2.2 System sustainability

Sustainability of a system is a vital measure to decide the future of any technology. Generally, cost of the systems, environmental impacts, and social acceptance define the sustainability of the system. Cost is the primary indicator to choose the most economical technology among all available options. It includes all types of costs including start-up, installation, operation, and maintenance cost. Environmental impact is another important parameter which considers the effects of any technology on the environment from its initiation to disposal. Severity of this parameter in decision-making is increasing continuously because of greenhouse gas emissions and consequent global warming [7].

#### 2.2.1 Cost

As described earlier, the cost of any system is the most important factor for the sustainability of the system. It is quite logical that any renewable energy technology will be able to penetrate market if the cost associated with its unit production is less than the unit cost of electricity through grid station operated on fossil fuels. It is defined as grid parity, and it is based on the levelized electricity cost (LEC) which can be estimated using Eq. (1):

$$LEC = \frac{f\_{cr}IC + C\_{O\&M}}{E\_{el}} \tag{1}$$

where fcr is the annuity factor, IC is the investment cost, CO&<sup>M</sup> is the annual operation and maintenance cost, and Eel is the annual net electricity output, and annuity factor can be calculated using Eq. (2):

$$f\_{cr} = \frac{k\_d \left(\mathbf{1} + k\_d\right)^n}{\left(\mathbf{1} + k\_d\right)^n - \mathbf{1}} + k\_{ins} \tag{2}$$

where kd is the real debt interest rate, kins is the annual insurance rate, and n is the depreciation period in years [7].

In both cases, the primary cost component is the initial cost of the system. According to the International Energy Agency (IEA), estimated initial cost for PV plant ranges from 2000 to 5200 US\$/kW, while it lies in the range of 4200–8400 US \$/kW for CSP plants. Further, the maintenance cost for PV is 1% of the initial cost. This value is approximately 2% of the initial cost in CSP. The difference in such

costs is due to the complexity of the CSP system. Interestingly, even after the initial and maintenance cost difference, economic returns and incentives of CSP plant are higher as compared to PV plants. PV technology works only during daytime and totally unavailable during peak consumption hours of electricity. CSP technology has the capability to shift its production to peak consumption hours and also takes advantage of higher tariff rates during peak consumption hours [7].

#### 2.2.2 Environmental impact

Impacts of any technology on the environment throughout the life cycle of the technology are an important measure to define sustainability of the system. The approach usually considered from cradle to grave is called life-cycle assessment (LCA). In terms of PV and CSP plants, most of the carbon footprints are during the manufacturing/installation and decomposing. During operational stage, there is almost no impact on the environment [7, 8].

In the case of PV plants, primary reason is the manufacturing of PV cells and modules, and the measure of greenhouse gas emissions is almost 50 g CO2 eq/kWh for PV plants throughout the life of the plant according to NREL. It involves such ways and materials that pose severe threat to the environment [7, 8]. Particularly, the cell materials in second generation are more hazardous, and breathing in silicon dust is dangerous for workers according to NREL claims. In CPV, the issue is mainly due to mirrors and collector tube. The institute also reported that greenhouse gas emissions for CSP plants range from 22 to 23 g CO2 eq/kWh during the life cycle of such plants. Overall, environmental impact of CPV is higher throughout life as compared to CSP [7, 8].

#### 2.2.3 Social acceptance

Adoption of a new technology by the customers and end user is extremely important for the success of the technology. In the case of PV and CSP, the technology is warmly welcomed by all societies around the globe. Mainly, such plants are developed in Spain, the United States, and India. Solar energy is used in street lights, for pumping water and solar cooking, domestic level applications, and grid level mega power plants. The growth in both sectors is continuously increasing as the cost of the technology is getting lower than the fossil fuel-based electricity. Further, the public is aware of the clean and noise-free generation of electricity. Mainly, CSP is used for large-scale applications; however, the scale of PV is extremely large spanning from domestic use to the grid-integrated mega power plants [7].

Next sections deal with the concentrated solar power (CSP) technology from different design, thermal fluid and heat transfer characteristics.

#### 3. Heat transfer in concentrated solar power plants

Basic principle of CSP lies on thermal energy capturing, transportation, and harnessing it. In all stages, heat transfer is involved. All modes of heat transfer in CSP are detailed in the subsequent section.

#### 3.1 Heat transfer by radiation

Radiation is energy emitted by a solid object, liquid, or gas that is at a finite temperature. This matter can also dissipate radiant energy impinging on it by

Advances in Concentrated Solar Power: A Perspective of Heat Transfer DOI: http://dx.doi.org/10.5772/intechopen.84575

reflection and can be capable of absorption. It is classified into two, short wavelength of high energy originating from the sun and long wavelength of low energy originating from lower-energy sources [9]. The radiation energy can be balanced in CSP plants as [10]

$$(\mathbf{1} - r)\mathbf{S} + L = L + H + \lambda E + G \tag{3}$$

where (1 � r)S represents short radiations, L represents long radiations, H is sensible heat, λE is latent heat, and G is heat exchange by conduction.

Therefore, the net radiations are

$$R\_n = (\mathbf{1} - r)\mathbf{S} + L - L = H + \lambda E + G \tag{4}$$

The total energy absorbed into the system is converted into sensible heat, latent heat, and heat conductions [10].

Sunlight includes different spectra of wavelength starting from very short (extreme energy) to very long (low energy). The relation of wavelength and frequency is given as

$$
\lambda = \frac{c}{\nu} \tag{5}
$$

where λ is the wavelength, ν is the frequency, and c is the speed of light.

For a radiative-emitting surface of an arbitrary element of area dA1, a differential solid angle dω may subtend a point onto a differential area dA2; the differential solid angle can be defined as

$$dw = \frac{dA\_2}{r^2} \tag{6}$$

where dA2 is the differential area. Spectral radiation (G) can be calculated as

$$G\_{\lambda}(\lambda) = \int\_{0}^{2\pi} \int\_{0}^{2\pi} I\_{\lambda}(\lambda, \theta, \mathcal{Q}) \cos \theta d w \tag{7}$$

where

$$dw = \sin\theta d\theta d\bigotimes\tag{8}$$

Considering total radiations as the rate of radiation from all sides per unit area from all directions and at all wavelengths

$$\mathbf{G} = \int\_0^\infty \mathbf{G}\_\lambda(\lambda) d\lambda \tag{9}$$

For the case of diffuse radiations, Iλ(λ) is free of θ and φ as

$$\mathbf{G}\_{\dot{\lambda}}(\lambda) = \pi I\_{\dot{\lambda}}(\lambda) \tag{10}$$

The amount of reflected radiation radiations is the rate at which radiation of wavelength λ leaves a unit area of the surface per unit wavelength interval dλ. It can be calculated as

$$J\_{\lambda}(\lambda) = \int\_{0}^{2\pi} \int\_{0}^{2\pi} I\_{\lambda, \epsilon + r}(\lambda, \theta, \varphi) \cos \theta \sin \theta d\theta d\varphi \tag{11}$$

Finally, in general, most engineering heat transfer applications are employed to characterize the radiative heat transfer interaction between an object and its environment with respect to wavelength:

$$
\dot{Q}\_{rad} = \sigma \varepsilon\_k A \left( T^4 - T\_\infty^4 \right) \tag{12}
$$

where σ is the Stefan-Boltzmann constant, 5.67 x 10�8 W/m2 K4 , A is the object surface area, and T<sup>∞</sup> is the ambient temperature.

#### 3.2 Heat transfer by conduction

Heat transfer by conduction is occurred due to lattice vibration in solids and particle collision in stationery fluids. In a solid with temperature gradient onto surfaces, the one with higher temperature experiences higher level of collision among particles, so it transfers its energy to the neighboring particles which transfer it further [11]. In the same way, heat is transferred from hot to cold surface until steady state is achieved. The rate of heat transfer by conduction is given by Fourier's law as

$$
\dot{Q}\_{cond} = kA \frac{dT}{dx} \tag{13}
$$

where A is the surface area, k is the thermal conductivity, dT is the temperature gradient across surfaces, and dx is the length between the surfaces between heat transfers that are measured.

In CSP plants, heat transfer due to conduction is always changing with time; that's why it is necessary to understand the transient nature of conduction heat transfer. In certain scenarios, lumped systems are assumed while calculating heat transfer at the interface of solid and liquid. The reason is that heat conduction within the solid is comparatively negligible as compared to the heat transfer from solid to the fluid at its interface. It is further necessary to confirm that there are no spatial temperature changes within the solid to assure its lumped natured. After a specific time, the system will reach a steady state when high thermal energy of solid is transferred to the low-temperature fluid to eventually reaching the same level of temperatures [12]. The time can be calculated as

$$\frac{T - T\_{\infty}}{T\_i - T\_{\infty}} = \exp\left(-\frac{hA\_s}{\rho V c\_p}\tau\right) \tag{14}$$

where T is the temperature of hot-surfaced solid,T<sup>∞</sup> is the ambient temperature, Ti is the initial temperature, h is the convective heat transfer coefficient, As is the surface area at the solid-fluid interface, ρ is the density of the fluid, cp is specific heat capacity, and τ is the thermal time constant. The constant can be calculated as

$$
\pi = \frac{\rho V c\_p}{hA\_s} = RC \tag{15}
$$

where R is the convective resistance and C is the lumped capacitance of the solid. To confirm the validity of lumped capacitance, Biot number (Bi) can be calculated as

$$Bi = \frac{hL\_c}{k} = \frac{R\_{cond}}{R\_{conv}} = \frac{L\_c/\_{hA}}{1/\_{hA}} = \frac{T\_{s,1} - T\_{s,2}}{T\_{s,2} - T\_{\infty}}\tag{16}$$

Advances in Concentrated Solar Power: A Perspective of Heat Transfer DOI: http://dx.doi.org/10.5772/intechopen.84575

For the value of Biot number less than 0.1, it is assumed that temperature within the solid is nearly the same, and the maximum temperature difference is at the interface of solid-fluid. Rearrangement of equations provides us

$$\frac{T - T\_{\infty}}{T\_i - T\_{\infty}} = \exp\left(-Bi.F\_0\right) \tag{17}$$

where F0 is a dimensionless number which characterizes transient problems and can be calculated as

$$F\_0 = \frac{\left(\frac{k}{\rho c\_p}\right)t}{L\_c^2} \tag{18}$$

where Lc is the characteristic length which is different for rectangular, cylindrical, and spherical coordinate systems [12].

