The maximum output of the solar receiver is achieved when the solar receiver is perpendicular to the Sun's rays. Different attempts were made for making the solar receiver utilizing the maximum portion of incident solar radiation. The use of a dual-axis sun tracker versus a fixed-flat position is evidently profitable, but from economic point of view it is questionable. A mathematical conception has been developed and applied in this chapter to determine the energy gain resulted from different installations of PV systems. The experimental measurements and the model results show that, it is not economical to track the sun in hot and sunny regions because of the overheating effect on the PV panels' performance. The provided data, in literature, compare the performance of dual or single axis tracking with fixed solar receiver even the long term solar tracking is possible and effective with a negligible increase of the price of the unit of useful energy. This can be achieved by choosing the best monthly or even seasonally optimum tilts. The introduced concept of energy gain, see chapter 3, is calculated in this chapter all over the world and it was found that it is very useful in evaluating the performance of different types of tracking. This concept allows to evaluate the effectiveness of daily, weekly, fortnightly, monthly, seasonally, biannually and yearly adjustment of the solar receiver tilt angle in relation with the ideal instantaneous dual tracking.
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Optimization is a method of finding the conditions that give maximum or minimum value of the objective function to obtain the accurate results under specified conditions. It is useful in the design, construction and maintenance of any engineering system (Rao, 2010). For finding optimum tilt angle, solar radiation on the tilted surface is taken as an objective function which is solved using different optimization techniques like Genetic Algorithm (GA), Simulated Annealing (SA) technique and particle swarm optimization(PSO). Genetic algorithm (GA) is suitable for optimization problems which include complex nonlinear variables, a sit can find the global optimum solution with a high probability (Goldberg, 1989). A population of points is used for starting the GA instead of a single design point (Sivanandam and Deepa, 2008). It involves principles of natural genetics and natural selection. The natural genetics are reproduction, crossover and mutation which are used in the genetic search procedure (Beasley, Bull and Martin, 1993). Talebizadeh, Mehrabian and Abdolzadeh (2011) used GA to calculate hourly, daily, monthly, seasonally and yearly optimum tilt angle for Iran and showed that the optimum hourly surface azimuth angle is not zero and optimum tilt angles of photovoltaic panels and solar collector are found to be the same. The solar energy gain at daily, monthly optimum tilt angle is found to be the same but energy gain is more at hourly tilt angle. Therefore, the solar tracker is beneficial for hourly variation of tilt angle. Čongradac, Prica, Paspalj, Bojanič and Čapko, (2012) used GA and fuzzy logic process to find out optimum blind tilt angle (angle rotated in anticlockwise and clockwise direction) for maintaining accurate brightness of the room. This process is useful in maintaining user′s comfort and saving energy. Simulated Annealing (SA) derives its name from the simulation of thermal annealing of critically heated solid sand is used to find the global optimum with a high probability of objective functions which contain numerous local minima. Chen, Lee and Wu (2005) used SA for calculating the optimum installation angle for fixed solar-cell panels. Particle Swarm Optimization (PSO) is a stochastic technique for exploring the search space for optimization (Kennedy and Eberhart, 1995). It is achieved by particles in multidimensional space that have a position and a velocity (Beasley, Bull and Martin, 1993). In PSO particles are flying through hyper space and adjust their own best position i.e. the smallest objective function values. Chang (2010a) used the varying inertia weight methods (Shi and Eberhart, 1998; Shi and Eberhart, 1999; Eberhart and Shi, 2001; Ratnaweera, Halgamuge and Watson, 2004; Chatterjee and Siarry, 2006) and proposed a particle-swarm optimization method with nonlinear time-varying evolution (PSO—NTVE) to determine the tilt angle of PV modules for maximum output electrical energy of the modules in Taiwan. The yearly optimal angle for Taipei area is 18.16o and 17.3o, 16.15o, 15.79o, 15.17o, 17.16o, 15.94o for Taichung, Tainan, Kaosiung, Hengchung, Hualian, Taitung respectively. The PSO NTVE is faster than the other three PSO methods and the GA method for achieving an optimum solution. Therefore, these optimization techniques will give better results than the other methods (latitude based method, maximizing radiation by changing β from 0o to 90o at fixed steps).