Optimum sizing of wind-battery systems incorporating resource uncertainty Anindita Roy, Shireesh B. Kedare, Santanu Bandyopadhyay * Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India article info Article history: Received 14 November 2009 Received in revised form 12 February 2010 Accepted 29 March 2010 Keywords: Wind-battery system Chance constrained programming Sizing curve Design space Wind resource uncertainty abstract The inherent uncertainty of the wind is a major impediment for successful implementation of wind based power generation technology. A methodology has been proposed in this paper to incorporate wind speed uncertainty in sizing wind-battery system for isolated applications. The uncertainty associated with the wind speed is incorporated using chance constraint programming approach. For a pre-specified reliability requirement, a deterministic equivalent energy balance equation may be derived from the chance con- straint that allows time series simulation of the entire system. This results in a generation of the entire set of feasible design options, satisfying different system level constraints, on a battery capacity vs. gen- erator rating diagram, also known as the design space. The proposed methodology highlights the trade- offs between the wind turbine rating, rotor diameter and the battery size for a given reliability of power supply. The optimum configuration is chosen on the basis of the minimum cost of energy (US$/kWh). It is shown with the help of illustrative examples that the proposed methodology is generic and flexible to incorporate alternate sub-component models. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Renewable energy options may be effectively used for isolated power systems [1,2]. However, high variability and uncertainty associated with renewable energy sources pose major challenges in designing isolated power systems. In order to overcome the diurnal and seasonal fluctuations of power supplied by renewable energy technologies, integration of an energy storage device be- comes necessary. Many applications such as a remote telecommu- nication towers, hospitals and commercial energy systems are required to abide by rigorous norms of power supply reliability; thus, making it obligatory to design the system by accounting for uncertainty associated with various design variables. A reliability based technique will lead to higher customer satisfaction and eventually bring societal acceptability of renewable based technol- ogies. A methodology for designing as well as identifying the upper and lower bounds of the design variables (rotor diameter, genera- tor rating and battery bank capacity) of a standalone wind-battery power system by considering the uncertainty in wind speed avail- ability has been proposed in this paper. Design procedures for wind-based isolated power systems have seen a widespread application of deterministic parameter model- ing [3–8]. For example, sizing the battery bank for higher number of days of autonomy [5,9,10], sizing of the generator(s) based on the worst wind availability time period [9,11], and provision of capacity reserve margin [12]. Over sizing the battery bank and the generator do not necessarily quantify the reliability of the over- all system and on the other hand, increase the cost of the system significantly. The capacity reserve margin criterion may not be appropriate to size systems containing only renewable sources, since the capacity of renewable systems is fundamentally fluctuat- ing by nature due to meteorological dependence. As uncertainty associated with the wind resource is high, deterministic tech- niques cannot guarantee pre-specified system reliability. The primary step towards incorporating wind speed uncer- tainty in the system design methodology is to appropriately char- acterize the wind regime. The availability of discrete wind speeds at the site of interest may be statistically described by a probability density function (PDF), provided sufficient time series wind speed data at the site are available. Ramakumar et al. [13] have character- ized the variability of the wind regime by considering three dis- tinct values of the mean wind speed: low (4 m/s), medium (6 m/ s) and high (8 m/s). With each of these mean wind speeds, three different values of standard deviation are considered. Considering the wind speed as a random variable following a Weibull distribu- tion and with a known power curve (power output vs. wind speed characteristic) of the wind machine, the average power output for a particular time step (e.g., 1 h/1 day/1 month) may be predicted [14]. Tina et al. [15] have used a probability distribution function of wind power derived from the probability function of wind speed assuming an empirical power curve model of the wind turbine. Ek- ren and Ekren [16,17], Ekren et al. [18] have fitted the observed wind speed during each time step (1 h) with different theoretical distribution functions or combination of two theoretical distribu- tions. The mean wind speed for each hour as determined from 0306-2619/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2010.03.027 * Corresponding author. Tel.: +91 22 25767894; fax: +91 22 25726875. E-mail address: santanu@me.iitb.ac.in (S. Bandyopadhyay). Applied Energy 87 (2010) 2712–2727 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy