Methodology Simulation Simulation: Transactions of the Society for Modeling and Simulation International 1–9 Ó The Author(s) 2019 DOI: 10.1177/0037549719831362 journals.sagepub.com/home/sim Optimal design of photovoltaic solar systems considering shading effect and hourly radiation using a modified PSO algorithm Mohammad Hossein Shams 1 , Mohsen Kia 2 , Alireza Heidari 3 and Daming Zhang 3 Abstract Regarding the significant potential of solar energy in Iran, implementation of optimally designed photovoltaic (PV) sys- tems can be effective. Hence, this study proposes two objective functions: first, the maximum possible output energy for a given area and, second, the minimum area receiving a given yearly energy from PV fixed collectors in a solar field, both of which are calculated. In addition, the shading and masking effects are considered in the calculations. A modified parti- cle swarm optimization (MPSO) algorithm is used to solve the optimization problem. The case study of this article is a shopping center in Isfahan-Iran (latitude 32.5°N) with the minimum yearly energy demand of 171 MWh and the 5000 m 2 roof area. To evaluate the yearly energy, the calculated hourly radiation approach is applied to the case study. The results show that the maximum possible generated energy is 881 MWh/year for the given area. In addition, to provide the mini- mum demand, 720 m 2 area of roof is needed. To verify the effectiveness of the proposed MPSO, the results are com- pared with those of obtained by the relevant commercial software. Keywords Photovoltaic systems, solar radiation, solar energy, modified particle swarm optimization 1. Introduction The amount of energy obtained from photovoltaic (PV) collectors in a solar field mostly depends on the total radia- tion on the tilted PV surfaces and deployment of PV col- lectors in a solar field. In order to increase the efficiency of a PV system, the factors that affect the performance of a PV panel should be analyzed. 1 So far, many approaches have been presented to increase the efficiency of solar farms. Some of these meth- ods include deployment of PV arrays, 2 varying the archi- tecture of the system, such as using central or distributed inverters, 3 and changing in the circuit topologies. 4,5 Among these methods, deployments of PV arrays is one of the most effective approaches. 6 These methods are divided into two groups: electrical and mechanical deployments. In the electrical deployments group, the electrical intercon- nections can be changed by switches when partial shading is recognized by sensors. 7 However, in the mechanical deployments group, the physical locations of the modules in the solar field are relocated, while the electrical inter- connections remain unchanged. Between these groups, the electrical deployments group has lower complexity. Also, there is no need of any extra apparatus such as switches or sensors. These can reduce the initial costs and needed maintenance. Despite these advantages, the relocation of modules is a time-consuming process and it is only imple- mented in the site construction stage. Latitude of the solar field region, due to its solar radia- tion and ambient temperature, will affect the output of PV collectors. In addition to the area of collectors, the number of rows and arrangement of collectors in a solar field will affect the output energy and power. Increasing the area of PV collectors and the number of rows increases the output energy, but, in contrast, increases the shading for a given 1 Department of Electrical and Computer Engineering, Babol Noshivani University of Technology, Babol, Iran 2 Department of Electrical Engineering, Islamic Azad University, Pardis, Iran 3 School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, Australia Corresponding author: Mohsen Kia, Department of Electrical Engineering, Pardis Branch, Islamic Azad University, Pardis Branch, Pardis, Tehran, Iran. Email: mohsenkia80@gmail.com