Linear parabolic trough solar power plant assisted with latent thermal energy storage system: A dynamic simulation

Applied Thermal Engineering 161 (2019) 114204

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Research Paper

Linear parabolic trough solar power plant assisted with latent thermal energy storage system: A dynamic simulation Hassan Jafari Mosleha, Rouhollah Ahmadib, a b

T

⁎

Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran School of New Technologies, Iran University of Science and Technology, Tehran, Iran

HIGHLIGHTS

of assisting a latent thermal energy storage (LTES) system using PCM is investigated in this system. • Impact dynamic investigation applying several PCMs are examined and compared. • APCMs with a melting point closer to the superheat steam temperature is more appropriate using in LTES system. • Solar fraction PCM (NaNO ) is higher owing to a lower thermal loss in the collectors. • Payback periodofofselected equipping PTC with LTES system is obtained 11 years, in this study. • 3

ARTICLE INFO

ABSTRACT

Keywords: Parabolic trough collector (PTC) Solar power plant Latent thermal energy storage (LTES) PCM Thermodynamic

One of the efficient solar energy harvesting technics is the parabolic trough concentrated solar power plant. However, if the concentrated solar power plant were not equipped with a storage system, the power plant capacity factor would be deficient. Latent thermal energy storage system using phase change material (PCM) is a high energy density storage system to provide durable energy with a constant temperature. In this study, first, a dynamic analysis is performed implementing TRNSYS software on the parabolic trough concentrated solar power plant located in Shiraz, Iran. Consequently, this system is assisted by the latent thermal energy storage system to improve its performance and capacity factor. Several high-temperature PCMs, namely H250, NaNO3, KNO3, and KOH, are examined in the latent thermal energy storage system. The simulation depicts that owing to the operational condition of Rankin cycle in this study, using NaNO3 in the latent thermal energy storage system is the best option with a higher solar fraction (34.14%) among other examined PCMs. In this case, the solar fraction has been enhanced by 90.5% in comparison with the solar power plant without the latent thermal energy storage system. The economic analysis illustrates that the payback period, IRR and NPV of the added LTES system are obtained as 11 years, 15.6% and, 617825$, respectively. The result of the sensitivity analysis on NPV revealed that the electricity price has the most effect on NPV and enhancing the electricity price has a positive impact on NPV.

1. Introduction Energy demands and environmental problems at present are the main sources of concern for human life [52]. Regard to the limitation of fossil fuel resources as well as their adverse impacts on the environment, it can be predicted that the fossil fuels will be replaced by renewable energies, in the near future [1]. The solar energy as an original resource of other renewable energies can be directly employed to generate power by two technical methods. Solar energy can be absorbed by the solar cells to produce electricity, directly (the

⁎

Photovoltaic (PV) solar power plant), or it can be absorbed by heat transfer fluid (HTF) in the concentrated solar thermal power plants (CSP) to generate electricity in heat engines [1]. To enhance performance and reliability of the solar energy systems, they integrated with other systems such as concentrated photovoltaic thermal collectors (CPVT) [2] and solar desalination systems [3,4]. The benefits of the PV solar power plants can be considered in low cost of panels and short time for start-up compared with the CSPs, but the most significant disadvantage is its low efficiency [5]. According to the Volker [6], the solar thermal power plants provide the best-cost solution in comparison

Corresponding author at: Narmak, Tehran 1684613114, Iran. E-mail address: [email protected] (R. Ahmadi).

https://doi.org/10.1016/j.applthermaleng.2019.114204 Received 13 December 2018; Received in revised form 7 July 2019; Accepted 2 August 2019 Available online 03 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

Nomenclature a A Ap At ANN C Cc Co cp Cm CGC Csc CE Cr CSP CPVT d DPB DSG f Ft FWH h hfg hin _t hout _t hout . s . t hp hsf HTF HX IRR ISCCS L LCOE LMTD LTES m mT mPCM NPV

NTU PTC Qaux Qboiler Qcond Qp Qsolar q RMSD SFthermal SEGS SG STPP T Tcond Tm TES TMY U Wg WT

Aperture (m) Surface area (m2) Total surface area of PCM storage tank (m2) Total surface area of heat exchanger (m2) Artificial neural network Heat capacity (kJ/kg) Capital cost ($) Annual operating cost ($) Specific heat capacity (kJ/kg K) Annual maintenance cost ($) Annual gas consumption cost ($) Salvage value ($) Annual electrical revenue ($) Heat capacity ratio Concentrated solar power plants Concentrated photovoltaic thermal collector Discount rate (%) Duration of payback period Direct steam generation Focal length (m) Annual profit ($) Feed water heater Specific enthalpy (kJ/kg) Latent heat of vaporization (kJ/kg) Inlet specific enthalpy of turbine (kJ/kg) Outlet specific enthalpy of turbine (kJ/kg) Isentropic outlet specific enthalpy of turbine (kJ/kg) Heat transfer coefficient of PCM storage tank (W/K m2) Latent heat of solidification (kJ/kg) Heat transfer fluid Heat exchanger Internal return rate (%) Integrated solar combined cycle system Collector length (m) Levelized cost of electricity ($/kWh) Logarithmic mean temperature difference Latent thermal energy storage Mass flow rate (kg/s) Turbine mass flow rate (kg/s) PCM mass (kg) Net positive value ($)

Number of heat transfer units Parabolic trough collectors Auxiliary power (w) Heat transfer in boiler (w) Heat transfer in condenser (w) Heat transfer in PCM storage tank (W) Solar power (w) Heat transfer power (w) Root mean square deviation Solar fraction (%) Solar electricity generating system Steam generator Solar–thermal power plant Temperature (°C) Condenser temperature (°C) Melting point of PCM (°C) Thermal energy storage Typical meteorological year Heat transfer coefficient of heat exchanger(W/K m2) Generator power (W) Turbine power (W)

Greek symbols

Tmin

( )

Effectiveness of heat exchanger Pinch point temperature difference (°C) Efficiency Incidence angle Incidence angle modifier

