Energy Conversion and Management 225 (2020) 113378

Available online 18 September 20200196-8904/© 2020 Elsevier Ltd. All rights reserved.

Performance enhancement of solar tower power plant: A multi-objective optimization approach

Ahmed Bilal Awan a,*, Kotturu V.V. Chandra Mouli b, Muhammad Zubair c

a Department of Electrical and Computer Engineering, College of Engineering and Information Technology, Ajman University, Ajman, UAE b Department of Mechanical Engineering, College of Engineering, Majmaah University, Almajmaah, Saudi Arabia c Department of Electrical Engineering, College of Engineering, Majmaah University, Almajmaah, Saudi Arabia

A R T I C L E I N F O

Keywords: Solar tower plant Thermal energy storage Solar multiple Multi-objective optimization Particle swarm optimization LCoE

A B S T R A C T

The aim of this research is to design, optimize, and evaluate the performance of the solar tower (ST) power plant. The plant is initially designed for solar multiple (SM) of 2, tower height of 190 m and 10 h of full load thermal energy storage (TES). The initial design of the plant is optimized for number of full load storage hours, tower height and SM using multi-objective optimization technique. A fuzzy goal programing approach and an evolu-tionary computational technique, particle swarm optimization are used. The optimized design parameters converge to SM of 2.7, tower height of 205 m and TES system of 8.7 h. The optimized and initial designs of the plant are compared based on annual and lifetime energy output, capacity utilization factor (CUF), land use factor, solar to electric efficiency, levelized cost of energy (LCoE), and net capital cost (NCC). The main opti-mization objectives are LCoE and energy output. Although the optimized ST plant design has 13.5% more NCC and 0.9% less solar to electric efficiency, but the optimized design has outperformed the initial design in all the other performance parameters. It has 16.2% better CUF with 35.6% better energy output, 3.1% better land use factor and 16.9% lower LCoE compared to the initial design. The optimized design utilizes the TES system more effectively and it can produce electricity for longer duration after the sunset. It has long average operational hours from 8 am to 3 am as compared to initial design from 8 am to 10 pm.

1. Introduction

Exploitation of solar energy is indispensable to resolve the problems such as fossil fuels crises, global warming, high electricity prices, and increasing demand of energy due to industrial and population growth [1]. In recent years, concentrated solar power (CSP) technologies have been the focus of many researcher due to their ability to generate huge amount of electrical power at utility scale with reasonable levelized cost of energy (LCoE) [2]. It is expected that CSP would be able to fulfill around 11% of the world’s electrical energy demand by 2050 [3]. There are four major types of CSP technologies, namely parabolic dish system, linear Fresnel reflector, parabolic trough collector and solar tower (ST). The ST technology has a distinctive edge of high efficiency and scal-ability over the rest of CSP technologies [4,5]. Central receiver ST technology comprises a large number of heliostat mirrors and central receiver situated on the tip of tower which receives the concentrated sun rays from heliostats. This CSP technology can attain temperatures above 1000 ◦C [6]. The converted solar thermal energy can be used to run a

thermodynamic cycle and the excess thermal energy can be stored in thermal energy storage (TES) system. The TES system solves the inconsistency and instability problems of renewable energy systems [7]. The thermal energy stored in the TES system can be utilized to produce electricity even after sunset. Furthermore, the fluctuations of solar ra-diations in inclement weather can be supplemented by energy stored in TES system. Thus the TES augments the CUF of the plant and the value of generated electrical energy [8].

The thermal size of the heliostat field can be defined by solar mul-tiple (SM) concept. SM is the fractional over sizing of the heliostat field as compared to the designed thermal power capacity of the plant. It is the ratio of maximum thermal power received by the heat transfer fluid (HTF) to the power block input thermal power at design point. It is an important design parameter for economic performance of the plant because a major part of the investment (around 50%) of a ST plant is required for heliostat field [9,10]. Therefore, it is essential to carry out an optimal design layout and find an optimal size of the heliostat field.

Wang et al. [11] used multi-objective optimization approach to

* Corresponding author. E-mail address: a.awan@ajman.ac.ae (A.B. Awan).

Contents lists available at ScienceDirect

Energy Conversion and Management

journal homepage: www.elsevier.com/locate/enconman

https://doi.org/10.1016/j.enconman.2020.113378 Received 8 June 2020; Received in revised form 25 August 2020; Accepted 26 August 2020

Energy Conversion and Management 225 (2020) 113378

2

achieve homogeneous distribution of solar flux on cavity receiver without really affecting the optic losses. They proposed and optimized the multi-point aiming strategy instead of the single-point strategy. Two conflicting objectives of curtailing optical losses while minimizing non- uniform distribution of solar flux were considered in their optimization approach. Both the aiming points distribution on the receiver and aim-ing points allocation to different heliostats were concurrently optimized. Farges et al. [12] presented an optimization approach to maximize the annually captured thermal energy and optical efficiency of heliostat field by coupling of Monte Carlo algorithm and Particle Swarm Opti-mization (PSO) algorithm. The size of the heliostat field is normally expressed in term of SM. A small sized heliostat field with small SM decreases the performance of the plant. On the other hand, too large heliostat field with very large SM is not fully utilized during peak solar irradiance intervals and also number of less efficient heliostats increases in large fields [13]. Zhao et al. [14] optimized a hybrid solar–coal plant for SM. Their results show that optimization of SM leads to minimize the payback period and LCoE.

The optimization of heliostat field layout has been widely studied since 1970s [15,16] but relatively less attention has been paid on the optimal size of the heliostat field in context of full load TES hours. The TES capacity is defined by the number of hours the storage system can provide thermal power to power block to operate at its rated capacity. The optimal size of TES system and heliostat field are interdependent. Therefore, it is important to optimize these two parameters simulta-neously for maximizing the energy out of the plant and consequently achieving minimum LCoE. Coelho et al. [17] studied the impact of control strategy, TES capacity and SM on the LCoE of a volumetric central receiver ST plant. They concluded that optimization of these parameters can lead to better performance and economic benefits. Avila- Marin et al. [8] first optimized the SM by designing a heliostat field for a gross electrical output of 111 MW. The authors then optimized the TES by varying the gross turbine power and optimizing the TES hours for different sizes of turbine. The authors concluded that the optimized TES system minimizes the LCoE for 14–16 h of TES with gross turbine power in the range of 33 MW to 78 MW. Thaker et al. [18] developed five scenarios based on the method and type of storage. The considered scenarios of storage options were thermochemical, latent heat, one tank direct sensible heat, two tank direct sensible heat, and indirect sensible heat storage. Flueckiger et al. [19] optimized the TES and SM of a 100 MW ST plant for size of thermocline tank. Their result proved that the LCoE is minimum for a 16 h of TES capacity with a SM factor of 3.

Carrizosa et al. [20] optimized the ST plant with multiple receivers. They considered the aperture size, aperture tilt angle, azimuth angle and height of tower along with layout of heliostat field in the optimization process to achieve minimum levelized cost of thermal energy. The height of ST is an important design parameter because it decides the height of receiver and it affects the optical efficiency of the heliostat field because of shading, blocking, cosine, and attenuation losses. A lower tower height causes more shading, blocking, and cosine losses [21] for the same boundary limits while a very high tower causes more attenuation losses due to increase in slant height from heliostats to receiver [22]. The location of receiver (height of tower) and SM are interdependent [20]. Similarly, TES and SM are interdependent as well [17]. Since, all these three parameters are interdependent; therefore, it is very important to optimize the height of tower along with SM and TES capacity to enhance the overall performance of the plant in terms of energy and LCoE.

The optimal design of ST power plant should be such that energy is maximized and LCoE is minimized simultaneously. In the optimization process, at certain values of SM, tower height and TES hour parameters, optimal energy and optimal LCoE functions are conflicting each other and dominated solutions are observed. A common problem encountered in solving a multi-objective optimization problem is that the decision maker has to choose a problem dependent function to identify a compromise solution. In this paper PSO algorithm is applied to solve the

constrained optimization function and generate an ideal solution for each objective function. Fuzzy constraints are developed taking linear membership of each objective function and corresponding ideal solu-tion. Using fuzzy max–min operator approach [23] a compromise so-lution of multi-objective function is obtained by maximizing overall satisfactory level with minimum membership of each objective function [24]. To the extent of authors’ knowledge, the existing literature does not consider all these three interdependent parameters (SM, tower height and TES hours) in the optimization process.

2. Modeling

The working model of ST power plant is shown in Fig. 1. It comprises three major sub-systems called heliostat field along with tower and receiver, power block, and TES system. The heliostat field consists of a huge number of mirrors which track the sun and concentrate the sun rays on to the receiver situated on the tower top. The HTF circulating in receiver tubes absorbs the thermal energy of the concentrated solar ra-diations and takes it to the power block which utilizes this heat to run a thermodynamic cycle with steam or gas turbine coupled with electric generator. The excess heat during the peak solar irradiance time is stored in the TES system.

2.1. Power block

The maximum losses take place in the power block. The thermal power that is required at the input of the power block to generate the design capacity of the plant is given by [26]

Ppb =Pd

ηpb

where, Pd is design capacity of plant, Ppb is power block thermal power input, and ηpb is the efficiency of power block. The thermal power of the HTF that will generate the design capacity is

Phtfd =Ppb

ηhe=

Pd

ηhe.ηpb

where, Phtfd is the thermal power of HTF for design capacity and ηhe is the efficiency of the heat exchanger.

2.2. Heliostat field

The thermal energy needed to be collected from heliostat field and reflected on receiver for design capacity is demonstrated by the following relation [26]

Phfd =Phtfd

ηrec=

Pd

ηrec.ηpb.ηhe

where ηrec is receiver efficiency. The reflected solar power of the helio-stat field on to receiver is given by

Phf = Pf ηh

where, ηh is the heliostat optical efficiency and it incorporates mirror reflectance, shading and blocking losses, atmospheric attenuation fac-tor, and cosine factor. The Pf is the solar power hitting the heliostat field and is given by

Pf = DNI.Ah

where, Ah is the total area of heliostats and DNI is direct normal irra-diance. The instantaneous optical efficiency of the heliostat k is expressed as [4,27]

ηh = ρ.cosθin,k.ηatt,k

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

3

where, cosθin,k is cosine factor of heliostat k at hour n, ρ is the reflectivity of the heliostat, ηatt,k is the atmospheric attenuation factor of heliostat k and it depends on weather and position of the heliostat with respect to tower. The cosine factor has a major impact on the performance of he-liostats. It is the incidence cosine between incident ray and the normal to the heliostat surface. It can be determined by using the reflected and incident vectors as explained in [4]

cosθin = cos(

arccos(

S→.R→)/

2)

where, S→ and R→ are incident and reflected vectors. Heliostats are ar-ranged in circular arcs around the tower. The blocking and shading losses are curtailed by reducing the packing density in the field at larger radial disctances from the tower. The packing density is ratio of surface area of heliostat mirrors to heliostat field land area and its variation was calculated by Srilakshmi et al. based on the heliostat field data of the existing ST plants (PS10, PS20, Gemasolar and Crescent Dunes) [26].

ρpd = 0forrh<(r

h

)

min

ρpd = 0.492 − 0.0939.rh

for(r

h

)

min≤

rh≤ 2.8

ρpd =0.6(r

h

)2− 1

√ forrh> 2.8

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

where, r is radial distance, h is tower height, and ρpd is the packing density. The attenuation factor represents the beam losses of the re-flected rays and it mainly depends on the distance between receiver and the heliostat. There are different attenuation models available in liter-ature such as DELSOL model (hazy day and clear day model) [28], MIRVAL model [29], Pitman & Vant-Hull model [30], and Sengupta & Wagner model [31]. The DELSOL model has separate expressions for hazy day and clear day while the other attenuation models do not differentiate between hazy and clear day. The MIRVAL model [29] is a preferred option because the atmosphere at the proposed location is mostly clear and this model has the ability to calculate attenuation losses

more accurately for a large heliostat field by dividing the attenuation model into two parts, i.e. for slant height of up to 1000 m and slant height of greater than 1000 m. It was theoretically calculated by Leary and Hankins using a computer code and they develped the following expression for its calculation [29]

ηatt,k =0.99321 − 0.0001176dk + 1.97 × 10− 8d2

k fordk ≤ 1000mexp( − 0.0001106dk)fordk > 1000m

}

where, dk is the distance between heliostat k and receiver. At any hour n, the solar energy available for receiver can be calculated as [26]

Precn = (h)2×

(

Ah × ρ ×∑Nh

k=1DNIn × cosθin,k × ηatt,k × ρpd

)

where, DNIn is DNI at any hour n, and Nh is the number of heliostats. In order to prolong the working hours of the plant after the sunset, nor-mally the SM of the plant is greater than one. The SM indicates the amount by which the heliostat field is oversized. It is the quotient of thermal energy received by the HTF from the field and the thermal power of HTF required for the design electrical capacity [32]

SM =Phtfhf

Phtfd

where, Phtfhf is the thermal energy transferred to the HTF from heliostat field. The relation between the tower height and SM is expressed as [33]

hSM = h ×SM

√

where, hSM is the tower height required for given SM and h is the tower height for the design capacity (SM = 1). Therefore equation (10) for solar energy reaching the receiver for a given SM is modified as

PrecSM = (hSM)2×

(

AhSM × ρ ×∑NhS M

k=1DNIn × cosθin,k × ηatt,k × ρpd

)

where, AhSM is the total area and NhSM is the number of heliostats for given SM. The thermal energy of the HTF for a given SM at any hour n is

Fig. 1. Working model of ST power plant [25].

