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Review on applications of particle swarm optimization in solar energy systems Article in International journal of Environmental Science and Technology · August 2018 DOI: 10.1007/s13762-018-1970-x
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International Journal of Environmental Science and Technology https://doi.org/10.1007/s13762-018-1970-x
REVIEW
Review on applications of particle swarm optimization in solar energy systems A. H. Elsheikh1 · M. Abd Elaziz2,3 Received: 5 June 2018 / Revised: 3 August 2018 / Accepted: 12 August 2018 © Islamic Azad University (IAU) 2018
Abstract Solar energy is one of the most important factors used in the development of the countries. Since it is a renewable energy source, it reduces the demand on the non-renewable energy sources such as fossil fuels, oil, natural gas, nuclear, and other sources. Therefore, many researchers have sought to improve the performance of solar energy systems via applying several metaheuristic methods such as particle swarm optimization (PSO) which simulates the behavior of the fish schools or bird flocks. PSO has been used in different applications including engineering, manufacturing, and medicine. The main process of the PSO is to determine the optimal position for each particle inside the population. This is performed through updating the position using the velocity of each particle and the shared information between the particles. The aim of this paper is to provide a review on the PSO’s applications to improve the performance of solar energy systems and to identify the research gap for future work. The literature review used in this study indicates that the PSO is a very promising method to enhance the performance of solar energy systems. Keywords Solar energy · Metaheuristic methods · Particle swarm optimization · Solar collectors · Solar cells · Photovoltaic/thermal systems · Solar stills
Introduction Energy and water are the most important elements required to ensure the survival of human beings. The demand for energy and water is growing worldwide due to the rapid population growth and industrial revolution. In the last two centuries, fossil fuels have been the main energy source. However, the conventional fossil fuels are expendable resources which have serious environmental problems such as air pollution and global warming. Therefore, the need to clean inexhaustible renewable energy resources has arisen to overcome the energy shortages (Awan and Khan 2014). Editorial responsibility: Parveen Fatemeh Rupani. * M. Abd Elaziz
[email protected] 1
Department of Production Engineering and Mechanical Design, Tanta University, Tanta 31527, Egypt
2
School of Computer Science and Technology, Wuhan University of Technology, Wuhan, China
3
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
The renewable energy resources, as biomass (Barnes 2015), wind (Alhmoud and Wang 2018), geothermal (Lu 2018), and solar energy (Kannan and Vakeesan 2016) have attracted considerable attention in many industrial and engineering applications such as electricity generation (Jain et al. 2018), water desalination (Sharshir et al. 2016), and domestic space heating (Sharma et al. 2017). Among all renewable energy resources, solar energy has the widest range of applications. There are many solar energy-based systems which can be utilized in heat generation, water desalination, and electricity production such as solar collectors, solar air heaters, solar water heaters, solar cookers, solar dryers, solar stills, solar-assisted heat pumps, and photovoltaic–thermal (PV/T) systems. Improving the thermal performance of these systems is a crucial issue. There are numerous experimental studies carried out to assess and augment the performance of these systems (Verma et al. 2017; Sathyamurthy et al. 2015; Biglarian et al. 2018). However, the experimental studies are too time consuming and costly. Moreover, classical statistical-based design of experiments methods may not be able to do that job. Many optimization methods have been used to achieve this target such as genetic algorithm (GA) (Durão et al. 2014), harmony search (HS) (Banerjee
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et al. 2014), whale optimization (WO) (Oliva et al. 2017), simulated annealing (SA) (Mousavi et al. 2017), artificial bee colony optimization (ABCO) (Mohamed et al. 2014), ant lion optimization (ALO) (Hadidian-Moghaddam et al. 2017), and particle swarm optimization (PSO) (Kuok et al. 2010; Rezaee Jordehi 2018; Rey and Zmeureanu 2018). PSO as an evolutionary computation technique has been used for different optimization problems such as continuous non-linear, constrained and unconstrained, and nondifferentiable multimodal functions (Marini and Walczak 2015). PSO, compared to other optimization techniques such as GA, has less number of adjusting parameters, and hence, it has higher computational efficiency. Therefore, PSO has attracted the attention of many researchers in different engineering applications. There are many published review articles focus on the application of PSO on different engineering applications such as solar photovoltaic systems (Khare and Rangnekar 2013), economic dispatch (Mahor et al.
