A computationally efficient method for the design of the heliostat field for solar power tower plant Saeb M. Besarati, D. Yogi Goswami * Clean Energy Research Center, University of South Florida, 4202 E. Fowler Av., ENB 118, Tampa, FL 33620, USA article info Article history: Received 13 June 2013 Accepted 24 March 2014 Available online Keywords: Concentrated solar power Heliostat field design Shading and blocking calculation Phyllotaxis Optimization abstract A number of codes have been developed in order to optimize the heliostat field layout for solar power tower plants. These codes are intended to improve calculation accuracy as well as computational time. Of all the factors that need to be taken into account in these codes, shading and blocking calculations introduce significant complexity as they are computationally intensive. In this paper, a new and simple method is proposed to identify the heliostats with the greatest potential for shadowing and blocking a heliostat. Using the new method, the computational time is considerably reduced as unnecessary cal- culations are avoided. The Sassi method [1] is then used to calculate the shading and blocking efficiency. The results are compared with the literature and good agreement is obtained. As a case study, the paper also investigates optimization of a 50 MWth heliostat field layout for Dagget, California. Yearly insolation weighted efficiency is selected as the objective function while two parameters of the prophylaxis pattern [2], which define the shape of the field layout, are the design variables. The acceptance angle of the cavity receiver and distance between the adjacent heliostats are the physical constraints which are included in the optimization. The optimization algorithm is explained in detail and the optimal field layout is presented. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Solar power tower technology is deemed advantageous over other concentrated solar power (CSP) technologies due to its ability to achieve high operating temperatures, resulting in greater power cycle efficiency. This advantage, along with the recent surge of interest in reducing the cost of CSP plants, has prompted significant research in the power tower technology. In these systems, the sun’s rays are reflected and concentrated by a number of mirrors that are collectively called the heliostat field. The concentrated rays are focused onto a receiver that absorbs the radiation and transfers the thermal energy to a fluid. The thermal energy is then converted into power using conventional power cycles [3]. Optimal design of the heliostat field is of great importance and has been the subject of many studies. The main reason is that 50% of the total cost of the power plant [4] and 40% of the energy losses [5] are associated with the heliostat field. Since the 1970s, several codes have been developed for this purpose, some of which are described in Ref. [6]. All of these codes use different approaches to maximizing the overall field efficiency which is defined as: h ¼ h cos  h att  h int  h s&b  h ref (1) where h cos represents the cosine effect efficiency, h att is the at- mospheric attenuation efficiency, h int is the interception efficiency which accounts for the fraction of the reflected rays that hit the target, h s&b is the shading and blocking efficiency, and h ref is the reflectivity of the heliostats. It is noteworthy that interception ef- ficiency is dependent on the sun-shape error, mirror slope error, astigmatic effect and tracking error, which are described in the subsequent sections. Of all the factors included in the equation, the shading and blocking factor ðh s&b Þ is the most computationally intensive parameter because it not only depends on the sun’s position and the heliostat locations, but is also a function of the location of the neighboring heliostats. During the optimization process, the rela- tive position of each heliostat with respect to others is varied in order to maximize the overall efficiency, which requires significant computational time. A number of methods have recently been proposed to reduce the time required to calculate the shading and blocking factor. * Corresponding author. Tel.: þ1 813 974 0956; fax: þ1 813 974 5250. E-mail addresses: goswami@usf.edu, solargoswami@gmail.com (D. Yogi Goswami). Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene http://dx.doi.org/10.1016/j.renene.2014.03.043 0960-1481/Ó 2014 Elsevier Ltd. All rights reserved. Renewable Energy 69 (2014) 226e232