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

4

demonstrated by the following equation

PhtfSM = (hSM)2×

(

AhSM × ρ × ηrec

∑NhS M

k=1DNIn × cosθin,k × ηatt,k × ρpd

)

The annual thermal energy of the HTF is given by the following equation

Eth =∑8760

n=1PhtfSM

where, n denotes the number of hours in one year (8760 h). The annual electrical energy of the plant is computed as

Eg = ηstoηpbηhe

∑8760

n=1PhtfSM

2.3. Receiver

The receiver collects the solar power reflected by the heliostats and transfers it to the HTF. The power balance equation of the receiver is

Pr = Prec − Prloss

where, Pr is the power delivered to the HTF, Prec is the power reaching the receiver from the heliostat field, and Prloss is the receiver power losses, which are expressed as

Prloss = Pref +Prad +Pcon

where, Pref is power loss due to reflection from the surface of the receive tubes, Prad is radiation loss and Pcon is convection loss. These losses are given by

Pref = (1 − δ)Prec

Prad =∑

εKAt(T4

w − T4amb

)

Pcon =∑

fmixAt(Tw − Tamb)

⎫⎪⎪⎪⎬

⎪⎪⎪⎭

(19)

Where, δ is solar absorptance of panel tubes (0.94), ε is the emittance (0.88), At is the lateral surface of the tube, K is the Stefan-Boltsman constant, Tamb is the ambient air temperature, Tw is the wall tempera-ture, and fmix is the mixed convection coefficient.

2.4. Thermal energy storage

The ST plant with SM greater than one must have a TES system. If PhtfSM > Phtfd , the TES system will store the excess thermal energy. The maximum storage capacity of the TES system is detemined as [34].

Estomax =Phtfd × ts

ηsto

where, ts is number of full load TES hours and ηsto is the efficiency of the TES system.

3. ST plant design

The proposed 100 MW ST plant is designed for Majmaah (25.86◦ N and 45.42◦ E), Saudi Arabia. Literature reveals that a DNI of 1800 kWh/ m2/year (approximately 5 kWh/m2/day) is the threshold value for economic viability of CSP technologies [35,36]. The average DNI at the

proposed location is 6.63 kWh/m2/day which is well above the mini-mum required DNI for a CSP project. The monthly average distribution of the DNI is tabulated in Table 1. The plant is initially designed for a SM factor of 2 and 10 h of full load TES. The design compendium of the initial design is presented in Table 2 and the step by step procedure for sizing of different constituents of the plants is detailed below.

3.1. Heliostat field

The circular heliostat field having radial staggered layout is adopted for the proposed ST plant because this configuration is more common in the existing commercial scale power plants [37] and it has better optical efficiency [38]. The heliostats in this layout are arranged to surround the tower in circles of different radial distances. The distances between the adjoining heliostats are shown Fig. 2 [13]. The azimuthal and radial spacings of adjoining heliostats are demonstrated as [39,40].

ΔR = Hh(1.44cotθk − 1.094+ 3.068θk − 1.125θk

2)

ΔA = Wh

(

1.749+ 0.6396θk +0.2873

θk − 0.04902

)

where, θk is altitude angle of receiver to kth heliostat, Hh is height and Wh is width of heliostat. To reduce blocking losses, the gap between helio-stats needed to be increased at larger radial distances from tower. Therefore, the packing density of heliostats decreases at larger radial distance from the tower (equation 8).

The mirror area of the heliostat field and eventually the number of heliostats is determined based on the SM factor and the plant size. The sizing of the field involves following steps.

• Plant capacity, efficiencies of different components and DNI data as input

• Calculate the thermal power of the HTF (Phtfd ) required to generate designed electrical power (equation 2)

• Calculate the thermal power to be reflected (Phf ) on the receiver (equation 3)

• Based on the given data of DNI, decide the design point DNI. • Calculate the required heliostat mirror area for the solar power to be

reflected on the receiver for design capacity using design point DNI and optical efficiency of heliostats.

Ah =Phfd

DNI.ηh

• Calculate the number of heliostats based on total required mirror area.

Table 1 Monthly average DNI (kWh/m2/day) at Majmaah.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

6.26 5.57 7.36 6.11 6.36 7.80 7.48 7.04 7.00 7.45 4.77 6.20

Table 2 Design parameters for the initial design.

Parameter Value

Plant design capacity 100 MW Full load TES hours 10 Solar Multiple 2 Heliostat field TES hours 5 Power block inlet temperature (HTF) 574 ◦C Power block outlet temperature (HTF) 290 ◦C Cycle thermal power 269 MWt

Cycle thermal efficiency 0.412 Boiler pressure 100 bar

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

5

Nh =Ah

A

where, A is the area of single heliostat

• The number of heliostats for a given SM is calculated by

NhSM = Nh × SM

For the initial design with SM value of 2, the required number of heliostats are calculated to be 6818. The design parameters of the he-liostat field are shown in Table 3.

3.2. Tower height

Tower height is an important design parameter. It affects the blocking, shading, cosine, and attenuation losses and heliostat boundary [21,22]. The step by step procedure to calculate the tower height is given below:

1. Initially calculate the tower height for SM equal to one and attenu-ation efficiency of 100%

2. Calculate the thermal power of the HTF (Phtfd ) that will generate the design capacity power (equation 2)

3. Calculate the following power term (Pn) for each hour of the year

Pn = Ah × ρ × ηrec

∑Nh

k=1DNIn × cosθin,k × ρpd(26)

4. Determine the maximum value of Pn out of 8760 h (Pnmax) 5. Determine the initial height of tower by

h[1] =

Phtfd

Pnmax

√

6. Select the attenuation model 7. Calculate the power reaching the receiver for the initial tower height

for each hour of the year for SM = 1 (equation 10) 8. Determine the maximum value of this power reaching the receiver

(Precmax)

9. Calculate the maximum thermal power delivered to HTF

Phtfmax = Precmax×ηrec

If Phtfmax < Phtfd

- Then increase the tower height h[1] by a little fraction (Δh = 5m) and repeat steps 7,8, and 9 for updated tower height

If Phtfmax > Phtfd

- Decrease the tower height h[1] by a little fraction (Δh)

Then

- For further refining the calculations, decrease the height fraction ten times i.e. (Δh = Δh/10).

- Repeat steps 7,8, and 9 until (Δh < 0.1m)

10. The tower height for a particular SM is calculated as

hSM = h[1] ×SM

√

The tower height for the initial design of SM value of 2 with 10 h of storage is 190 m.

3.3. Receiver

The proposed design uses external cylindrical tubular receiver. The external cylindrical receiver is preferred over cavity receiver because it accepts reflected solar radiations from 360◦ while cavity receiver has only 60◦ angle of reception. The average flux of cavity receiver panels is lower due to these geometrical constrains. The cavity receiver is more expensive owing to its larger structure [41]. The procedural steps for receiver sizing are listed below:

• Calculate the maximum thermal power of receiver for a given SM from Eq. (13)

• Fix the maximum allowable receiver flux limit (Qmax) • Calculate the average receiver flux from the following relation [42].

