Short Communication Size optimization for a hybrid photovoltaic–wind energy system Zong Woo Geem ⇑ Gachon University, Department of Energy IT, 1342 Seongnam Daero, Seongnam 461-701, South Korea Johns Hopkins University, Environmental Planning and Management Program, 11833 Skylark Road, Clarksburg, MD 20871, United States article info Article history: Received 10 October 2011 Received in revised form 3 January 2012 Accepted 29 April 2012 Available online 4 June 2012 Keywords: Hybrid photovoltaic and wind system Optimization Renewable energy abstract Because photovoltaic (PV) and wind energies are renewable and free from greenhouse gas, they can be alternatives to fossil fuels. So far, many researchers have cost-optimally designed hybrid PV-wind systems. However, they have seldom provided whole datasets for other researchers to fully understand their approaches and to tackle the same problem with their novel techniques. Thus, this study shows one exam- ple of the optimal design of a hybrid PV-wind system by providing (1) regular optimization formulation, (2) full dataset, and (3) computing results with various design constraints. Hopefully many researchers will apply various optimization techniques to the problem in the future. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Sun and wind have powers which can be converted into energy (electricity) generated by solar panels and wind turbines. Because photovoltaic (PV) and wind energies are abundant, renewable, and clean without causing greenhouse gas, they can be alternatives to fossil fuels [1]. Also, these renewable energies can significantly contribute on reducing the electricity generation cost in off-the- grid remote places such as islands [2]. So far various researches have been performed for the optimal design of hybrid PV and wind power generating systems [3–8]. However, they have seldom provided full datasets for other researchers to replicate and to apply existing and novel algorithms [9–12]. Actually, so many novel methods for optimal design prob- lems have been developed during last decade or two, and research- ers want to test the performance of those techniques by applying them to renewable energy problems. The design of hybrid solar- wind systems can be a good example for those demands, however, the examples in previous literature are too large-sized to become bench-mark problems, or they do not provide detailed numerical datasets. Thus, the objective of this paper is to provide a full dataset for the design of a basic PV-wind system. In addition, this study in- tends to provide a better optimization formulation and solving technique for the design. 2. Optimization formulation The objective function of the PV-wind system design is the total design cost C T which consists of total capital cost C Cpt and total maintenance cost C Mtn as follows: Minimize C T ¼ C Cpt þ C Mtn ð1Þ Here, it should be noted that while the capital cost occurs in the beginning of a project, the maintenance cost occurs along the pro- ject life. Consequently, costs at different times cannot be directly compared, but should first be made equivalent through the use of discount factors that convert a monetary value at one time to an equivalent value at another time [13,14]. In this study, the ini- tial capital cost P is converted into annual capital cost A using the following capital-recovery factor: A P ¼ ið1 þ iÞ n ð1 þ iÞ n  1 ð2Þ where i is annual interest rate; and n is life span of the system (in years). Thus, total annual capital cost C Cpt can be: C Cpt ¼ A P ½N Sol C Sol þ N Wind C Wind þ N Batt C Batt þ C Backup  ð3Þ where N Sol is number of solar panels, which is decision variable; C Sol is unit cost of solar panel; N Wind is number of wind turbines, which is decision variable; C Wind is unit cost of wind turbine; N Batt is num- ber of batteries; C Batt is unit cost of battery; and C Bachup is cost of backup generator for the use when solar and wind energies are not sufficient and storage batteries are low. The unit cost of solar panel C Sol consists of panel price and installation fee; and the unit cost of wind turbine C Wind consists of turbine price and installation 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.04.051 ⇑ Address at: Gachon University, Department of Energy IT, 1342 Seongnam Daero, Seongnam 461-701, South Korea. Tel.: +82 31 750 5586, +1 301 251 2646. E-mail addresses: geem@gachon.ac.kr, geem@jhu.edu Electrical Power and Energy Systems 42 (2012) 448–451 Contents lists available at SciVerse ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes