Pv system sizing using observed time series of solar radiation

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Solar Energy 80 (2006) 46–50 www.elsevier.com/locate/solener

PV system sizing using observed time series of solar radiation
T. Markvart
a b


, A. Fragaki a, J.N. Ross


School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK Received 20 January 2005;received in revised form 1 August 2005; accepted 8 August 2005 Available online 10 October 2005 Communicated by: Associate Editor Aaron Sanchez-Juarez

Abstract Sizing represents an important part of photovoltaic system design. This paper describes a sizing procedure based on the observed time series of solar radiation. Using a simple geometrical construction, the sizing curve is determined as asuperposition of contributions from individual climatic cycles of low daily solar radiation. Unlike the traditional methods based on loss-of-load probability, the reliability of supply enters in this method through the length of the time series of data used in the analysis. The method thus resembles techniques used in other branches of engineering where extreme values are considered as functions ofcertain recurrence intervals. Ó 2005 Elsevier Ltd. All rights reserved.
Keywords: Photovoltaic systems; Sizing; Solar radiation

1. Introduction The sizing of stand-alone photovoltaic (PV) systems is an important part of the system design, and remains an active area for research (see, for example, a review of the sizing tools in Silvestre (2003). In the most fundamental form, sizing proceduresconsider the relationship between the sizes of the PV array and the battery which delivers energy to load with a certain reliability of supply which can be tolerated by the user. The result of the sizing

* Corresponding author. Tel.: +44 2380 593783; fax: +44 2380 593016. E-mail address: tm3@soton.ac.uk (T. Markvart).

procedure can often be summarised in the form of a sizing curve. Asatisfactory definition of supply reliability is key to this analysis. Loss of load probability (LLP)—the traditional power engineering indicator—is most often used for this purpose, but other descriptions have also been given (Silvestre, 2003). The subject was reviewed in a particularly clear form by Gordon (1987). A more recent review was given by Egido and Lorenzo (1992) (see also Lorenzo et al., 1994,Chapter 6) who used an elaboration of the methods of Barra et al. (1984) and Bartoli et al. (1984) to simulate the operation of a PV systems in a number of Spanish sites, and tabulated the results for the sizing curve, including the dependence on the loss-of-load probability as a

0038-092X/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2005.08.011

T.Markvart et al. / Solar Energy 80 (2006) 46–50


parameter. Bucciarelli (1984, 1986) developed an elegant sizing method based on the principles of random walk. Markvart (1996) used the sizing curve to investigate the sizing of PV/wind hybrid systems. The construction of a sizing curve based on LLP requires the modelling of PV system operation over substantial periods of time. Time series ofsolar radiation then cannot come directly from observation but need to be reproduced ‘‘synthetically’’ based on an algorithm which is faithful to the solar radiation statistics. The relationship between the LLP values and the perceived reliability requirements of the user are then indirect, although generally accepted correspondence exist for most standard applications (Lorenzo et al., 1994). Thispaper develops a somewhat different approach to the reliability of supply, and the use of this concept to size a PV system. The method is based on a direct use of solar radiation data near the site where the PV system is to be installed. By using a standard model based on daily energy balance (see, for example, Fragaki, 2005; Fragaki and Markvart, 2005) configurations can be determined, defining a...
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