Qave =Qmax

peaktoaveragefluxratio

Normally, range of maximum flux for molten salt external cylindrical receiver is between 600 and 1200 kW/m2 [41]. The maximum receiver flux for the proposed design is 1000 kW/m2 [43]. The peak-to-average flux ratio for Gemasolar ST plant is 1.9 [42] while Falcone in his 100 MW ST plant design used a peak-to-average flux ratio of 1.78 [41]. The peak-to-average flux ratio of 1.8 is used for the proposed plant design.

Fig. 2. Adjacent heliostats’ radial and azimuthal distances [13].

Table 3 Design parameters of the heliostat field.

Parameter Value

Width of individual heliostat 12.2 m Height of individual heliostat 12.2 m Reflective area ratio 0.97 Individual heliostat area 144.375 m2

Total reflective area 984347 m2

Number of heliostats 6818 Mirror reflectance and soiling 0.9 Ratio of radial distance to tower height (min) 0.75 Ratio of radial distance to tower height (max) 9

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

6

• Calculate the receiver area from receiver thermal power and average flux [42]

Arec =PrecSM

Qave

• Calculate the dimensions appertaining to aspect ratio (quotient of height and diameter)

Aspect ratio can be selected anywhere in the range from 1.2 to 1.5 [44]. The emittance and absorbance of the receiver coating are 0.88 and 0.94 respectively [45]. The design parameters of the receiver are listed in Table 4.

3.4. Thermal energy storage system

The initial design considers 10 h of TES. The volume of TES tank is computed by following steps:

• The thermal energy for required number of full load TES hours is calculated as

ThermalEnergy = Phtfd × ts

• In order to store the required thermal energy, molten salt mass is calculated by the following relation [34,46].

msalt =ThermalEnergy

cp × (Thot − Tcold)=

Phtfd × ts

cp × (Thot − Tcold)

where, cp is specific heat, Tcold and Thot are temperatures of cold and hot tank.

• In order to calculate the storage tank size, the volume of salt is calculated as [34]

Vsalt =msalt

ρsalt

where, ρsalt is molten salt density

• The required salt volume is needed to be stored and the volume of TES tanks is calculated by using the below equation

Vtank =Vsalt

ηsto

The design parameters for the TES system are listed in Table 5.

4. Performance analysis

This section presents the energy and economic analysis of the initial design of the ST power plant with SM factor of 2 and 10 h of full load TES.

4.1. Energy

The proposed 100 MW ST plant produces an annual energy of 397,692 MWh. Fig. 3 shows the monthly average electrical output of the plant. Maximum average electrical power is produced in June (56.1 MW) and minimum in November (29.1 MW). Daily average electrical output, incident solar power on the total area of heliostats, TES charge and discharge pattern are shown in Fig. 4. The electrical output of the plant is available even after the sunset when no thermal energy is available in the heliostat field. It can be observed in the Fig. 4 that TES is charged during the daytime when maximum solar irradiance is incident on the heliostat field. The TES starts discharging in the evening when incident solar irradiance decreases. The TES discharges and helps to generate electrical power in the evening when sun is not available. The yearly electrical energy output of plant over the lifespan of 25 years is shown in Fig. 5. The annual energy output decreases with each passing year because of degradation of heliostat mirrors. The annual degrada-tion rate of 0.2% is taken in this analysis [47].

4.2. Solar to electric efficiency

It is an important parameter to illustrate the overall efficiency of solar power technology. It shows how efficiently the available solar energy is transformed into electricity. It is calculated as [47]

Solartoelectricefficiency =annualelectricalenergyoutputoftheplant

totalannualsolarenergyavailable

The solar to electric efficiency of the initial design of the proposed plant is 16.70%

4.3. Capacity utilization factor

The CUF of the proposed plant is 45.4%. It is an important parameter to show the efficacy of a solar power technology. It shows to which percentage the plant has actually utilized its nameplate capacity. It can be demonstrated by the following equation [48]

CUF =annualelectricalenergyoutputoftheplant

plantdesigncapacity × 8760

Table 4 Receiver design parameters.

Parameter Value

Plant design capacity 100 MW Tower height 190 Receiver diameter 15.2 Receiver height 18.2 Coating emittance 0.88 Coating absorptance 0.94 Receiver flux (max) 1000 kWt/m2

HTF type Molten Salt Receiver thermal power 539 MWt

Table 5 TES system design parameters.

Parameter Value

Storage duration 10 h TES capacity 2694 MWt

Volume of TES tank 13194 m3

Available volume of HTF 12534 m3

Storage tanks 2 Temperature (cold tank) 290 ◦C Temperature (hot tank) 574 ◦C

Fig. 3. Monthly average electrical power output.

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

7

4.4. Land use factor

The land use factor is an important parameter in urban environment and in areas where land availability is a main constraint. It is a useful parameter to show how effectively the land is being used to collect the available solar resource. It is expressed as [47]

Landusefactor =heliostatfieldactivearea

totalareaoftheplant

where, heliostat field active area is the total area of heliostats’ surface while total area of the plant is the total land area of the heliostat field and power block. The initial proposed design has a land use factor of 13.6%. One of the major reasons for this low land use factor is the wide spacing between heliostats due to shading losses and also packing den-sity reduces at the larger distance from central tower to minimize the blockage of reflected rays and this further increase the gaps between heliostats.

4.5. Economic analysis

The economic parameters of the ST plant are presented in Table 6. The after-tax cash flow of the plant is shown in Fig. 6. The after-tax cash flow represents the sum of positive and negative cash flows in each year. The positive cash is the earning by selling the generated electricity to the grid, while the negative cash is the debt installment, operation and maintenance cost, insurance cost, and tax amount. It can be observed in Fig. 6 that after-tax cash flow is negative until year 18 of the project when it starts generating net positive income. It can be observed that the net positive income increases with each passing year although the plant energy output decreases due to mirrors degradation as the plant gets older. The increase in positive income is resulted from the power pur-chase agreement (PPA) escalation rate of 1%/year. The huge negative

value in year 0 of the project (Fig. 6) is due to capital investment of US$ 151.4 million. This project has a net capital cost (NCC) of US$ 605.4 million out of which debt amount is 75% (US$ 454.1 million) and equity is 25%. The LCoE is a major economic parameter which can show the economic feasibility of the plant. It is illustrated by the following rela-tion [49].

LCoE =Totalcostperyear

Totalelectricalenergygenerated

The LCoE of the proposed ST plant is 12.99 ¢/kWh.

Fig. 4. Daily average electrical output, heliostat filed incident solar power, TES system charge and discharge power.

Fig. 5. Annual electrical energy.

Table 6 Economic parameters [50,51]

Parameter Cost

Power Cycle 1200 US$/kWe

Tower 15,000 US$/m Heliostat 130 US$/m2

Receiver 69,189 US$/m2

Cite improvement 27 US$/m2

TES system 22 US$/kWt

Land 2000 US$/acre O&M 80 US$/kW/year Balance of plant 270 US$/kWe

Inflation rate 2.5% Discount rate (real) 5.5% Discount rate (nominal) 8% Contingency 7% of direct cost

Fig. 6. After-tax cash flow of initial design.

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

8

5. Optimization

The proposed plant is optimized for maximum energy output at minimum cost. The energy and LCoE functions are to be optimized simultaneously hence a multi-objective optimization approach is needed. The multi-objective optimization of these two functions is per-formed in this research under various design constrains, such as tower optical height, full load storage duration, and SM of the heliostat field.

5.1. Problem formulation

The plant was initially design for SM value of 2, full load TES of 10 h and tower height of 190 m. The optimization of these parameters can significantly enhance the performance of the plant. A ST plant with a small SM will not use the available solar resource effectively while a large SM requires more land area and the optical efficiency of the he-liostats located in the outer circles decreases significantly. The perfor-mance of the heliostats is tested in solar pilot software from national renewable energy laboratory (NREL). The heliostats’ efficiency and their thermal power are shown in Fig. 7a and b. Both the efficiency and power delivered by the heliostats decreases as we move away from the tower. In the peak solar irradiance hours, some of the heliostats do not make a significant contribution because they have to be defocused to avoid exceeding the maximum thermal flux rating of the receiver. Therefore, it is very important to determine the optimal value of SM which gives better performance of the plant. It is obvious that the larger field with large number of heliostats requires taller tower to reduce the blocking, shading, and cosine losses [21]. On the other hand, a very tall tower causes more attenuation losses, especially for those heliostats which are located in the outer circles due to larger slant height of receiver from heliostats in the outer circles [22]. The attenuation, and cosine effi-ciencies of heliostats in the heliostat field are shown in Fig. 7c and d, respectively. Therefore, a very tall tower will add construction cost with relatively higher attenuation losses and without further reducing the shading and blocking losses. The height of tower and SM are interde-pendent design parameters [20]. The SM and TES are interdependent as well [17]. A smaller TES capacity for large SM does not fully store the available thermal energy from the heliostat field and too large TES system has more heat losses because of larger volume of the tank.

Since, SM, tower height and TES are interdependent. In order to

address the interdependency of these optimization parameters, the process of optimization involves several iterations. The sizing of these interdependent parameters is optimized through multi-objective opti-mization process. In the multi-objective optimization process, one objective is described as prime objective, while others are conditions and constraints for solving the problem and achieving main objectives [52]. The energy function of the optimization problem is formulated as

MaximizeF1(x) = ηstoηpbηhe

∑8760

n=1PhtfSM

The LCoE is the net value of electricity cost per unit over lifespan of the project. The LCoE optimization problem can be formulated by following objective (fitness) function

MinimizeF2(x) =TPV × CRF

Eg

where, F2(x) is LCoE, TPV is the present worth of all system costs, CRF is the capital recovery factor and Eg is annual electrical energy generated. The CRF is given by [49]

CRF =r(1 + r)N

(1 + r)N− 1

where, N is lifespan of the project and r is interest rate.

TPV = CC +(O&M)NPV + INPV − RselN PV

where, CC is capital cost, (O&M)NPV is present worth of operation and maintenance cost, RselNPV is the net present worth of the revenue generated by selling electricity to grid, and INPV is the net present value of loan installment. These net present values of costs and revenue are given by [53]

Fig. 7a. Total efficiencies of heliostats in the field.

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

9

Operationandmaintenancecost(O&M)NPV =∑N

q=1C(O&M) ×

(1 + J)q

(1 + r)q

LoaninstallmentsINPV =∑N

q=1I ×

(1 + J)q

(1 + r)q

RevenueRselN PV =∑N

q=1Rsel ×

(1 + J)q

(1 + r)q

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

(43)

where, C(O&M) is the operation and maintenance cost of the plant in year q, I is the loan installment in year q, Rsel is the revenue of electricity sold to the grid in year q, and J is the annual inflation rate. The final form of the LCoE optimization objective (fitness) function is formulated by substituting Eqs. (41)–(43) and (16) in Eq. (40).

MinimizeF2(x) =

(

CC +∑N

q=1(C(O&M) + I − Rsel) ×(1+J)q

(1+r)q

)

×r(1+r)N

(1+r)N− 1

ηstoηpbηhe∑8760

n=1 PhtfSM

In order to solve the optimization problem, by optimizing SM value, TES system and tower height, the following constraint must be satisfied.

SMconstraint1 ≤ x ≤ 4TESconstraint0 ≤ x ≤ 15

Towerheightcontraint150 ≤ x ≤ 300

⎫⎬

⎭

5.2. Multi-objective optimization method

The full load TES hours, SM and tower height optimization problem F(x) comprises of two functions one is energy function F1(x) and the

Fig. 7b. Thermal power delivered by heliostats.

Fig. 7c. Attenuation efficiencies of the heliostats.

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

10

other is LCoE function F2(x) subject to given storage hours, SM and tower height constraints. Although the LCoE objective function F2(x)depends on the energy function F1(x) but the other factors in LCoE function cause conflicting values of the optimized parameters (TES hours, SM and tower height) for these two objective functions. Hence, these two objective functions are to be solved using a multi-objective optimization approach.

The general multi-objective or multi-criteria optimization problem in mathematical terms can be formulated as shown by equation below

optimizingafunctionF(x) = [F1(x),F2(x),⋯.,Fm(x)](46)

subject to gj(x) ≤ 0, j = 1, 2, .., j and x ≥ 0,where, m(m ≥ 2) is the number of conflicting linear or nonlinear objective functions and j is the number of equality and inequality, linear or nonlinear constraints. In this work, a fuzzy goal criterion is used to arrive a comprise solution of multi objective functions. The methodology is presented consists of following steps

Step 1: Solve all the objective functions only one objective at a time ignoring the other objective functions under the given constraints. Let x1*, x2*,… xm* are the respective optimal values of the objective func-tion, F1

(x*

1),F2(x*

2),⋯,Fm

(x*

m),are the optimal solutions of m objective

functions and obtain upper (Um) and lower bounds (Lm) of Fm(x) from Fm(x*

1), Fm(x*2).., Fm(x*

m).

Step 2: Define a linear fuzzy membership function of Fm(x), (m = 1,2) on the basis of upper (Um) and lower bounds (Lm) of Fm(x) for each objective function as below

μ[Fm(x) ] = 1if Fm(x) ≥ Um

μ[Fm(x) ] =Um − Fm(x)

Um − Lmif Lm < Fm(x) < Um

μ[Fm(x) ] = 0otherwis

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

Step 3: Generate a goal constraint including two goals, one is over and the other is under achievement goal for objective function Fm(x) for all m (m = 1,2)

Fm(x)+ d+1 − d−

2 ≤ μ[Fm(x) ]

Step 4: Define a maximization-minimization fuzzy variable repre-sented by λ, and construct given problem into a fuzzy goal programming problem as

[x*] = Maximizeλ(0 ≤ λ ≤ 1)

subject to initial problem constraints and goal constraint generated in step 3.

