Motivated by the challenges induced by the so-called Target Model and the associated changes to the current structure of the energy market, we revisit the problem of day-ahead prediction of power production from Small Hydropower Plants (SHPPs) without storage capacity. Using as an example a typical run-of-river SHPP in Western Greece, we test alternative forecasting schemes (from regression-based to machine learning) that take advantage of different levels of information. In this respect, we investigate whether it is preferable to use as predictor the known energy production of previous days, or to predict the day-ahead inflows and next estimate the resulting energy production via simulation. Our analyses indicate that the second approach becomes clearly more advantageous when the expert's knowledge about the hydrological regime and the technical characteristics of the SHPP is incorporated within the model training procedure. Beyond these, we also focus on the predictive uncertainty that characterize such forecasts, with overarching objective to move beyond the standard, yet risky, point forecasting methods, providing a single expected value of power production. Finally, we discuss the use of the proposed forecasting procedure under uncertainty in the real-world electricity market.

Short-term forecasting of energy production is of high importance for power systems of all scales. This task becomes even more crucial for the renewable sources, which are governed by stochastic drivers, namely weather processes (e.g., wind velocity, solar radiation, streamflow), that make particularly difficult to ensure a credible power supply scheduling. At the same time, the new legal framework in energy market called “Target Model”, introduce further complexities to day-ahead trades, thus making short-term forecasting not only a challenging technical problem but also an emerging need in the imminent new era of decentralized electricity, dominated by renewable energy sources.

The associated research and operational applications so far mostly span over two main directions. The first refers to the short-term energy production forecasting by solar and wind power systems, typically on the basis of Numerical Weather Prediction (NWP) models, providing deterministic point forecasts. The second field of interest deals with the long-term energy production by large hydropower reservoirs, based on projections of their inflows (e.g., Cassagnole et al., 2021). Nowadays, emphasis is given to data-driven approaches (e.g., machine learning), also combined with stochastic-probabilistic schemes for representing uncertainties that are ignored by NWP models (Felder et al., 2018; Talari et al., 2018; Croonenbroeck and Stadtmann, 2019).

Small hydroelectric works are classified as one of the most cost-effective technologies, establishing them as one of the most widespread form of renewable energy. This concerns hydropower systems up to a specific capacity value (e.g., 15 MW in Greece), commonly of negligible storage capacity, where the energy production is a direct conversion of the streamflow arriving at the intake. In contrast to other renewables, the short-term energy forecasting problem, in the field of SHPPs without storage, has not gained the necessary attention from the research community (Yildiz and Açikgöz, 2021). The typical input information used in forecasting schemes appears to be the observed energy production and rainfall (e.g., Li et al., 2015), while some researchers also use forecasted precipitation, provided by NWP models (Monteiro et al., 2013). However, we should highlight that the accuracy of NWPs with respect to rainfall forecasting is still questionable, particularly in complex mountainous reliefs (Ólafsson and Ágústsson, 2021).

Surprisingly, streamflow forecasting procedures, followed by turbine operation models employing flow-energy conversions, seem to be missing. A plausible explanation is the scarcity of streamflow observations, since most of SHPPs are located in small remote catchments, lacking of hydrometric infrastructures. On the other hand, given that the technical and operational characteristics of the SHPP are known (e.g., turbine scheduling and efficiency curves), the past inflows can be retrieved with quite satisfactory accuracy, on the basis of observed power production data, through reverse engineering (Sakki et al., 2022).

Taking as an example a run-off-river SHPP, in the upper course of river Achelous, Western Greece, we investigate different day-ahead power forecasting approaches, driven by alternative data sources. Since the limited scale of the SHPP industry makes difficult to support highly sophisticated operational forecasting systems, we seek for establishing simple and parsimonious regression-type approaches, instead of more complex schemes, e.g., from the domain of machine learning (ML) (cf. Papacharalampous et al., 2019), that yet require significant expertise to be properly used and often demanding computational infrastructures. This fact is probably associated with the growing interest in explainability of such techniques (cf. discussion by Ribeiro et al., 2016). Key objective, and at the same time novelty of this research, is the maximization of information gathered from the available data, by taking advantage of the hydrological expertise and knowledge about the system's properties (i.e., turbine capacity, operational flow range, and efficiency). Our research also highlights the training and evaluation procedure of each forecasting approach, as well as the representation of uncertainty and its practical interpretation. In this vein, our overall objective is to move beyond the standard, yet risky, point forecasting methods, providing a single expected value of hydropower production, thus quantifying the overall predictive uncertainty of each method, and use it as a guidance for modelling energy market behaviors and support decision-making.

