Probabilistic Flow Duration Curves for Small Hydro Plant Design and Performance Evaluation

Abstract

This work presents a probabilistic flow duration methodology that can be used as an alternative approach to the design and performance evaluation of small hydro plants. The probabilistic approach aims to quantify the uncertainty influencing the design and the economic outlook of small hydropower projects thus overcoming the limitations of the standard design methodology, which is based on a deterministic approach through the historical flow duration curve at the intake site. A simple probabilistic flow duration curve model is presented and an applied case study of the probabilistic approach to plant design and evaluation is provided based on a typical small hydro plant in a mountainous region of Greece. The results of this study however are not restricted to any particular geographical region and the methodology can be applied in a variety of hydrologic and economic environments. Keywords Flow duration curve . Small hydro plants . Probabilistic flow model . Log-normal distribution . Energy output . Financial risk . Environmental flow Notations Q Mean daily flow (m 3 /s) Q 0 Location parameter representing a lower boundary of flow (m 3 /s) a, b Parameters of LN distribution (annual) a f , b f Parameters of Normal distribution (global) Z u u-percentile of the standard normal variate s[ln(Q)] Standard deviation of log-transformed flows Water Resour Manage (

Understanding Hydrological Variability for Improved Water Management in the Semi-Arid Karkheh Basin, Iran

“…The FDC is a cumulative distribution of flows at a site showing the flow assurance of how often any flow is equaled or exceeded. The details on the concept and applications can be found in literature (Linsley et al 1949;Vogel and Fennessey 1995;Smakhtin 2001a;Gupta 2008;Niadas and Mentzelopoulos 2008). The FDC analysis was carried out for the daily, monthly and annual time scales and various exceeding percentiles representing high, median and low flows (e.g., Q1, Q5, Q10, Q25, Q50, Q75, Q90, and Q95) were derived.…”

A Procedure for Evaluating the Compatibility of Surface Water Resources with Environmental and Human Requirements

“…& Methods based on an analogy between the duration curve and probability distribution (Niadas and Mentzelopoulos, 2008) of mean daily discharge at the river cross-section of interest; in this case the moments of distribution are "regionalized" in order to parameterize the duration curve at the cross-section of interest (Fennessey and Vogel, 1990;Waylen, 1993a, 1993b;Claps and Fiorentino, 1997;Singh et al, 2001;Castellarin et al, 2004); & Methods that do not hypothesize any connection between the duration curve and probability theory but represent the duration curve by means of an analytic equation: in this case several discharges of given duration are "regionalized" so that the type of curve selected can be adapted accordingly at the site of interest (Quimpo et al, 1983;Mimikou and Kaemaki, 1985;Franchini and Suppo, 1996;Yu et al, 2002;Castellarin et al, 2004;Vezza et al, 2010); & Methods that make reference to dimensionless formulations of the duration curve; in these cases a "discharge index" is selected and appropriate dimensionless duration curves, valid for hydrologically homogeneous sub-regions, constructed on the basis of observed duration curves. The "discharge index" is regionalized by means of equations that relate it to meteorological and geomorphological factors.…”

The soil water characteristic as new class of closed-form parametric expressions for the flow duration curve

“…Ever since, the FDC has been used in many fields of study including (among others) the design and operation of hydropower plants (Singh et al, 2001;Niadas and Mentzelopoulos, 2008), flow diversion and irrigation planning (Chow, 1964;Warnick, 1984;Pitman, 1993;Mallory and McKenzie, 1993), streamflow assessment and prediction (Tharme, 2003), sedimentation (Vogel and Fennessey, 1995), water quality management (Mitchell, 1957;Searcy, 1959;Jehng-Jung and Bau, 1996;Moftakhari et al, 2015), waste-water treatment design (Male and Ogawa, 1984), and low-flow analysis (Wilby et al, 1994;Smakhtin, 2001;Pfannerstill et al, 2014). Recent studies have used the FDC as a benchmark for quality control (Cole et al, 2003), and signature or metric for model calibration and evaluation (Refsgaard and Knudsen, 1996;Yu and Yang, 2000;Wagener and Wheater, 2006;Son and Sivapalan, 2007;Yadav et al, 2007;Yilmaz et al, 2008;Zhang et al, 2008;Blazkova and Beven, 2009;Westerberg et al, 2011;Vrugt and Sadegh, 2013;Pfannerstill et al, 2014;Sadegh and Vrugt, 2014;Sadegh et al, 2015).…”