2009), acoustic signal (Al-geelani et al. 2015), geotechnical engineering (Hajihassani et al. 2018), light scattering (Xu 2015), and clustering high-dimensional data (Esmin et al. 2015). Moreover, there are many published articles on the applications of PSO in solar energy systems; the inputs and the optimization outputs for each system are summarized in Table 1. However, to the best knowledge of the authors, there are no previous reviews on the applications of PSO in solar energy systems. The remainder of this review offers the following: • A brief explanation about the inspiration and the math-
ematical model of the PSO algorithm is introduced.
• The applications of PSO in different solar systems such
as solar collectors, solar cells, solar power tower, photovoltaic/thermal systems, and solar stills are summarized in detail. • Conclusions and scope for further research are also presented.
Table 1 Inputs and outputs of PSO models for different solar energy systems Solar device
Input parameters
Parabolic trough solar collector (Cheng et al. 2015) Flat-plate solar air heater (Siddhartha et al. 2012)
Focal length Aperture width Ambient temperature Wind velocity Plate emissivity Tilt angle Building heating system (Bornatico et al. 2012) Solar collector area Auxiliary power unit size Tank volume Solar cell (Ye et al. 2009; Hamid et al. 2013; I-V data Mughal et al. 2017) Photovoltaic/thermal (PV/T) systems (Tabet et al. 2014; Shi et al. 2015) Solar power tower (Li et al. 2017, 2018)
Solar thermal power plant (Farges et al. 2018)
Multi-tower heliostat (Piroozmand and Boroushaki 2016) Solar still (Al-Sulttani et al. 2017a)
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Geographical terrain inputs (altitude, longitude, and attitude) I-V data Field layout Cosine factor Intercept factor Atmospheric attenuation factor Shadowing and blocking factor Receiver width Receiver height Receiver tilt angle Tower height Design and layout of a multiple solar power tower system Unknown constant (C) and the exponent (n) for the Nusselt number expression used to formulate the equation for the estimation of the hourly yield
Optimized output Maximize the optical efficiency Maximize the thermal efficiency
Minimize the energy consumption Minimize cost of installations Maximize the solar fraction Optimize solar cell parameters such as: series resistances, shunt resistances, photogenerated currents, diode saturation currents and Ideality factors Optimize tilt angle setting Maximize output power Maximum potential daily energy collection
Maximize the yearly collected thermal energy Maximize yearly optical efficiency Maximize the optical efficiency Solar still productivity
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Particle swarm optimization Inspiration The Particle swarm optimization (PSO) is one of the most popular metaheuristic methods proposed by (Kennedy and Eberhart 1995). The PSO emulates the social behavior of birds to search the food sources in which these birds share the information between them (the position of each one and the nearest particle to the source of food). In the PSO method, the position xi of each particle represents the solution of the given problem and the best solution represents the source of solution. In the PSO method, each particle has its own memory to save the previous best position reached by the particle and the global best position of the entire population (that belongs to it). According to the information saved in the memory of each individual (particle) and its velocity vi, it can update its position xi (t + 1) as in Fig. 1.
Mathematical model In general, the PSO method represents the population by X, where this population is generated using a random number generator according to the following equation:
X = L + rand × (U − L) (1) where L and U represent the lower and upper boundaries, respectively, of the search domain of the given problem. Each individual/particle xi of X can update its velocity (vi) using the following equation: p
where c1, r1, c2, and r2 represent random numbers, in which w is an inertia weight used to improve the speed of convergence; meanwhile, c1 and c2 represent the coefficients of acceleration, and t represents the current time (iteration). Thereafter, the position of particle xi is updated as
xi = xi + vi (3) The next step in the PSO model is to evaluate the quality of each particle through computing the fitness function. Then g the global best solution (xi ) is determined, also, the best p position that the current particle (xi ) reached is determined (also, called best personal position). These previous steps are performed until the stopping conditions are met. The final steps of the PSO algorithm are given in Algorithm 1. Algorithm 1: The particle swarm optimization algorithm 1- Initialize the parameters such as number of particles N, dimension d, and lower (L) and upper (U) boundaries of the search space. 2- Generate random solutions (X). 3- Generate a random velocity for each solution (vi). 4- While (termination criterion doesn’t meet) 5- For each particle in X 6- Compute the objective function value. p 7- Update the best personal position (xi ). g 8- Update the global best position (x ). 9- Update a new velocity using Eq. (2). 10- Update the position of current particle using Eq. (3). 11- End For 12- Return the global best solution (xg ).