Subscripts

boil in min max out oil PCM sub super w

with the PV power plants in high irradiation regions. Many studies were performed to simulate solar thermal power plants. Shahnazari and Lari [7] investigated two different configurations for a CSP in Yazd, Iran. The first one is, a standalone solar electricity generating system (SEGS) and the second one is the integration of a solar field with a combined cycle system (ISCCS). The results showed that upgrading the power plant to the ISCCS will increase the net capacity factor, and electricity production much more than the standalone system. Baghernejad and Yaghoubi [8] performed the exergy analysis on an ISCCS. They addressed the higher exergy destruction in the combustor (29.62%), collector (9%), stack and heat exchangers (7.78%), pump and turbines (8%), respectively. Furthermore, they reported that the exergy and energy efficiencies in the ISCCS were higher than a commercial combined cycle power plant. In another energy and exergy analysis of a typical solar thermal power plant, it was found that the collector-receiver assembly is the maximum exergy loss component [9]. Also, Gupta and Kaushik [10] were accomplished the energy and exergy analysis for a conceptually proposed direct steam generation (DSG) solar–thermal power plant (STPP) having only one feedwater heater (FWH). The significant energy loss occurred in the condenser and

Boiling region Inlet Minimum Maximum Outlet Thermal oil Phase change material Sub-cooled region Superheat region Water

followed by the solar collector field. This analysis showed that to reduce the exergy loss in the collector and receiver of the DSG STPP, the temperature of the water at the inlet of the parabolic-trough collectors (PTC) must be designed at the optimal point. Separately, solar energy indeed is not always available for energy harvesting. Hence, the thermal energy storage systems gain importance to provide continuous solar energy conversion. The thermal energy storage systems are used for balancing the demand and supply of renewable energy systems [11]. Implementing the thermal energy storage systems, it is possible to store the solar thermal energy in the day time and release it during the peak demand hours at night [12]. Thereby, in the solar thermal power plants with thermal energy storage systems, electricity could be produced while there is no sunlight, and hence, operation time expands from day to night [13]. Three primary thermal energy storage methods are the sensible heat storage [14], the latent thermal energy storage (LTES) [15], and the thermo-chemical energy storage [16]. In sensible thermal storage method, energy is stored by increasing the temperature of materials [17]. In the latent thermal energy storage, owing to the phase change process, the thermal energy at a nearly constant temperature can be 2

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H. Jafari Mosleh and R. Ahmadi

stored in a smaller volume in comparison with the sensible heat storage. Therefore, the LTES systems are more compressed and energy dense system [18]. The thermo-chemical storage has high energy storage density per unit volume comparing with the sensible and latent thermal storage systems [1], but due to the complexity of the reaction happens, safety, economics, and technical aspects, it has been laid aside and not been used in conventional industries, yet. Hence, the phase change material (PCM) with high latent heat is now an effective and feasible solution to store the thermal energy. For these reasons, thermal storage with PCM has become an essential topic among researchers around the world [19]. In recent years, researchers have presented different experimental and numerical studies in the fields of economics [20], properties of different phase change material [21], thermal performance and geometric configurations of the latent thermal energy storage systems [22] in the CSP plants. Jacob et al. [23] investigated the economics and environmental effects of the several thermal energy storage systems for the CPS plants. By comparing embodied energy with the capital cost for three systems (EPCM, coil-in-tank system and two-tank molten salt system) it was

found that the EPCM system had the lowest embodied energy (38.9 TJ/ MWht) and the two-tank molten salt had the maximum embodied energy (1521 TJ/MWht). Also Jacob et al. [24] investigated the capital cost for the aforementioned storage systems and found that the EPCM system and the coil-in-tank system will result in the reduction of the capital cost about 50% and 25% compared to the two-tank molten salt. Gasia et al. [17] reviewed the material and requirements of the TES systems to attain the optimal performance. They studied more than 25 provisions that were divided into two parts: materials requirements that grouped into chemical, physical and thermal properties, and system requirements namely economics, environmental and technologic requirements. A numerical study was presented by Bhagat and Sah [25] on the transient response of the latent thermal energy storage system. This study indicated the effective strategies for eliminating the heat transfer fluid (HTF) temperature fluctuations during the charging and discharging period. It is found that the performance of the system increased by increasing the mass flow rate and inlet charging temperature. Furthermore, the HTF temperature fluctuations decreased by reducing the

Fig. 1. (a): Schematic diagram of CSPP [39], (b): schematic diagram of CSPP with thermal storage system. 3

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H. Jafari Mosleh and R. Ahmadi

