Disentangling flow-energy transformations for small hydropower plants: from reverse engineering to uncertainty assessment and calibration

Due to their negligible storage capacity, small hydroelectric plants cannot offer regulation of flows, thus making the control of energy production a very difficult task, even for small time horizons. Further uncertainties arise due to limited information, both in terms of upstream inflow data and technical characteristics. Usually, the sole available measurements refer to power production, which is a nonlinear transformation of the river discharge. In this thesis we investigate the three configurations of this transformation, named the forward, the inverse and the calibration problem. The major outcome is a generic stochastic framework for the so-called inverse problem of hydroelectricity, i.e. the extraction of streamflow from observed energy data, focusing on two key potential sources of uncertainty, i.e. in energy production (observational error) and the efficiency curve of turbines (parameter error). Key issue of this reverse engineering approach is that the model error is expressed in stochastic terms, which allows for embedding uncertainties within calculations. Another interesting issue is the extrapolation of high and low flows outside of the range of operation of SHPs, which is employed by combining empirical hydrological rules for representing the rising and falling limbs. The methodology is tested in hypothetical problems as well as in a real-world case, i.e. the oldest (est. 1926) small hydroelectric plant of Greece, located at Glafkos river, in Northern Peloponnese. Among other complexities, this comprises a mixing of Pelton and Francis turbines, which makes the overall modelling procedure even more challenging and also requires to extract the efficiency curves of the two turbines through calibration. Our analyses indicate that the proposed framework may be the basis for handling several practical problems and open research questions in the broader area of simulation and optimization of small hydroelectric works.