To solve the function to be optimized subject to problem constraints, PSO approach is used.

5.3. Particle swarm optimization and program development

The PSO is one of the evolutionary computation optimization tech-niques. Kennedy and Eberhart developed this population-based opti-mization technique in 1995 [54]. In this paper, PSO algorithm is used to find optimal solution of an objective function within the given con-straints. The PSO approach is coded and implemented in C language. Penalty terms are added to the objective function and each penalty term is associated with one constraint only. A given objective function either maximized or minimized in such a way that if problem constraints are not satisfied, then associated penalty terms value is chosen as very high, otherwise the penalty terms is kept to be zero. After several rounds of program iterations and to converge functions, PSO parameters consid-ered are c1 and c2 = 2, size of swarm = 100 and Vmax = 4.

The full load TES hours, SM and tower height optimization problem F(x) is simultaneous optimization of two functions one is energy output F1(x) and the other is LCoE function F2(x) subject to the constraints of (45). The compromise solution obtained at number of SM value [x*] =

2.7, storage hours [x*] = 8.7, and tower height [x*] = 205.

6. Comparison of the initial design and optimized design

The optimized ST plant contains 9745 heliostats compared to 6818 heliostats in the initial design. The year one energy output of the opti-mized plant is 539,225 MWh which is a 35.6% improvement in the year one energy output compared to the initial design. Although the opti-mized design has around 40% more heliostats compared to the initial design, but it has 35.6% more energy output. This difference in per-centage increase in heliostat field size and energy output is due to the low efficiency of the heliostats located in the outer circles of the heliostat field (Fig. 7). This decrease in heliostats’ efficiency is caused by the high attenuation, blocking and cosine losses of the heliostats located at the

Fig. 7d. Cosine efficiencies of the heliostats.

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

11

larger radial distance from tower Another pertinent reason for this relatively less improvement in the energy output compared to the number of added heliostats is that some heliostats are needed to be the defocused during peak solar irradiance intervals to avoid exceeding the maximum thermal flux rating of the receiver. The annual energy output of the optimized and initial designs over the lifespan of the project is shown in Fig. 8. The optimized design has produced 3,454,702 MWh of more energy than the initial design over the lifespan of the project. The optimized design has much better average monthly power output as shown in Fig. 9. The comparison of other technical and economic per-formance parameters is presented in Table 7. The solar to electric effi-ciency of the optimized design is 0.9% less than the initial design. This slightly lower efficiency of optimized design is caused by more losses in the TES system because more excess energy is being stored in the TES system in case of optimized design due to bigger SM which results in more heat loss. Although, the optimized design has slightly lower solar to electric efficiency, but it has better CUF because the larger heliostat field in the optimized design collects more solar energy to be utilized in the power block. The optimization of the design parameters has improved the CUF of the initial design by 16.2%. Although the opti-mized design has 81.9 million US$ higher NCC but its higher energy output due to better CUF leads to 16.9% lower LCoE compared to initial design. The ST plant with optimized parameters starts producing posi-tive after-tax cash income from year 7 onwards as compared to year 18 for initial design. The after-tax cash flow comparison of the initial and optimized designs are shown in Fig. 10. The optimized design has 3.1% better land use factor which is an important factor in land constrained areas.

The average electrical output, total incident solar power on the he-liostat field, TES charge and discharge pattern comparison of the opti-mized and initial designs are depicted in Fig. 11. Although the TES size of initial design is 10 h of full load storage compared to 8.7 h for the optimized design, yet the Fig. 11 shows that the optimized design has stored more thermal energy and its TES system keeps supplying thermal power to the power block for long period of time. The optimized plant has long working hours until 3 am compared to 10 pm for the initial design due to better utilization of TES system.

The results of the proposed ST plant are validated by comparing the initial and optimized designs with the existing ST plants. Currently there are 4 operational ST plants that have capacities of more than 100 MW. The ISEG (377 MW), Crescent Dunes (110 MW), Ashalim Plot B (121 MW), and NOOR III (134 MW). The Ashalim Plot B ST plant has no TES system while capacities of the ISED and NOOR III are much bigger than the proposed plant. The Crescent Dunes ST plant has the capacity and other major design parameters close to the initial design of the proposed plant. The performance of the initial design is very close to the Crescent Dunes plant. The Crescent Dunes plant has around 25% more annual energy output because it has 10% bigger size and the DNI at the Crescent Dunes location is 11% better than the DNI at the proposed design location. The LCoE of the initial design are close to the PPA of the Crescent Dunes plant. The detailed comparison of initial and optimized design with the Crescent Dunes ST plant is shown in Table 8. Despite smaller capacity and relatively low DNI, the performance of the

optimized design is superior than the Crescent Dunes plant.

7. Conclusion

A detailed analysis and optimization of the three parameters, SM, TES and tower height of ST plant is carried out in this paper. The 100 Fig. 8. Annual energy output of optimized and initial design.

Fig. 9. Monthly average power output of optimized and initial design.

Table 7 Comparison of initial and optimized designs of ST plant.

Parameter Initial design Optimized design

Annual energy output 397,692 MWh 539,225 MWh Lifetime energy output 9,707,288 MWh 13,161,990 MWh CUF 45.4% 61.6% NCC 605.4 million US$ 686.9 million US$ LCoE 12.99 ¢/kWh 10.79 ¢/kWh Solar to electric efficiency 16.7% 15.8% Land use factor 13.6% 16.7%

Fig. 10. After-tax cash flow comparison of initial and optimized designs of ST plant.

Fig. 11. Daily average electrical output, total incident solar power, TES charge and discharge pattern of optimized and initial design of ST plant.

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

12

MW ST plant is initially designed for 10 h of full load TES, SM factor of 2 and tower height of 190 m. Considering the limiting values of TES, SM and tower height parameters, energy is maximized and LCoE is mini-mized separately using a PSO optimization tool. To find a solution of simultaneous optimization of energy and LCoE, a fuzzy based max-min operator with goal programing is used. The optimized design parameters converged to SM of 2.7, TES of 8.7 h and tower height of 205 m. Several performance parameters have been investigated and compared for the optimized and initial design. It is found that the optimized design has significantly improved the performance of the plant. The optimized design has produced 3,454,702 MWh of more energy during the lifespan of the project which is a 35.6% improvement in the energy output. Therefore, it has 16.2% better CUF than the initial design. The optimized deign has relatively higher NCC because of larger heliostat field but its LCoE is 10.79 ¢/kWh compared to 12.99 ¢/kWh for initial design and its after-tax net income becomes positive in year 7 compared to year 18 for the initial design. The optimization of the three parameters has improved the land use factor of the plant by 3.1% which is an important factor in urban environment and land constrain areas. The results of this paper show that the optimization of TES, SM and tower height has a significant impact on both technical and economic performance of the plant.