encapsulation diameter of PCM. Nithyanandam and Pitchumani [26] investigated the effects of design and operating parameters on the dynamic energy and exergy efficiency of the EPCM-thermal energy storage system. Galione et al. [27] represented the cascade concept and use of the multi-layer solid PCM for designing the thermal energy storage system in the CSP plant, and consequently analyzed the thermal performance by numerical methodology. Li and Wu [28] performed a numerical simulation and investigated the effects of different parameters (such as the geometric configuration for the shell-and-tube TES units with extended fins, and using different PCMs) on the thermal performance. Finally, it is concluded that by using the extended fins and composite of NaNO3, the thermal performance improves and the melting and solidification time will be shortened at least 14%. Peng et al. [29] investigated the behavior of the encapsulated PCM packed bed LTES system included molten salt as the HTF. The effects of the capsulated PCM diameter, the HTF inlet velocity and the storage tank height on the charging efficiency were investigated using a finite-difference approach. Fornarelli et al. [30] numerically simulated the melting process for a LTES system which the PCM included binary eutectic salt (NaNO3–KNO3 60–40% wt.) and had a melting temperature of about 230 °C. Also, the effect of the PCM motion resistance parameter during the phase change process was investigated. Bellan et al. [31] numerically and experimentally investigated the thermal performance of the high-temperature LTES system comprises encapsulated Sodium Nitrate salt as the PCM in the CSP plants. Moreover, a parametric analysis was performed to study the effects of the mass flow rate, Stefan number, thickness, and shell thermal conductivity coefficient. The results indicated that the Stefan number had an important role on the thermal storage capacity and the capsule shell properties had a significant impact on the thermal performance. Gil et al. [32] reviewed and classified various ways of energy storage and identified many thermal energy storage materials required for energy storage. There are only a few numbers of power plants around the world that tested the high-temperature thermal energy storage systems, but up to now, the high-temperature PCM technologies are not available on commercial scales. Liu et al. [33] reviewed the CSP plants with the PCM storage systems, which their melting temperature are above 300 °C. In their study, various techniques for increasing the thermal performance of the LTES systems were investigated. Manfrida et al. [34] developed a strong mathematical model for a LTES system. Their LTES system comprised of the PCM spheres. The storage energy and exergy efficiencies were also adopted as indexes to evaluate the performance of the thermal storage system. Ya-Qi Li et al. [35] used a mathematical model to analyze the overall exergetic efficiency of the storage system with two PCM (named PCM1 and PCM2) for a solar thermal power plant. The results showed that using two PCMs instead of a single PCM could increase the overall exergetic efficiency significantly by about 19–53.8%. Boukelia et al. [36] developed a unique artificial neural network (ANN) model to predict the levelized cost of electricity (LCOE) for two different parabolic trough solar thermal power plants integrated with thermal energy storage and fuel backup system. In another study [37], they used artificial neural network models to find the best approach for prediction and techno-economic optimization of parabolic trough solar thermal power plant. According to the above investigations, LTES system can play an essential role in proceeding CSPP system to enhance the power plant capacity factor. Acquire knowledge about the effect of PCM types used in the LTES system during charging and discharging in a real operation condition would prepare meaningful data in LTES system designation. The main aim of this study is devoted to the dynamical simulation of the existence parabolic trough solar power plant in Shiraz, Iran assisted with a LTES system implementing TRNSYS software. The performance of several different high-temperature PCMs such as H250, NaNO3, KNO3, and KOH are compared to find out the most efficient one. Moreover, detailed analysis for several heat exchangers in different parts of the cycle like a steam generator and the condenser is considered

to investigate the effect of practical and environmental variations. 2. Methodology and system description The aim of this study is the simulation of a concentrated solar thermal power plant to investigate the effectiveness of adding a latent thermal energy storage system on the enhancement of power plant capacity factor. Shiraz CSPP located in Shiraz, Iran is considered here as the base design. In consequent, a latent thermal energy storage (LTES) system using the phase change material (PCM) is added to the present system. 2.1. Solar power plant without LTES system Shiraz solar power plant is located at latitude and longitude of 36° 29 and 52° 32, respectively. Shiraz has 3000 sun hours per year, and average daily radiation is about 20 MJ/m2. The schematic diagram of Shiraz CSPP is shown in Fig. 1(a), which as can be seen, it uses linear parabolic trough solar collectors (PTCs). The power generation system is an indirect type system and comprises of two separate cycles. The solar collectors’ cycle is composed of the PTCs, evacuated receiver tubes as absorber subsystems, circulation pump, and thermal oil as heat transfer fluid (HTF). The power generation system is a simple Rankine cycle with a steam turbine [38]. In the PTCs, the solar irradiation is concentrated on the evacuated tubes at the focal line. The thermal oil as the heat transfer fluid (HTF) is heated up to a specific temperature in the receiver tube. Consequently, the hot thermal oil flows to a series of heat exchangers as the steam generator (SG) to convert water to superheated steam. In the Rankine cycle, the superheated steam passes over turbine blades to rotate power shaft, and finally generates electricity in the generator. The pressure, temperature, and flow rate at different points of the cycle based on the performance data of the Shiraz power plant [39] are indicated in Fig. 1. All other states have not been specified in Fig. 1 are variable parameters in the study. 2.2. Solar field The Shiraz CSPP comprises of 48 PTCs in eight rows that were installed in the north-south direction. Each PTC has 25 m long and 3.4 m span. Six cylindrical absorber tubes were located on the focal line of collectors. The solar collectors’ system was installed on a rotating structure to track sunlight during daytime. All the technical specifications of the linear PTC have been listed in Table 1 ([39,40]). It should be mentioned that the incidence angle modifier for the PTCs is considered as [41]:

f a2 1+ tan L 48f 2

( )=1 where

( ) , f, a, L and

(1)

are incidence angle modifier, focal length,

Table 1 Technical specifications of parabolic trough collectors ([39,40]).

4

Collector characteristics

Quantity

Collector characteristics

Quantity

Length (m) width (m) Aperture

25 3.4 3.1

0.94 0.25 0.14

Receiver tube diameter (cm) Cover tube diameter (cm) Focal length (cm) Mirror Reflectivity (ρ)

7

Receiver Absorptivity (α) Emissivity of Cover Emissivity of receiver at 300 °C Intercept factor

12.5 88 0.873

0.98 14 0.78

Cover transmission (τ)

0.96

Collector heat removal factor Concentration ratio Maximum optical efficiency (ρτα) Rim angle

0.93

90°

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

aperture, collector length and incidence angle, respectively.