g
vi (t + 1) = wvi (t) + c1 r1 (xi (t) − xi (t)) + c2 r2 (xi (t) − xi (t)) (2)
Fig. 1 a The movement of particle in the environment; b Velocity and position updates of particles in the PSO algorithm
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Applications of PSO in solar energy This section provides a comprehensive review of the published articles on PSO’s applications in solar energy devices, such as solar collectors, solar cells, solar power tower, photovoltaic/thermal systems, and solar stills.
Solar collectors Solar collectors are mainly used to receive and collect the sun radiation and transform the collected radiation into thermal energy, which is transferred to a working fluid (Colangelo et al. 2016). Therefore, they have an important role in different solar energy systems. There are many types of solar collectors such as flat-plate collectors, evacuated tube solar collectors, and parabolic trough solar collectors (Salgado Conrado et al. 2017). It is desired to minimize the construction cost and maximize the thermal efficiency of solar collectors via reducing their size while collecting the same heat energy (Buttinger et al. 2010). Cheng et al. (2015) investigated the performance of parabolic trough solar thermal power system as one of the most efficient commonly used solar energy systems. However, it still suffers from high construction and operating cost compared with traditional fossil fuel power plants (Cheng et al. 2014). The parabolic trough solar collector is the most important subsystem of the solar thermal power system as shown in Fig. 2a; therefore, there is a need to develop an efficient optimization method to select the optimal value of each parameter of such collector. Optical efficiency, defined by the ratio between the absorbed solar radiation and the incident solar radiation on the collector opening, was considered as the main objective function to be optimized using PSO algorithm and the Monte Carlo ray tracing (MCRT) method. Among all design parameters shown in Fig. 2a, the focal length, the aperture width, the rim angle, the outer glass cover diameter, the outer absorber diameter, the tracking error, and the surface imperfection error, only the focal length and the aperture width were used as decision variables. To assure the accuracy and robustness of the PSO/MCRT approach (Cheng et al. 2014), the standard deviation and the mean absolute percentage error between predicted and actual experimental data were calculated in the error analysis of the PSO model. The standard deviations for the predicted optical efficiency, aperture width, and focal length were 0.03, 3.48, and 0.98, respectively. The mean absolute percentage error of the predicted optical efficiency was 0.0312%. Siddhartha et al. (2012) developed a PSO algorithm to estimate optimal thermal performance of a smooth
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Fig. 2 a Schematic of a cross-section view of a parabolic trough solar collector; b flowchart of the hybrid PSO/MCRT algorithm (reproduced with permission from Cheng et al. 2015)
flat-plate solar air heater by optimizing its operating parameters such as ambient temperature, wind velocity, plate emissivity, and tilt angle. The obtained results indicate that the turbulence effect as well as the mass flow rate is enhanced by increasing Reynolds number, and hence, heat transfer rate increases which results in enhancing the thermal performance. Moreover, the thermal performance was enhanced by increasing the number of glass cover plates or decreasing the top loss coefficient. The thermal efficiency has been maximized using the proposed algorithm and has reached about 72% when three glass covers were used at solar radiation intensity of 600 W/ m2, wind speed of 1 m/s, tilt angle of 68.36°, plate emissivity of 0.89, and ambient temperature of 7.28 °C. To verify the accuracy and robustness of this proposed PSO
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approach (Siddhartha et al. 2012), its results were compared with actual experimental data. The obtained results had a mean bias error and a root mean squared error of 0.22 and 0.47, respectively. The obtained results showed a good agreement with experimental results which testifies the algorithm’s robustness. In Bornatico et al. (2012), a PSO algorithm proposed to determine the optimal size of solar thermal system components such as the solar collector area, the auxiliary power unit size, and the tank volume. A wide search range for each model parameter has been used, namely solar collector area (1–40 m2), the auxiliary power unit size (5–50 kW), and the tank volume (100–300 l). According to the parameter sensitivity analysis results, the collector size is the main parameter that affects the installation cost, the energy use, and the solar fraction, while the effect of auxiliary power unit size on the installation cost and the energy use is negligible. The proposed algorithm showed better performance compared with those obtained using GA.
Solar cells Solar cell is an electrical device used to convert solar energy (sunlight) directly into electricity (Assadi et al. 2018). However, it suffers from its low efficiency and high cost. Many studies have been carried out to enhance
the conversion efficiency of different types of solar cells. PSO as a powerful optimization tool has been proposed to achieve this purpose. Ye et al. (2009) illuminated current–voltage characteristics of a solar cell used to extract the solar cell parameters using PSO for the single- and double-diode models shown in Fig. 3a, b (Humada et al. 2016). The first model is based on a modified Shockley diode equation by using the quality factor of a diode to describe the recombination effect. It is suitable for modeling and describing the behavior of solar cells under normal operating conditions. However, at low illuminations, this model shows low accuracy. The second model is a good tool to describe the physical phenomena that occur in the solar cell and gives a good insight into its relationship with the solar cell parameters by using exponential voltage dependence to describe a separate current component. In general, the single-diode model has low accuracy in representing the behavior of solar cells compared with double-diode model (Wolf et al. 1977). The experimental illuminated I-V data and the unknown model parameters adjusted by PSO algorithm are used as decision variables to minimize an objective function. In PSO, the best fitness of an individual is obtained by minimizing the objective function as possible. The following procedures are applied in the proposed algorithm:
Fig. 3 a Single and b double models of a solar cell; and the evolving processes of PSO and genetic algorism for both c the single and d the double solar cell models (reproduced with permission from Ye et al. 2009)
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(i) Swarm particles positions and velocities as well as the inertia weights are randomly initialized according to prescribed conditions. (ii) The PSO inputs are determined from the solar cell current–voltage characteristics. (iii) The fitness of each particle is evaluated (iv) The best of each particle is compared with its current fitness (v) The position of the particle that has the best fitness defines the global best (vi) The velocity vector for each particle is updated (vii) The position for each particle as well as the inertia weights is updated (viii) The algorithm is repeated (beginning from iii) until the stop criteria is fulfilled Moreover, the PSO performance was compared with the performance of GA for both investigated models. However, the PSO has low convergence speed compared to GA, and the former shows a better performance as it has much lower fitness value compared to the latter as shown in Fig. 3c, d. This is because of the ability of PSO to converge the global optimal solution for non-linear problems characterized by the existence of many local minima. In Hamid et al. (2013), the parameters of a solar cell are extracted considering single-diode model using time-varying acceleration coefficient and inertia weight-based PSO algorithm. Five different parameters of the solar cell current–voltage characteristics have been estimated using the proposed algorithm, namely generated photocurrent, shunt resistance, series resistance, saturation current, and ideality factor. A commercial silicon solar cell was tested, and the obtained experimental results were used to verify the accuracy of the estimated parameters. The procedures used in the parameter identification using the PSO method are illustrated in the flowchart shown in Fig. 4. The obtained results of the proposed algorithm were compared with those obtained from other optimization methods, namely simulated annealing algorithm, chaos particle swarm optimization algorithm, and artificial bee swarm optimization algorithm. Among all tested algorithms, the modified PSO algorithm showed the best performance in terms of standard statistical performance evaluation criteria. The root mean squared error for the three optimization algorithms under investigation, namely simulated annealing algorithm, chaos particle swarm optimization algorithm, and artificial bee swarm optimization algorithm was 0.0017, 0.00139, and 9.9124 × 10−4, respectively, while it was 9.86024 × 10−4 for the proposed approach. Kumar et al. (2017b) proposed a global PSO algorithm to determine hybrid solar cells parameters, namely open circuit voltage, short circuit current ideality factor, series resistance, and shunt resistance, from experimental current–voltage characteristic curves. A wide search range
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Fig. 4 Flowchart of the proposed PSO algorithm (reproduced with permission from Hamid et al. 2013)
(more than ± 100%) for each model parameter has been used. Moreover, to figure out the effect of polymer-processing temperature on the ZnO/PCDTBT co-polymer-based solar cell, the optical absorption, charge transport properties, chemical compositional behavior, and surface morphology of PCDTBT co-polymer films have been investigated and correlated with the extracted parameters of the global PSO approach. The results showed that high-temperature annealing of the polymer results in enhancing ordering in the system via deliberate motion of the polymer chains. Consequently, the charge transport property of the polymer increases. In Mughal et al. (2017), parameters of a silicone solar cell are estimated considering it as an optimization problem solved by hybrid PSO and simulated annealing as a metaheuristic optimization algorithm based on
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experimentally measured current–voltage data. Both single- and double-diode models have been considered. The estimated parameters are shunt resistance, series resistance, photocurrent, diode saturation current, and the ideality factor. The parameter estimation has been achieved via minimizing the difference between measured and calculated data of the solar cell current. The proposed hybrid PSO/simulated annealing (PSOSA) algorithm overcomes the premature converge problem by achieving a global minimum and avoiding trapping in local minimums in all test runs. Moreover, the algorithm performance was evaluated via comparing it with other optimization algorithms, namely conventional PSO, pattern search, improved artificial bee colony, harmony search, and simulated annealing. The comparison results reveal the capability of the proposed algorithm to solve the problem in hand compared with other tested algorithms. The proposed hybrid PSOSA algorithm showed better results compared with those of conventional PSO algorithm in terms of standard deviation which decreased from 4.3154 × 10−4 to 4.07 × 10−17 and the root mean squared error decreased from 1.52 × 10−3 to 7.73 × 10−4. Moreover, among all investigated algorithms (such as harmony search, improved artificial bee colony, simulated annealing, and pattern search) the proposed approach showed the best performance in terms of root mean squared error and mean absolute error. The root mean squared error was 9.95 × 10−4, 10.00 × 10−4, 190.00 × 10−4, 149.36 × 10−4, and 7.73 × 10−4, respectively, while the mean absolute error was 6.78 × 10−4, 28.51 × 10−4, 27.84 × 10−4, 51.10 × 10−4, and 42.146 × 10−4, respectively, which reveals the superior accuracy of the proposed approach compared with other existing approaches.
Photovoltaic/thermal (PV/T) systems PV/T is a hybrid system that utilizes the solar energy to simultaneously generate electricity and heat (Al-Waeli et al. 2017). However, the main disadvantages of such systems are their high installation cost, low available power, and low conversion efficiency. Moreover, the non-uniform distribution of the solar radiation striking the surface of the PV panel results in reducing the power output of the system due to unequal characteristics of the PV cells. Therefore, optimization of the PV/T systems is highly desirable (Michael et al. 2015). In Tabet et al. (2014), PSO method was applied to obtain the optimal tilt angle setting of PV/T collector shown in Fig. 5a to overcome the large data sets required to assess the performance of the system which is time consuming and expensive. Geographical terrain inputs (altitude, longitude, and attitude) were used as input variables to calculate the solar irradiance, while tilt angle of the PV/T collector was considered as the main parameter to be optimized to maximize the PV/T efficiency. The optimization results indicated
Fig. 5 a PV/T collector; b Tuning of the inclination of the PV/T collector with PSO (reproduced with permission from Tabet et al. 2014)
that tilt angle should be changed throughout the year to obtain maximum efficiency in a range of 10°–60°. The received solar irradiation was increased by 10.06–58.34 W/ m2 when the optimized tilt angle was used. The block structure of the proposed PSO algorithm is shown in Fig. 5b. Shi et al. (2015) proposed a hybrid control model for a PV system based on dormant PSO algorithm and conventional incremental conductance algorithm. First, the former algorithm is used to determine global peak area and then the latter algorithm is used to determine the maximum output power of photovoltaic arrays. Dormant PSO is activated when partially shaded conditions are fulfilled and is used to find global peak area. The particles are switched to dormant state one by one. Once all activate particles are converted, the global peak area is located. Then, incremental conductance algorithm is used as it guarantees the performance stability for single peak curve (Sera et al. 2013). The obtained results revealed that dormant PSO has significantly low computational time, improves the efficiency, and reduces the output waveform fluctuation compared with the conventional PSO and incremental conductance algorithms. Sawant and Bhattar (2016) applied a PSO algorithm to optimize PV
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system considering dynamic meteorological parameters and partially shaded conditions which may impair the performance of photovoltaic system as it results in hot spot phenomenon in the PV cell. The PSO performance has been assessed considering different shading patterns and has been compared with perturb-and-observe approach under the same operating conditions. The obtained results revealed the ability of PSO to determine maximum power point under dynamic weather conditions. Mansour et al. (2017) used PSO to maximize the received solar radiation by solar panel surface by selecting the optimum orientation. The PSO algorithm resulted in increasing the received solar radiation by 11.59, 17.53, and 39.9 kWh/m2 compared with those of conventional south-facing attained solar panels for yearly, semiyearly and seasonal periods, respectively. Mao et al. (2017) proposed two-stage PSO algorithm to optimize PV system performance considering maximum power point tracking control and multiple peaks in the output current–voltage curve. The proposed algorithm consists of shuffled frog leaping algorithm coupled with traditional PSO algorithm, this combination ensures accurate and fast searching and avoids trapping in local minima. Moreover, to enhance the convergence speed of the proposed algorithm, an adaptive speed factor is also combined into the proposed two-stage PSO. The obtained results from numerical simulation experiments showed that the convergence speed of the proposed algorithm is twice the convergence speed of the conventional PSO. Moreover, the maximum power point tracking error was decreased from 26.33% in the case of conventional PSO to 2.141% in the case of the proposed algorithm, while the output power was increased by 15.03 W when the proposed algorithm was compared with the conventional one.
was determined based on four different factors (Collado and Guallar 2012; Collado 2008, 2009), namely cosine factor, intercept factor, atmospheric attenuation factor, and shadowing and blocking factor. Seven different parameters are used to control the optimization process, namely two acceleration coefficients, probability of crossover operation in the GA part of the hybrid PSO-GA, probability of mutation of the GA operation in the GA part of the hybrid PSO-GA, and two random unknown numbers. Following optimization, the highest and the lowest observed increase in energy collection are 1.8 × 105 MJ and 0.9 × 105 MJ for the summer and winter solstices, respectively. Moreover, the highest and lowest energy collected per unit cost are achieved during the summer and winter solstices, respectively. Farges et al. (2018) proposed PSO and Monte Carlo algorithms to optimize the performance of solar power tower considering the following design parameters: width, height and tilt angle of the receiver and the tower height. The former algorithm is used to maximize the yearly collected thermal energy at the solar receiver, while the latter is used to maximize yearly optical efficiency. Optical efficiency was determined based on mirror reflectivity, cosine effect, interception efficiency, shading, blocking and spillage phenomena, and atmospheric attenuation. The obtained results, based on the optimized design, indicated that the collected thermal energy has increased by 23.5%, and the optical efficiency of heliostat field has been enhanced by 9%. In Piroozmand and Boroushaki (2016), the optimal design and layout of a multiple solar power tower system via applying PSO investigated to overcome the problem of impairing the optical efficiency due to shading effects. As
Solar power tower A solar power tower system, also known as heliostat power plants or central tower power plants, is a complex solar system in which a tower is used to receive the focused sunlight (Kumar et al. 2017a). It is composed of many subsystems such as a heliostat field, receiver, tower, plant control, power conversion system, heat transport system, and optionally thermal energy storage system (Rea et al. 2018). The solar radiation is concentrated by the heliostat field and then reflected onto a receiver. Then the received concentrated solar energy is utilized to generate heat. Finally, this heat is used as an input to a thermodynamic cycle in which electricity is produced. The optimization of the performance of such systems is highly desirable (Bravo and Friedrich 2018). In Li et al. (2017, 2018), a hybrid PSO and GA algorithm was proposed to determine the maximum potential daily energy collection of a heliostat via optimizing the field layout. The filed efficiency and the optimal combination of heliostats are also determined. Optical efficiency
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Fig. 6 Influence of adjacent heliostats orientations on shading loss (reproduced with permission from Piroozmand and Boroushaki 2016)
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shown in Fig. 6, heliostats layout and orientations lead to different shading losses which have a great effect on the overall system efficiency. The obtained results revealed that the optical performance of the multiple solar power tower system has been improved and the annual efficiency reached 54.58% using the proposed PSO algorithm. The optical performance was enhanced by 0.21% and 0.26% by applying the proposed approach compared with the case without considering the interactions and the separated single-tower fields, respectively.
Solar stills A solar still is a simple device in which solar energy is utilized to distillate brackish water (Sharshir et al. 2017a; Abed et al. 2017; Elsheikh et al. 2018). Brackish water is inserted into the still basin and heated up by sun radiation passing through a glass cover. After water is heated up, it begins to evaporate, and the evaporated water is cooled down when it strikes the inner side of the glass cover and begins to condense as purified water. Many researchers have investigated different designs and techniques to enhance the solar still productivity (Sharshir et al. 2017b, c; Dsilva Winfred Rufuss et al. 2016; Panchal and Patel 2017). One of the important parameters that affect the solar still productivity is the inclination angle of the glass cover. It has been reported that, to maximize the still productivity, the glass cover inclination angle must be approximately equal to the latitude angle of the location (Khalifa 2011). For locations with latitude angle less than 10°, although the solar radiation that enters the solar still is increased by using glass cover inclination angle equal to the location latitude, the condensed water at the inner surface of the glass cover may fall down toward the basin of the solar still. This may result in impairing the solar still productivity and affect the accuracy of any mathematical model used to estimate the solar still performance (Abdallah et al. 2008). To overcome this problem, rubber scrapers have been used in double-slope solar still which results in enhancing the productivity by 63% (Al-Sulttani et al. 2017b). Many mathematical models have been built to predict the hourly productivity of this kind of solar stills (Tripathi and Tiwari 2006; Tiwari et al. 2003; Tsilingiris 2009). However, these models suffer from the lack of accuracy in estimating the still productivity as they neglect the effect of the condensed water falling from the glass cover to the basin on the estimated
productivity. Moreover, most of the aforementioned models are based on trial-and-error procedures which may affect the estimated results. To overcome these problems, Al-Sulttani et al. (2017a) proposed PSO algorithm to estimate the hourly yield of double-slope solar still with rubber scrapers shown in Fig. 7a. The obtained results showed a good consistency between the predicted and experimental results of the solar still yield based on the percentage of absolute relative error as statistical evaluation criterion as shown in Fig. 7b. The proposed approach used an accurate PSO optimization technique coupled with the use of an accurate experimental data. Therefore, the proposed PSO model presented better results compared with Dunkle’s model, as the latter used traditional trial-and-error methods which may lead to a lack of accuracy in the final results. The coefficient of variation (COV) of the obtained results from the proposed model and Dunkle’s model was 4.1% and 14.1%, respectively, which reveals the high accuracy of the proposed model.
Conclusion This paper has reviewed previous published works on the application of PSO in different solar systems including solar collectors, solar cells, solar power towers, photovoltaic/thermal systems, and solar stills. PSO has been an important tool in optimizing the performance of different engineering systems. It has the ability to find global maxima and minima solution for non-linear problems characterized by the existence of many local minima. The obtained results by PSO for different studies showed a good agreement with experimental results which testifies the robustness of the method. Compared with other optimization methods, such as GA, simulated annealing algorithm, chaos particle swarm optimization algorithm, and artificial bee swarm optimization algorithm, PSO showed the best performance. Moreover, the modifications done in PSO algorithm as well as the hybridization of PSO with other algorithms result in better performance in terms of execution, accuracy, and efficiency. Further studies with more focus on integrating different optimization methods as well as artificial neural networks with PSO algorithm should be carried out. Also, the investigation of dynamic PSO to solve multi-objective optimization problem should be considered.
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Fig. 7 a Double-slope solar still with rubber scrapers; b Absolute relative error (ARE) distribution for the proposed PSO-HYSS model, AlSulttani et al. model, and Dunkle’s model (reproduced with permission from Al-Sulttani et al. 2017a)
Compliance with ethical standards Conflict of interest The authors declared that there is no conflict of interest.
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