CRediT authorship contribution statement

Ahmed Bilal Awan: Conceptualization, Methodology, Software, Validation, Investigation, Writing - original draft, Writing - review & editing, Supervision, Project administration. Kotturu V.V. Chandra Mouli: Methodology, Software, Validation, Writing - original draft. Muhammad Zubair: Formal analysis, Resources, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References

[1] Bellos E, Tzivanidis C, Tsimpoukis D. Multi-criteria evaluation of parabolic trough collector with internally finned absorbers. Appl Energy 2017;205:540–61. https:// doi.org/10.1016/j.apenergy.2017.07.141.

[2] Fuqiang W, Ziming C, Jianyu T, Yuan Y, Yong S, Linhua L. Progress in concentrated solar power technology with parabolic trough collector system: a comprehensive review. Renew Sustain Energy Rev 2017;79:1314–28. https://doi.org/10.1016/j. rser.2017.05.174.

[3] Philibert C. International Energy Agency (IEA), Technology Roadmap: Solar Thermal Electricity. 2014.

[4] Li C, Zhai R, Yang Y. Optimization of a heliostat field layout on annual basis using a hybrid algorithm combining particle swarm optimization algorithm and genetic algorithm. Energies 2017;10:1–15. https://doi.org/10.3390/en10111924.

[5] Reyes-Belmonte MA, Sebastian A, Romero M, Gonzalez-Aguilar J. Optimization of a recompression supercritical carbon dioxide cycle for an innovative central receiver solar power plant. Energy 2016;112:17–27. https://doi.org/10.1016/j. energy.2016.06.013.

[6] Cagnoli M, de la Calle A, Pye J, Savoldi L, Zanino R. A CFD-supported dynamic system-level model of a sodium-cooled billboard-type receiver for central tower CSP applications. Sol Energy 2019;177:576–94. https://doi.org/10.1016/j. solener.2018.11.031.

[7] Kim S, Lee I, Lee BJ. Development of performance analysis model for central receiver system and its application to pattern-free heliostat layout optimization. Sol Energy 2017;153:499–507. https://doi.org/10.1016/j.solener.2017.05.093.

[8] Avila-Marin AL, Fernandez-Reche J, Tellez FM. Evaluation of the potential of central receiver solar power plants: configuration, optimization and trends. Appl Energy 2013;112:274–88. https://doi.org/10.1016/j.apenergy.2013.05.049.

[9] Piroozmand P, Boroushaki M. A computational method for optimal design of the multi-tower heliostat field considering heliostats interactions. Energy 2016;106: 240–52. https://doi.org/10.1016/j.energy.2016.03.049.

[10] Besarati SM, Yogi GD. A computationally efficient method for the design of the heliostat field for solar power tower plant. Renew Energy 2014;69:226–32. https:// doi.org/10.1016/j.renene.2014.03.043.

[11] Wang K, He YL, Xue XD, Du BC. Multi-objective optimization of the aiming strategy for the solar power tower with a cavity receiver by using the non-dominated sorting genetic algorithm. Appl Energy 2017;205:399–416. https://doi.org/ 10.1016/j.apenergy.2017.07.096.

[12] Farges O, Bezian JJ, El HM. Global optimization of solar power tower systems using a Monte Carlo algorithm: application to a redesign of the PS10 solar thermal power plant. Renew Energy 2018;119:345–53. https://doi.org/10.1016/j. renene.2017.12.028.

[13] Hussaini ZA, King P, Sansom C. Numerical simulation and design of multi-tower concentrated solar power fields. Sustainability 2020;12:1–22. https://doi.org/ 10.3390/su12062402.

[14] Zhao Y, Hong H, Jin H. Optimization of the solar field size for the solar–coal hybrid system. Appl Energy 2017;185:1162–72. https://doi.org/10.1016/j. apenergy.2016.01.069.

[15] Zhang M, Yang L, Xu C, Du X. An efficient code to optimize the heliostat field and comparisons between the biomimetic spiral and staggered layout. Renew Energy 2016;87:720–30. https://doi.org/10.1016/j.renene.2015.11.015.

[16] Yao Y, Hu Y, Gao S. Heliostat field layout methodology in central receiver systems based on efficiency-related distribution. Sol Energy 2015;117:114–24. https://doi. org/10.1016/j.solener.2015.04.029.

[17] Coelho B, Varga S, Oliveira A, Mendes A. Optimization of an atmospheric air volumetric central receiver system: Impact of solar multiple, storage capacity and control strategy. Renew Energy 2014;63:392–401. https://doi.org/10.1016/j. renene.2013.09.026.

[18] Thaker S, Oni AO, Kumar A. Techno-economic evaluation of solar-based thermal energy storage systems. Energy Convers Manage 2017;153:423–34. https://doi. org/10.1016/j.enconman.2017.10.004.

[19] Flueckiger SM, Iverson BD, Garimella SV. Economic optimization of a concentrating solar power plant with molten-salt thermocline storage. J Sol Energy Eng Trans ASME 2014;136:1–8. https://doi.org/10.1115/1.4025516.

[20] Carrizosa E, Domínguez-Bravo C, Fernandez-Cara E, Quero M. Optimization of multiple receivers solar power tower systems. Energy 2015;90:2085–93. https:// doi.org/10.1016/j.energy.2015.08.005.

[21] Sanz-bermejo J, Gallardo-Natividad V, Gonzalez-Aguilar J, Romero M. Comparative system performance analysis of direct steam generation central receiver solar thermal power plants in megawatt range. J Sol Energy Eng 2015;136: 1–9. https://doi.org/10.1115/1.4026279.

[22] Marzo A. Solar radiation attenuation in solar tower plants. Sol Energy 2012;86: 388–92. https://doi.org/10.1016/j.solener.2011.10.010.

[23] Zimermann H. Fuzzy mathematical programming. Comput Oper Res 1983;10: 291–8. https://doi.org/10.1016/0305-0548(83)90004-7.

[24] Verma R, Biswal MP, Biswas A. Fuzzy programming technique to solve multi- objective transportation problems with some non-linear membership functions. Fuzzy Sets Syst 1997;91:37–43. https://doi.org/10.1016/S0165-0114(96)00148-0.

[25] Gomez-vidal J, Or E, Kruizenga A, Fern AG, Cabeza LF, Sol A. Mainstreaming commercial CSP systems: a technology review. Renew Energy 2019;140:152–76. https://doi.org/10.1016/j.renene.2019.03.049.

[26] Srilakshmi G, Suresh NS, Thirumalai NC, Ramaswamy MA. Preliminary design of heliostat field and performance analysis of solar tower plants with thermal storage and hybridisation. Sustain Energy Technol Assess 2017;19:102–13. https://doi. org/10.1016/j.seta.2016.12.005.

[27] Sagha M, Gadalla M. Thermo-economic analysis of air bottoming cycle hybridization using heliostat fi eld collector: a comparative analysis. Energy 2016; 112:698–714. https://doi.org/10.1016/j.energy.2016.06.113.

[28] Vittitoe C, Biggs F. Terrestrial propagation loss. Am. Sect. ISES Meet., Denver: Sandia Laboratories, SAND78-1137C; 1978.

[29] Leary PL, Hankins JD. A User’s guide for MIRVAL: a computer code for comparing designs of heliostat-receiver optics for central receiver solar power plants, Sandia Laboratories, SAND77-8280. 1976.

[30] Pitman CL, Vant-Hull L. Atmospheric Transmittance Model for a Solar Beam Propagating Between a Heliostat and a Receiver. Houston, Texas: Sandia National Laboratories,SAND83-8177; 1984.

Table 8 Comparison of the proposed design of ST plant with Crescent Dunes ST plant.

Parameter Initial design Optimized design

Crescent Dunes

Capacity 100 MW 100 MW 110 MW SM 2 2.7 2 TES 10 h 8.7 h 10 h Storage type 2-tank direct 2-tank direct 2-tank direct Tower height 190 m 205 m 195 m DNI 6.63 kWh/m2/

day 6.63 kWh/m2/ day

7.36 kWh/m2/ day

Annual energy output 397,692 MWh 539,225 MWh 500,000 MWh CUF 45.4% 61.6% 51.89% NCC 605.4 million

US$ 686.9 million US $

737 million US$

LCoE/PPA 12.99 ¢/kWh 10.79 ¢/kWh 13.5 ¢/kWh Solar to electric

efficiency 16.7% 15.8% 15.5%

Land use factor 13.6% 16.7% 18.4%

A.B. Awan et al.

Energy Conversion and Management 225 (2020) 113378

13

[31] Sengupta M, Wagner M. Atmospheric attenuation in central receiver systems from dni measurements. Energy Forum, Denver: ASES Conf. World Renew; 2012.

[32] Montes MJ, Abanades A, Martínez-Val JM. Performance of a direct steam generation solar thermal power plant for electricity production as a function of the solar multiple. Sol Energy 2009;83:679–89. https://doi.org/10.1016/j. solener.2008.10.015.

[33] Srilakshmi G, Suresh NS, Thirumalai NC, Ramaswamy MA. A novel approach to determine the non-dimensional heliostat field boundary for solar tower plants. Sustain Energy Technol Assess 2016;17:26–37. https://doi.org/10.1016/j. seta.2016.08.001.

[34] Zhao Z, Arif MT, Oo AMT. Solar thermal energy with molten-salt storage for residential heating application. Energy Proc 2017;110:243–9. https://doi.org/ 10.1016/j.egypro.2017.03.134.

[35] Praveen RP, Baseer MA, Awan AB, Zubair M. Performance analysis and optimization of a parabolic trough solar power plant in the middle east region. Energies 2018;11:741-1–18. https://doi.org/10.3390/en11040741.

[36] Boukelia TE, Mecibah MS. Parabolic trough solar thermal power plant: Potential, and projects development in Algeria. Renew Sustain Energy Rev 2013;21:288–97. https://doi.org/10.1016/j.rser.2012.11.074.

[37] Srilakshmi G, Venkatesh V, Rao BS. Global Review of Solar Tower Technology. vol. 53. 2014. https://doi.org/10.1017/CBO9781107415324.004.

[38] Zhang M, Du X, Yang L, Xu C, Yang Y. Comparing study of biomimetic spiral and radial staggered layouts of the heliostat field. Energy Procedia 2015;69:242–9. https://doi.org/10.1016/j.egypro.2015.03.028.

[39] Stine WB, Geyer M. Power from the sun. vol. 104. 2001. [40] Deshmukh S, Gadhe PM, Yadav RJ. Design of heliostat field for small scale central

receiver system. Int J Curr Eng Technol 2017;7:363–7. [41] Falcone PK. A handbook for solar central receiver design (Sand 86-8009 report).

Sandia National Laboratories Livermore. 1986. https://doi.org/10.2172/6545992. [42] Albarbar A. Performance assessment and improvement of central receivers used for

solar thermal plants. Energies 2019;12:1–27. https://doi.org/10.3390/ en12163079.

[43] Lata JM, Rodríguez M, Alvarez De Lara M. High flux central receivers of molten salts for the new generation of commercial stand-alone solar power plants. J Sol Energy Eng 2008;130:0210021–5. https://doi.org/10.1115/1.2884576.

[44] Zavoico AB. Solar Power Tower - Design Basis Document. 2001. https://doi.org/ 10.2172/786629.

[45] Collado FJ, Guallar J. Two-stages optimised design of the collector field of solar power tower plants. Sol Energy 2016;135:884–96. https://doi.org/10.1016/j. solener.2016.06.065.

[46] Awan AB, Zubair M, Chandra Mouli KVV. Design, optimization and performance comparison of solar tower and photovoltaic power plants. Energy 2020;199: 117450. https://doi.org/10.1016/j.energy.2020.117450.

[47] Desideri U, Campana PE. Analysis and comparison between a concentrating solar and a photovoltaic power plant. Appl Energy 2014;113:422–33. https://doi.org/ 10.1016/j.apenergy.2013.07.046.

[48] Awan AB, Zubair M, Praveen RP, Bhatti AR. Design and comparative analysis of photovoltaic and parabolic trough based CSP plants. Sol Energy 2019;183:551–65. https://doi.org/10.1016/j.solener.2019.03.037.

[49] Lazou AA, Papatsoris AD. Economics of photovoltaic stand-alone residential households: a case study for various European and Mediterranean locations. Sol Energy Mater Sol Cells 2000;62:411–27. https://doi.org/10.1016/S0927-0248(00) 00005-2.

[50] Abbas M, Aburideh H, Belgroun Z, Tigrine Z, Kasbadji MN. Comparative study of two configurations of solar tower power for electricity generation in Algeria. Energy Procedia 2014;62:337–45. https://doi.org/10.1016/j.egypro.2014.12.395.

[51] Cekirge HM, Elhassan A. A Comparison of Solar Power Systems (CSP): Solar Tower (ST) Systems versus Parabolic Trough (PT) Systems. Am J Energy Eng 2015;3: 29–36. https://doi.org/10.11648/j.ajee.20150303.11.

[52] Mahesh A, Sandhu KS. A genetic algorithm based improved optimal sizing strategy for solar-wind-battery hybrid system using energy filter algorithm. Front Energy 2020:139–51. https://doi.org/10.1007/s11708-017-0484-4.

[53] Gonzalez A, Riba JR, Rius A. Optimal sizing of a hybrid grid-connected photovoltaic and wind power system 2015;154:752–62. https://doi.org/10.1016/ j.apenergy.2015.04.105.

[54] Kennedy J, Eberhart R. Particle swarm optimization. IEEE Int Conf Neural Networks - Conf Proc, Perth, Australia 1995:1942–8. https://doi.org/10.1109/ ICNN.1995.488968.

A.B. Awan et al.