saturation liquid water to the saturation vapor is the duty of the evaporator section. Finally, increasing the saturation vapor temperature to the super-heating temperature occurs in the super-heater heat exchanger. The diagram of enthalpy-temperature of the hot and cold streams in the SG is illustrated in Fig. 2. Generally, if all parts of the SG are active, the pinch point occurs at T5. Here in this study, according to the SG parameters of Shiraz power plant in hot and cold sides (working temperatures, heat capacities, and flow rates), the Tmin at pinch point was obtained 3 °C. Since the temperature of the thermal oil left the solar collectors (T3) is directly dependent on the amount of absorbed solar power, different cases for the heat transfer could occur in the SG. Four different situations that may arise in the SG are demonstrated in Table 3. Fig. 2 would help the reader to understand different cases, easily. The first case, T3 ≤ T15, means the outlet temperature of thermal oil from the collectors is lower than the working fluid (water) so that it even makes the water to be colder. If this condition is met, the thermal oil flow does not allow entering the SG, and hence the auxiliary heater heats the water flow in the steam cycle to the desired temperature condition. To describe other cases which T3 > T15, first, the threshold of T3 (outlet temperature of the collector) which transfers sub-cooled water into the saturation water in the economizer (T3_max_sub) and into the saturation vapor in the evaporator (T3_max_boil) must be determined. The NTU method is implemented to evaluate the heat exchanger perNTU method, an overall area is considered formance. Through the for heat exchanger, and general heat transfer coefficients for different states (the sub-cooled, two-phase, and super-heat flow) have been recognized as parameters. The UA for the heat exchanger at the reference state is provided as a parameter to the heat exchanger model. The UA of each heat exchanger at the reference state can be determined from the state points offered in the technical assessment of the power plant [44]. The UA at an operational condition for the heat exchangers (according to ref [39] are presented in Table 4. When the heat exchanger is in the single-phase region, the performance coefficient of the heat exchanger is equal to [45]:

2.3. Solar power plant with LTES system Since solar energy is one of the time-dependent energy resources, the employment of the thermal energy storage systems would increase the reliability and capacity factor of the system. Although it increases the total capital cost, it decreases the levelized costs of electricity production. In this study, owing to the high energy density of the LTES, this kind of TES system was selected. Fig. 1(b) depicts the schematic of the solar power plant with the LTES system. As can be seen in this figure, the PCM storage tank was connected to a new solar collector field at the left side, and it is also connected to the SG at the right side. Along with the daytime, the circulation of the thermal oil through the solar collectors in the left cycle of the LTES system would provide a condition to store solar thermal energy in the PCM storage tank. By passing the hot thermal oil through the PCM storage tank, the solid PCM turns to liquid and store sensible and latent thermal energy. Consequently, during the nighttime, the left cycle of the LTES system is deactivated, and instead, the right sequence of the LTES system will be activated. Therefore, the thermal energy stored in the PCM storage tank is utilized to generate steam for the power generator cycle. 2.4. Dynamic simulation tools In this study, owing to the transient process of the solar power plant, TRNSYS software [42] was used to perform a dynamic simulation. Simulation is based on the weather data and solar radiation of Shiraz. The type TMY2 was used to read the weather data of Shiraz. The simulation time step is considered 10 min. The described solar power plant was modeled using the specified components in the software. Furthermore, MATLAB software was employed to develop codes for the subsystems that are not available in TRNSYS. In Table 2, all the components used in this simulation were listed. It should be noted that the dynamic modeling and transient governing equations of the unavailable components in the software were presented in Section 3. 3. Mathematical modeling and performance criteria

=

Before presenting the modeling of the main components in this section, it should be noted that the governing equation is established for a time step. Solving all equations are started from a solar collector field to calculate outlet oil temperature at the first time step. Then, other variable parameters in other components are calculated using this temperature, at this time step. Changing the inlet temperature of solar collector and solar radiation will change the outlet temperature in the next time step and make a dynamic simulation during the time.

1 1

e ( NTU × (1 Cr )) Cr Cr × e ( NTU × (1 Cr ))

1 (2)

= NTU /(1 + NTU ) Cr = 1 where NTU = UA/Cmin, Cr = Cmin/Cmax, Cmax = max(Coil, Cw).

Cmin = min

(Coil,

Cw)

and

Moreover, when the heat exchanger is in the two-phase region, the performance coefficient of the heat exchanger is equal to: boil

3.1. Steam generator

=1

e

(3)

NTUboil

According to Fig. 1, the saturation steam temperature corresponding to the working pressure of the power cycle (2100 kPa), is 215 °C. Therefore, it is required to calculate the collector outlet temperature (T3_max_sub), which would increase the temperature of water from T15 to

A counter flow heat exchanger (HX) has been used to model the heat transfer process from the oil cycle to the steam cycle. The regular available heat exchangers Types in TRNSYS cannot be utilized to model the steam generator (SG); hence, a comprehensive program has been written in MATLAB to model the SG. The DOWTHERM Q Heat Transfer Fluid is used as the thermal oil [43]. As depicted in Fig. 1(a), the hot thermal oil leaves the solar collectors and enters the steam generator (SG) at one side (point 3), and sub-cooled water from deaerator is pumped into the SG at another side (point 15). Fig. 1(a) shows that the SG generally involves three heat exchangers of economizer, evaporator, and super-heater. In the economizer, the water temperature rises close to the saturation temperature. The water temperature after economizer is known as approach temperature. As it is depicted in Fig. 2, there is a small temperature difference between saturation temperature and approach temperature, which is neglected in the simulation process. Converting the near

Table 2 TRNSYS Models used in the simulation.

5

Thermodynamic System

TRNSYS model

Linear parabolic collector pre-heater and superheater Flow collector Flow Divider Weather information Pump Heat exchanger PCM storage Condenser

Type Type Type Type Type Type Type Type Type

536 700 11f 11 h 109 62 155 (MATLAB model) 155 (MATLAB model) 155 (MATLAB model)

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

the temperature and the mass flow rate of the cooling tower determine the condensation temperature and pressure of the steam. In the simulation of the condenser, the overall heat transfer coefficient (UA) is set as a parameter. Calculation algorithm of the temperatures and the amount of heat transfer in the condenser is depicted in Fig. 4. Hence, the heat transfer value, the condenser pressure, and temperature, and the temperature of the cooling water that exit the condenser were determined. 3.3. Turbine An adiabatic turbine is assumed to model it thermodynamically. Eq. (3) defines the isentropic efficiency of the turbine.

=

hin, T hin, T

hout , T hout , s, T

(4)

Moreover, the turbine outlet power and generator power are:

Fig. 2. Steam generator stream map.

WT = mT × (h19

Table 3 Different conditions in the heat exchanger.

WG = WT ×

h 6) (5)

G

where ηG is generator efficiency, and it is considered about 97%, here.

Case

Conditions

Description

1 2 3

T3 ≤ T15 T15 ≤ T3 ≤ T3_max_sub T3_max_sub ≤ T3 ≤ T3_max_boil

4

T3_max_boil ≤ T3

Thermal oil is by-passed The thermal oil only preheats the water T3 is high enough to vaporize some amount of the water but not superheat the steam T3 is high enough to produce the superheated steam

3.4. Deaerator As depicted in Fig. 1, in the sake of simplicity of Deaerator modeling, make up water is not considered in this study. Hence, a low flow rate extracted from the turbine was combined with the output flow from the condenser in the deaerator to remove oxygen and non-condensable gas from the boiler feed water. Implementing continuity relation as well as the first law of thermodynamics, the output enthalpy of the deaerator will be calculated as follow:

the saturation condition of 215 °C. Definitely, through this calculation, the total area of the economizer (At) and the universal heat transfer coefficient for the sub-cooled flow (Usub) has been presumed, parametrically. Algorithm to calculate T3_max_sub is demonstrated in Fig. 3a. Consequently, the maximum outlet temperature of the collector that causes the water flow approaches to the vapor saturation state (T3_max_boil), must be calculated. In this condition, a part of the heat exchanger in the steam side is in the sub-cooled region (economizer), and the other part is in the saturation state (evaporator). The universal heat transfer coefficient in the sub-cooled state (Usub) and saturated state Uboil is considered, parametrically. In Fig. 3a, the calculation algorithm is demonstrated in a flowchart structure. After obtaining the threshold temperature of T3, the water temperatures, and the amounts of heat transfer in cases 2, 3, and 4 listed in Table 3 can be determined. The Calculation algorithm at each time step is shown in Fig. 3b. It should be mentioned that in any case, if the SG were not able to produce the superheat steam at the desired temperature (250 °C), the required auxiliary energy would be supplied by the auxiliary heater.

m11 = m10 + m7 , h11 =

m10 h10 + m7 h7 m11

(6)

3.5. Thermal storage system The schematic of the LTES system is depicted in Fig. 1(b). In this figure, two thermal cycles which are interconnected by the PCM storage tank are demonstrated. Along with the daytime, the left cycle of the LTES system is activated, and the solar energy charges the thermal storage tank. Consequently, with the start of sunset, the circulation of HTF in the solar collectors’ side is stopped and the PCM storage tank services the Rankine cycle to generate steam. The amount of energy stored in the PCM tank at each time step can be obtained using the following relations [35]:

Qp = hp Ap

Tin

Tout T

ln T in

out

3.2. Condenser

Qp = moil coil (Tin

Tm Tm

= mpcm (cp, pcm Tpcm + hsf )

(7) (8)

Tout )

The output temperature from the storage tank could be obtained as follow:

In the simulation of the condenser, pressure and temperature fluctuations inside the condenser and the variation of the condenser performance due to the environmental and other cycle components effects (notably, the cooling towers impact) should be considered. Therefore, a MATLAB code to account such effects was developed. In the condenser,

Tout = Tm + (Tin

Tm ) e

(9)

NC

Which NC is:

Table 4 General heat transfer coefficients of the heat exchanger at reference condition [39]. Heat exchanger sections

Oil inlet temperature

Oil outlet temperature

water inlet temperature

water outlet temperature

LMTD

UA

Economizer Evaporator Super-heater

231.15 263.15 265.65

223.65 231.15 263.15

102.75 215.45 215.45

215.45 215.45 250.15

28.64 28.79 51.53

1.95 24.37 3.10

6

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

Fig. 3a. Calculation of threshold temperatures of T3.

NC =

n

hp Ap moil coil

mpcm =

(10)

mpcm × t 1

The total melted PCM at each time step is calculated as follow:

(11)

where Δt is time step, and n is the number of time step considered in this study. 7

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

Fig. 3b. Calculation algorithm of the temperatures and amount of heat transfer in the HX.

A MATLAB code was prepared to simulate the PCM storage tank. Based on the applied controllers, the charging and discharging modes of the system were set in the software. In the case of charging mode, if the oil temperature is 10 °C higher than the melting point of the PCM, the storage tank will be charged; otherwise, the oil is bypassed and pumped to the solar collector field to warm up. In the charging mode, the output temperature of the oil from the PCM storage tank was calculated, and

the amount of heat transfer and the fraction of melted PCM were determined. In the case of discharging mode, the oil (in the right cycle of the LTES system) gains the PCM’s latent heat and goes toward the SG. Hence, in this case, the amount of solidified PCM was determined. At the end of the day, the amount of the melted PCM and the storage heat capacity were determined using the above simulation methodology. 8

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi N

NPV = t=0

N

NPV = t=0

Ft (1 + d)t

(15)

Ft =0 (1 + IRR)t

(16)

4. PTC based Rankine cycle and verification Before simulation of the PTC solar power plant equipped with the LTES system, the PTC based Rankine cycle is analyzed to show the simulation validation. Using the operating data of Shiraz CSPP, the monthly solar generated power is obtained and compared with the results reported by Niknia and Yaghoubi [50]. Fig. 5 depicts the good consistency between our results and the received operation data in [50]. The slight difference can be attributed to the simplification of the components modeling and the climatic conditions difference in simulation and real data as well as some simplification in simulation. The root mean square deviation (RMSD) of the simulation results obtained as 8.2%. The developed model for the heat exchangers was compared with the actual performance of the heat exchangers at the plant, as presented in Reference [39]. In this case, the oil flow rate and temperature at the inlet of the heat exchangers are equal to 8 kg/s and 265.6 °C, respectively, and water inlet temperature at another side of the heat exchanger is about 102.7 °C. The results of temperatures in different parts of the heat exchanger (according to Fig. 1) have been shown in Fig. 6. As can be seen, the differences between the calculated temperatures and the reported temperatures in reference [39] are tiny. Also, the total heat transfer in the simulated heat exchanger differs from that of the actual one by 1%.

Fig. 4. Calculation algorithm of temperatures and amount of heat transfer in the condenser.