For rectangular coordinates, Lc ¼ L For cylindrical coordinates, Lc <sup>¼</sup> <sup>r</sup> 2

For spherical coordinates, Lc <sup>¼</sup> <sup>r</sup> 3

#### 3.3 Heat transfer by convection

Heat transfer through convection occurs between fluid in motion and its bounding surface. The heat transfer can happen naturally due to buoyancy effect in which medium moves due to the density difference caused by the variation in temperature. It is called natural convection. On contrary, a fluid can be forcefully pushed or pumped through mechanical means like fans or pumps. The heat transfer through this way is called forced convention. Heat transfer through convection can be measured as

$$
\dot{Q}\_{conv} = hA\_s(T\_s - T\_\infty) \tag{19}
$$

where h is the convective heat transfer coefficient, As is the surface area,Ts is the temperature of hot surface, and T<sup>∞</sup> is the ambient temperature. The range of convective heat transfer coefficient for gases is 2–5 and 25–250 W/m2 K for natural and forced convections, respectively [12]. The ranges 50–1000 and 100– 20,000 W/m2 K are for liquids in natural and forced convection cases, respectively [12]. For materials that involves phase change (boiling and condensation), the range is 2500–100,000 W/m2 K [12]. This extraordinary difference in the coefficient value is exploited in CSP plants using heat pipes involving boiling and condensations. In CSP applications, Newton's law of cooling (dt = Ts � T∞) can overpredict the heat transfer rate. More accuracy to calculate heat transfer rate per unit length can be obtained using [12]

$$\Delta T\_{lm} = \frac{(T\_s - T\_\infty) - (T\_s - T\_0)}{\ln \left(\frac{T\_s - T\_i}{T\_s - T\_\infty}\right)}\tag{20}$$

and the outlet temperature of the fluid passing through the pipe can be calculated using

$$\frac{T\_s - T\_i}{T\_s - T\_\infty} = \exp\left(-\frac{\pi DN\overline{h}}{\rho V N\_T S\_T c\_\hbar}\right) \tag{21}$$

where ST is the transverse pitch, D is the tube diameter, N is the number of tubes, and (h) is the average value of heat transfer coefficient. Finally, heat transfer can be obtained with the following

$$
\dot{Q}' = N(\overline{h}\pi D\Delta T\_{lm})\tag{22}
$$

## 4. Thermal energy storage in concentrated solar power

The prime difference between PV and CSP plant is an optional storage of solar energy in CSP and to harness it during the most demanding hours to produce electricity. This feature makes the CSP capable of electric power production during evening, the time after closing of offices, when the demand of electricity is at its peak [13]. At that time, output of CPV plant is zero, and it creates a big mismatch between supply and demand. Although a solution for such mismatch is to store electricity in large-scale batteries during sunshine hours so as to supply during evening and night, the option of batteries is very costly and environmentally unacceptable. Solar energy in the form of thermal energy storage (TES) is comparatively much better option as compared to the electrical energy storage in batteries because it is inexpensive and has minimal environmental impacts [14]. Few of the CSP plants are equipped with TES systems, while others do not have this feature.

Performance of a CSP plants with TES systems is dependent on the design of integration of TES into the power generation cycle (thermodynamic process) of the plants [15]. Generally, TES is classified into two main categories based on the motion state during charging and discharging, i.e., active systems and passive systems. Charging is the process in which heat is fed to the medium to raise its energy, while discharging is the process in which heat is extracted from the medium to bring it back to the original state. In active systems [16], thermal energy is stored into a medium which also acts as energy carrier. The medium with high thermal energy is pumped, and it transfers its energy to the thermodynamic cycle through forced convection. In passive system [17], thermal energy is stored into a stationery and motionless medium through which thermal fluid is circulated to extract heat, and the thermal fluid is circulated through the thermodynamic cycle to deliver thermal energy there. The following sections contain the further classifications of such systems with visual illustrations for clear understandings.

#### 4.1 Active direct concept for TES

Active systems are further categorized into direct and indirect systems. In direct active systems, energy materials serve the dual functions of energy storage and transportation. In such systems, TES materials absorb heat from solar absorber during charging and stored in a hot tank as shown in Figure 2 [13]. During discharging, the TES material is pumped from the hot tank to the thermodynamic cycle where it transfers its energy to the system and return back to cold storage. For the next charging cycle, the TES material is again pumped to solar absorber to gain energy for the next cycle. In this design, heat exchanger is not required; however, the TES material should have properties of heat storage capacity and good flowability [15].
