA. Fig. 8 reports for several values of radiation. As it can be seen, for a fixed value of, T U has a positive correlation with the radiation, i.e. the thermal performance increases as I direct increases. Then the correlation between and is opposite respect to the correlation between and. As the secondary loop and thermal cycle of Fig. 2 represent the standard operation of a common fossil fuel power station utilizing a Rankine cycle, the model proposed in this paper is limited to the only primary loop, i.e. the thermodynamic system. Fig. 7 reports the steps for modeling the primary loop of Fig. 2. It can be noted that two sets of input data are necessary. The former one regards the installation site: latitude, altitude, climate conditions, available surface, shadings and so on. The latter one is constituted by the geometric dimensions of each collector, number of collectors (depending on the desired electrical power), number of SCAs, typology of fluid and so on. The first set of input data allows to determine the DNI while the second one allows to define the layout of the solar field. Finally, a mathematical model of the thermodynamic system is obtained, considering the fluid starting from the cold tank and arriving to the hot one, flowing through the receivers network. The output data of the model are the thermal efficiency, the thermal power and the final fluid temperature, i.e. the temperature of the fluid just when it is stored in the hot tank. This last one is evaluated as: Q fluid TU = TI + G c where T U is the final temperature, T I is the initial temperature (i.e. the fluid temperature from the cold tank), Q fluid the thermal power of the fluid, G s the flow capacity and c ps the specific heat of the molten salts. It can be noted that T U decreases as G s increases: the larger the flow capacity the shorter the time necessary to pass through the receiver. Q fluid is calculated as: s ps Q = η I A fluid direct where A is the reflector surface, I direct the direct radiation and η the global efficiency taking into account the losses, the pointing system and so on. 4. Results Output Fig. 7 Modeling steps of primary loop of Fig. 2 After modeling the thermodynamic system, some simulations have been run in Matlab environment in order to evaluate its thermal performance and efficiency. For this Tu of Single SCA [K] Fig. 8 Thermal performance of a single SCA respect to the flow capacity Fig. 9 reports the final temperature, where represents the length of a single SCA, for different values of the flow capacity G s. It can be noted that, for 3 /, T U increases linearly as increases, whereas for 3 /, the correlation between T U and is yet positive but nonlinear. Fig. 9 has been obtained considering I direct = 35W/m 2 ; similar figures are obtained for different values of I direct. Fig. 1 represents the thermal efficiency of a single SCA with respect to the length of the SCA. Obviously, the efficiency decreases as increases because of the losses along the pipe; nevertheless, for higher values of G s (5-6 kg/s) the decrease is limited also for very long SCA (m). Instead, efficiency decreases quickly for lower values of G s as increases. Moreover, for the smallest value of G s, the relation is nonlinear. Also Fig. 1is obtained for I direct = 35W/m 2 and similar figures are obtained for different values of I direct. Finally, Fig. 11 diagrams the thermal power depending on the flow capacity of the molten salts, for a fixed value of I direct. Also in this case, the relation is linear for the higher values of G s, otherwise nonlinear. The previous analyses highlight that the control of the CSP is not trivial as the output have opposite correlations with respect to the input data, e.g. flow capacity, length of the SCA, direct radiation. For example, Fig. 1 suggest to use shortest SCA, but it is not possible if high electrical power is requested. 5. Conclusions Flow Capacity of Molten Salts [kg/s] Idirect=35 [W/m2] Idirect=5 [W/m2] Idirect=65 [W/m2] Idirect=8 [W/m2] Idirect=95 [W/m2] This paper has proposed a Matlab based model of the primary loop of a CSP. The model is based on a real CSP located in South of Italy, but another installation site has

5 been considered. In this paper the secondary loop and the electrical energy production cycle have not been considered as they follow a standard common fossil fuel power station. Respect to the only priamy loop, the model has allowed to verify that a suitable range of flow capacity have to be imposed if a linear operation is desired. Anyway, the control aspects result very important in order to obatin an optimal efficiency of the CSP. This typology of CSP is very interesting because the typical problems of solar plants (unpredictability of the energy production) are overcome by means of a couple of tanks, the hot one and the cold one. The hot tank represents the storage of the thermal energy to be used also when the radiation is not present or is not sufficient. Tu for single SCA [K] Thermal Efficiency of Single SCA[K] Gs=1 kg/s Gs=2 kg/s Gs=3 kg/s Gs=4 kg/s Gs=5 kg/s Gs=6 kg/s Length of SCA [m] Fig. 9 Thermal performance of a single SCA respect to the length of the receiver Gs=1 [kg/s] Gs=2 [kg/s] Gs=3 [kg/s] Gs=4 [kg/s] Gs=5 [kg/s] Gs=6 [kg/s] Length of SCA [m] Thermal Power [W] 2.5 x Idirect=35 [W/m2] Idirect=5 [W/m2] Idirect=65 [W/m2] Idirect=8 [W/m2] Idirect=95 [W/m2] Flow Capacity of the Molten Salts [kg/s] Fig. 11 Thermal power of a single SCA respect to the flow capacity of the molten salts References [1] Commission of the european communities, GREEN PAPER - A European Strategy for Sustainable, Competitive and Secure Energy, 26, 26_15_en.pdf [2] U. Herrmann and D. W. Kearney, Survey of thermal energy storage for parabolic trough power plants, J. Solar Energy Eng., vol. 124, pp , May 22. [3] V. Morisson, M. Rady, E. Palomo, and E. Arquis, Thermal energy storage systems for electricity production using solar energy direct steam generation technology, Chem. Eng. Process., Process Intensification, vol. 47, pp , Mar. 28. [4] M. Medrano, A. Gil, I. Martorell, X. Potau, and L. F. Cabeza, State of the art on high-temperature thermal energy storage for power genera-tion. Part 2 Case studies, Renewable Sustainable Energy Rev., vol. 14, pp , Jan. 21. [5] R. Sioshansi, P. Denholm., The Value of Concentrating Solar Power and Thermal Energy Storage, IEEE Trans. on Sustainable Energy, Vol. 1, n.3, 21, pp [6] G. Glatzmaier, Summary Report for Concentrating Solar Power Thermal Storage Workshop, NREL, 211. Fig. 1 Thermal efficiency of a single SCA respect to the length of the SCA.

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