3.6. Solar fraction Usually, the solar fraction is used to evaluate the performance of solar systems. The solar fraction indicates the part of the required energy that is provided by the sun against the total energy needed for the operation of the system. In this simulation, the solar fraction is defined as:

SFthermal =

Qsoalr

Qsolar + Qaux + Qboiler

5. Result and discussion Transient simulation of the system along a year would illustrate a clear perspective of the working condition of the system in various situations. Due to the working temperature of the CSP system, one of the critical factors in PCM selection is the melting temperature. Hence, several phase change materials have been investigated to find out the appropriate one. The PCM, which is used as the first trial is H250 with the melting point of 250 °C. Here in this study, 11th of June is a typical sunny day in Shiraz and thereby was chosen for better illustration of the performance data in different parts of the cycle. However, some data in

(12)

where SFthermal is the solar fraction, Qsolar is the solar energy, Qaux is the auxiliary energy, and Qboiler is the required energy in the boiler. 3.7. Economic model A brief economic analysis to show the cost-effectiveness of adding the latent thermal energy storage system to the CSPP has been conducted, here. To address the investment, operation, and maintenance cost, the adding LTES system to the CSPP was deal as a developing project. Hence, in this economic analysis, the total relevant costs were considered just for the LTES system, which is the difference between the existing solar thermal power plant and the developing system. All the economic parameters illustrated in Table 5 were used to find out the financial indexes like DPB, NPV, and IRR. The DPB is calculated as follow: Nmin = DPB t=0

Ft (1 + d )t

Table 5 Economic parameters. Parameters Investment costs: Solar collector/PCM Solar collector field and HTF system cost PCM cost Land and site development cost Miscellaneous cost Civil work cost

(13)

Total capital cost Annual operating and maintenance cost Annual gas consumption cost Annual electrical revenue

where Ft is an annual profit and is calculated as:

Ft =

Cc

Co

Cm

CGC + CSC + CE

(14)

Financial parameters: Salvage value Interest/Discount rate (d) Lifetime (N)

Cc, Co, Cm, CGC, CSC, and CE are the capital cost, annual operating cost, annual maintenance cost, yearly gas consumption cost, salvage value, and yearly enhanced electrical revenue, respectively. The NPV and IRR are calculated according to the following equations: 9

Value

Total

Ref

3720 m2/451400 kg 280 $/m2

1,042,160 $

[46]

0.2 $/kg 6 $/m2

90,280 $ 22,320 $

[47] [48]

183 $/kWe 169 (kWe)–0.00053 (kWe)0.75

45,750 $ 42,250 $

[48] [48]

4% of equipment cost ($/year) 3 $/m BTU 0.21 $/kwh

41,664 $

[48]

122064.8 $ 359772.5 $

[49] [49]

20% of equipment cost 10% 30 years

208,320 $

1,242,200 $

[48] [48]

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

300

250

Solar power (kw)

200

150

100

50

0

Months Simulation data

Real data

Fig. 5. Comparison of solar power in simulation and operating condition.

tracking system, the incidence angle of the collector is lower than that of the horizontal surface, and this causes that the collector surface receives more energy than the horizontal surface. The thermal oil was controlled to flow through the receiver just in existence of solar radiation. Hence, at sunrise, with increasing the solar radiation, the control system of the solar collectors turned on the solar collectors’ pump. Similarly, at sunset with decreasing the solar radiation, the control system turned off the solar collectors’ pump (see Fig. 7).

cloudy days have been presented for more clarification. 5.1. Collector field The total radiation on horizontal as well as the total radiation on the tilted surface of the PTC on the 11th of June has been illustrated in Fig. 7. As it is seen, the solar radiation increased from zero to the maximum value at noon, and then it diminished to reach zero at sunset. Indeed, it can be said that the trend of solar radiation is similar for all sunny days; however, the magnitude is different day by day. Moreover, the angle of incidence on the horizontal surface and the incidence angle for the collector aperture were shown in Fig. 7. It is observed that the solar tracking system increased the incidence of radiation on the collector aperture. As a checking point, it is seen that owing to the tracking system type adopted for the PTC (a north-south axis with east-west tracking), at noon when the collector aperture is parallel to the horizon, the incidence angle of the collector aperture and the incidence angle of the horizontal surface are identical. Furthermore, by using the solar

5.2. Steam generator heat exchanger The oil and steam temperature in different parts of the heat exchanger in the case of H250 as the PCM during 11th of June were shown in Fig. 8. As was described, along the day time solar thermal energy supplies the heat of the power cycle as well as the PCM tank charging, whiles in the night time the stored latent thermal energy is released from the PCM tank into the power cycle through the SG. Since

300 250

Temperature (ºC)

200 150 100 50 0 Data in Ref Simulated data

point 18 250.15 249.4

point 17 point 16 point 15 215.45 215.45 102.75 215.5 215.5 102.75

point 3 265.65 265.65

point 4 263.15 264

point 5 231.15 232

point 1 223.65 223.3

Fig. 6. Comparison of the developed model for heat exchanger in simulation and operating condition. 10

Angle (°)

180

4500

160

3500

140

2500

120

1500

100

500

80

-500

60

-1500

40

-2500

20

-3500

0

0

1

2

3

4

5

6

7

8

Incidence angle

Radiation (kj/hr/m2) & Flow rate (kg/hr)

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

-4500 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time (hour) Incidence angle on horizontal surface

Total radiation on horizontal

Total radiation on collector aperture

Collector flow rate Fig. 7. Total radiation, incidence angle and collectors flow rate on 11th of June.

the melting point of H250 is 250 °C, it cannot increase the thermal oil temperature up to 250 °C. However, the minimum required temperature for oil to generate superheated steam in the SG, as aforementioned in Section 3, is about 288 °C. Therefore, as can be seen in Fig. 8, through the discharging process of the LTES system, the superheated steam cannot be produced for the power cycle, and the auxiliary boiler is required (see also Fig. 9). By initiating of the sun shining at 6 Am, the solar energy absorbed by the thermal oil in the PTCs to supply the thermal energy of the power cycle. As depicted in Fig. 8, the thermal oil temperature increases by absorbing solar energy during day time, in part of the day it

can provide superheated steam. It should be mentioned that in some parts of the diagram during the day, the temperatures of point 3 and 4 in the heat exchanger were identical and therefore the superheated steam was not produced. In these cases, the auxiliary heater is turned on to generate steam at the desirable temperature (see Fig. 9). 5.3. Solar fraction According to Fig. 1, in the power cycle, part of the flow rate passes through the auxiliary boiler and part of it passes through the SG connected to PTCs. In Fig. 9, the required power which must be supplied in

400 Discharging

350

Charging

Discharging

Temperature ( °c)

300 250 200 150 100 50 0

0

T4

1

2

3 T5

4

5

6 T1

7

8

9 T3

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time (hour) T 3-max-boil

T 17

T 18

Fig. 8. Hourly temperature of the oil and steam in different parts of the heat exchanger. 11

Tin-turbine

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

Charging mode

Discharging mode

1.E+07

Discharging mode

1.E+07

Power ( kj/hr)

1.E+07 8.E+06 6.E+06 4.E+06 2.E+06 0.E+00

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time ( hour)

power of auxiliary heater power of boiler

power required in heat exchanger power of solar cycle

Fig. 9. Solar thermal power and auxiliary power.

the auxiliary boiler, as well as in the solar field, is demonstrated. Owing to the variation of solar power along the horizon of a day, as illustrated in Fig. 1, an auxiliary heater is installed after the SG. Therefore, as can be seen in Fig. 9, the sum of the solar power gathered in the PTCs and the auxiliary power prepared by the auxiliary heater equals the required power in the SG. Indeed, when the solar radiation is high, the auxiliary power is diminished, so that in some part of the day, the auxiliary heater is shouted down. Notably, adding the LTES system to the cycle, assisted the auxiliary system along with nighttime; Whiles, to prepare super-heated steam, the auxiliary heater is working at the night round. As a result, the solar fraction of the PTC assisted with the LTES system (H250 as PCM) is depicted in Fig. 10 on the 11th of June, typically.

temperatures of the oil in the LTES in the case of H250 is shown in Fig. 11. As illustrated in this figure, in the course of discharging of the LTES system, the thermal oil temperature is lower than the melting point temperature of H250. The oil output temperature from the thermal storage tank in the discharging mode is strongly dependent on the melting temperature of PCM. To find out the amount of the PCM required to preserve the power system in the horizon of nighttime, the melting and solidification process occurs in the LTES system during charging and discharging was investigated. In Fig. 12(a), the HTF flow rate during the charging mode (left cycle of the LTES in Fig. 1) and discharging mode (right cycle of the LTES in Fig. 1) as well as the amount of the melted PCM in the case of the H250 as the PCM on June 11th have been demonstrated. It is seen that from midnight to 6 a.m., the power cycle utilizes the latent thermal energy stored in the storage tank, and hence the melted PCM content diminishes until the solar radiation is initiated in the morning. Consequently, in the charging mode, due to the heat transfer from HTF to the PCM, the liquid PCM content is increased. At the end of the day, the right cycle of the LTES system was activated again, and power cycle

5.4. Latent thermal energy storage system The PTCs field size connected to the LTES is presumed as same as the PTCs field linked to the power cycle. The input and output 0.45 0.4

Solaer fraction

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hour) Fig. 10. Solar fraction on 11th of June. 12

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H. Jafari Mosleh and R. Ahmadi

450

Charging mode

Discharging mode

400

Discharging mode

350

Temperature ( °C)

300 250 200 150 100 50 0

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time (hour)

Tout-storage tank-discharging (T 24) Tout-storage tank-charging (T 22) PCM melting point

Tin-storage tank-charging (T 21) Tin-storage tank-discharging (T 23)

Fig. 11. Input and output temperature of the LTES during charging and discharging time (11 of June).

utilizes the stored latent thermal energy, and therefore the melted PCM is diminished. According to Fig. 12a, it is clear that the total melted PCM content during the charging period is more than the melted PCM that is utilized during the discharge time, and hence the total latent thermal energy stored in the thermal storage tank has not been used. Return to the power cycle and the PCM specification it can be inferred that the reason for this unbalancing in charging and discharging of thermal storage is related to the type of the PCM with low melting temperature. To examine the PCM performance in the LTES system, charging and discharging of different PCMs, namely H250, NaNO3, KNO3, and KOH, were investigated for ten subsequent days in July with different daily solar irradiation. The melting point of H250, NaNO3, KNO3, and KOH are 250, 308, 333, and 380 °C, respectively. The storage tank volume for both PCM was presumed to 200 m3. The results are depicted in Fig. 12b. In this figure, the melted PCM is reduced during the discharging period, and it increases in the charging period; however, the melted PCM is dependent on solar irradiation. In the case of H250, in the clear sky with high solar radiation, the producing of melted PCM during the charging period is higher than the consuming of melted PCM in the discharging period. Hence, in this case, the power cycle could not utilize the total stored heat in the LTES system. In other cases, in high solar radiation, the charging and discharging process are somewhat the same. In these cases, the power cycle utilizes the maximum of the LTES system capacity and have more contribution to the power cycle compared to H250. The reason returns to the melting point of the PCMs. In the course of discharging period of H250, this temperature level cannot produce super-heated steam for a power cycle, and therefore lower thermal energy is released from the LTES system. However, in the case of other PCMs, the LTES system can provide super-heated steam and therefore, more latent heat is transferred to the power cycle.

The total solar fractions utilized for the power generation employing different PCMs in LTES system are illustrated in Fig. 13. It is seen that NaNO3 own the higher solar fraction than other PCMs. The main reason returns to the proper melting temperature of the PCM. Using NaNO3, KNO3 and KOH in the LTES system with melting temperatures higher than 288 °C will provide superheat steam during the discharging period. However, in the case of KNO3 and KOH as PCM, one of the effective reasons that dump the solar fraction compared to the NaNO3 is the increase in the oil temperature in the solar collectors during the charging time of the heat storage tank; it leads to rising up the heat loss in the solar collectors. Hence, it can be concluded that a PCM with a melting point closer to the minimum temperature of the oil to provide superheated steam, is more appropriate. According to Fig. 13, the positive effect of the LTES system on the power cycle performance compared to the base Rankine cycle without LTES with the low solar fraction is obvious. In the case of using NaNO3 as the PCM in the LTES, the solar fraction has been increased by about 90.5% in comparison with the solar power plant without the LTES system. As was mentioned, the same solar field is assumed to preserve the LTES system. Hence, it is expected that with doubling the solar field size, the solar fraction must rise up twice times, but according to the results, this depends on the type of the PCM and only in the case of the NaNO3 this effect has happened. 6. Economic analysis Briefly, by applying the economic relation on the developing project, the payback period, IRR and NPV of the LTES system are obtained as 11 years, 15.6% and 617825$, respectively. Regarding the lifetime considered for the LTES system (30 years), this developing project can be regarded as a cost-effective project. In economic analysis, various parameters influence the economic analysis, and different values for economic parameters have been reported in different references. For consideration of different costs and economic parameters, a sensitivity analysis has been conducted, and the effects of different parameters such as electricity price, natural gas price, discount rate, solar collector field, and HTF system cost, and PCM cost on NPV have been investigated. For this reason, different prices for

5.5. Comparison of several PCMs and advantages For more comparison, the effects of different PCMs on the system performance have been discussed. In Table 6, several PCMs with different melting temperature and properties are considered to examine the effectiveness of them on the system performance. 13

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

50000

350000

45000

250000

Flow rate ( kg/hr)

35000 30000

Discharging mode

25000

Charging mode

Discharging mode

150000

20000 15000

100000

10000

50000

5000 0

200000

Amount of the melted PCM (kg)

300000

40000

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0

Time (hour) Flow rate of charging mode

Flow rate of discharging mode

The amount of the melted PCM

(a) 600000

2000 1000 0

400000

-1000 300000 -2000 200000

-3000

100000 0 3792

Radiation (kw/m2)

Amount of the melted PCM (kg)

500000

-4000

3816

3840

3864

3888

3912

3936

3960

3984

4008

-5000 4032

Time (hour) 7 to 17 th of June H250

NaNo3

KNO3

KOH

Radiation on collector span

(b) Fig. 12. (a) The amount of the melted H250 on 11 of June (b) The amount of melted PCMs (7 to 17 of June).

the natural gas price hurts NPV. Besides, with decreasing the discount rate, the NPV increases.

Table 6 Thermodynamic properties of different PCM used in simulations [32]. Material name

Density (kg/m3)

latent heat (kJ/kg)

Melting point (°C)

Thermal conductivity coefficient (W/m K)

NaNO3 KNO3 KOH H250

2257 2110 2044 2380

174 226 149.7 280

308 333 380 250

0.5 0.5 0.5 0.52

7. Conclusions In this study, the latent thermal energy storage (LTES) system was considered as an assistant system to enhance the concentrated solar power plant capacity factor and its reliability. First, the Shiraz solar power plant was simulated in TRNSYS to verify simulation methodology and find operation factors. Consequently, several phase change materials (PCMs) such as H250, NaNO3, KNO3, and KOH were studied in the LTES system appended to the CSP system. To model and simulate the transient behavior of the solar power plant equipped with the LTES system, a MATLAB code was developed for some subsystems in TRNSYS software. Simulation results revealed that:

electricity and natural gas was considered according to the stats quoted in the ref. [47]. For natural gas, the price range is 3 to 13.5 $/ m BTU, and for electricity, the price ranges from 0.08 to 0.33 $/kWh in different points of the world. The discount rate for solar energy technologies, according to ref [51]{Shafii, 2016 #67}, varies from 0.06 to 0.1. Also, 10 percent variation for solar collector field and HTF system cost and PCM cost considered in comparison with the prices mentioned in ref [44,45]. The result of the sensitivity analysis on NPV has been shown in Fig. 14. As can be seen, the NPV has the most sensitivity to the electricity price and the least sensitivity to the PCM cost. Enhancing the electricity price has a positive effect on NPV, and the other hand, rising

• NaNO has a higher solar fraction (34.14%) among other examined PCMs. In • the case of using NaNO as the PCM in the LTES, the solar fraction 3

3

has been increased by about 90.5% in comparison with the solar power plant without the LTES system.

14

Applied Thermal Engineering 161 (2019) 114204

H. Jafari Mosleh and R. Ahmadi

40% 35%

34.14%

33.10%

31.93% 28.68%

Solar fraction

30% 25%

17.92%

20% 15% 10% 5% 0% NaNo3

KNO3

KOH

H250

Without LTES

PCM name Fig. 13. Annual solar fraction for different phase change materials.

NPV -$60,00,000

-$40,00,000

-$20,00,000

Electricity price $/kwh

Natural gas price $/m BTU

$0

$20,00,000

$40,00,000

$60,00,000

0.33

0.08

13.50

3.00

discount rate

0.10 0.06

solar collector cost ($/m2)

308.00

PCM cost ($/kg)

252.00

0.22

Upside

0.18

Downside

Fig. 14. Sensitivity analysis on NPV.

• Choosing a PCM with a melting point closer to the minimum tem• • •

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perature of the oil to provide superheated steam is more appropriate. In the case of selecting KNO3 and KOH as PCM, one of the reasons that can reduce the solar fraction compared to the NaNO3 is the thermal loss in the collectors due to the increase of thermal oil temperature. According to the economic analysis, the payback period, the IRR and NPV of the LTES system are obtained as 11 years, and 15.6% and 617825$, respectively. The result of the sensitivity analysis on NPV revealed that the electricity price has the most effect on NPV and Enhancing the electricity price has a positive impact on NPV. On the other hand, enhancing the natural gas price hurts NPV.

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