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

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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.

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Abbreviations

Q :

Mean daily flow (m3/s)

Q 0 :

Location parameter representing a lower boundary of flow (m3/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

Y :

Log-transformed flow

F :

Percentage of time within a year, n/(365 + 1)

n :

Number of days within a year that Q is equaled or exceeded

f :

Probability of non-exceedance of the quantity Y(F) among years

s a , s b :

Standard deviations of a and b

N :

Number of years of flow record

Q(F) f :

Flow equaled or exceeded in F % of time with probability (1–f)

Q p,m :

p-percentile of the historical median annual FDC

Q p,k :

p-percentile of historical daily flow value in year k, where k = 1 ... N

P :

Percentile of daily flow values within the year

M :

Median value of flows Q

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Authors and Affiliations

  1. Z&A – P. Antonaropoulos & Associates S.A., 57 Souidias Street, 106 76, Athens, Greece

    Ioannis A. Niadas

  2. P. Mentzelopoulos Engineering Consulting, 1 Vosporou Str., 146 71 N. Erithrea, Athens, Greece

    Panos G. Mentzelopoulos

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  1. Ioannis A. Niadas
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  2. Panos G. Mentzelopoulos
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Correspondence to Ioannis A. Niadas.

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Niadas, I.A., Mentzelopoulos, P.G. Probabilistic Flow Duration Curves for Small Hydro Plant Design and Performance Evaluation. Water Resour Manage 22, 509–523 (2008). https://doi.org/10.1007/s11269-007-9175-y

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