To define a hydroelectric plant as “small”, the installed power capacity of the turbines must be under a certain limit, determined by the national legislation. This limit varies considerably globally, but the most common values are varying from 10 to 30 MW. While the above definition can include hydropower stations as additions to reservoirs, the common type of small hydropower plants (SHPPs) refers to systems without storage capacity, taking advantage of different combinations of discharge and head. These are actually diversion systems that exploit a specific range of the arriving streamflow, where the maximum flow value depends on the head and installed capacity of turbines, while the minimum one also depends on the turbine type.

The conversion of the turbine flow to hydropower is made via the well-known
formula:

Efficiency curve for the Francis turbine applied in the hydropower system under study (analytically-derived relationship provided by Sakki et al., 2021, based on nomographs by Papantonis, 2008, p. 231).

In the context of our analysis, we consider a run-of-river plant under
study, in the upper course of river Achelous, Western Greece. The available
hydrological information comprises spatially-averaged daily precipitation
data from five representative meteorological stations, and daily streamflow
data at the intake. The latter input is extracted by adjusting the observed
inflows to a downstream site, i.e., Kremasta reservoir (Efstratiadis et al.,
2014), by accounting for the ratio of the corresponding drainage areas
(about

Streamflow time series at the intake for hydrological year 1971–1972.

Before proceeding with the forecasting problem, it is essential to specify
the technical characteristics of the project. First, we estimate the
environmental flow to be released downstream of the intake, in order to
sustain the riverine ecosystems (Efstratiadis et al., 2014). Following the
Greek legislation for SHPPs, this is defined as the 30 % of mean discharge
of September, which here equals to 0.25 m

The operation policy of the SHPP is demonstrated in Fig. 3. This has been
obtained by seeking for the optimal hierarchy of the two turbines, in order
to maximize the power production across different discharge ranges. In
particular, from 0.12 to 0.85 m

Design characteristics of the two Francis-type turbines.

Optimal sharing of discharge conveyed to the two turbines and associated power production.

The consecutive conversions across SHPPs allows for establishing two
alternative routes to the power forecasting problem, here employed on a
day-ahead basis. The direct route aims at predicting the next-day energy
production via regression models that use as explanatory variables past
observations, in terms of power production and the past rainfall, as the
sole source of hydrological data. On the other hand, the indirect route
initially aims at predicting the day-ahead discharge, given that such data
exist. The forecasted flows are next introduced to the operation model of
the system, for extracting the forecasted energy. For each approach, we
assess alternative forecasting schemes, in terms of model structure and
data. In order to calibrate the free parameters of each model and evaluate
their predictive capacity, we introduce a quite strict skill score in terms
of the generic efficiency formula:

In the direct approaches we use as independent variables (predictors) for
the energy generated at time step (day)

In the indirect approaches we aim to provide day-ahead forecasts of the
discharge to feed the flow-energy conversion model, which is summarized in
the diagram of Fig. 3. In this respect we use as predictors of streamflow
at day

In order to remedy the above shortcomings, we adjust the fitting metric,
i.e., efficiency, to the turbine operation range (

An interesting question that arises is whether just a better day-ahead flow forecasting model that does not account for the operational characteristics of the system, would outperform the optimal model so far. In this respect, we apply a more complex approach from the Machine Learning (ML) family, namely a Deep Feedforward Neural Network (DNN). The DNN model is composed by three hidden layers with 128, 64 and 64 neurons, respectively, while the Rectified Linear Unit (ReLu) activation function is adopted for all neurons. As inputs, we use the streamflow of past 5 d and the rainfall of past two days. The model is fitted on the basis of Mean Square Error (MSE), for a number of 100 epochs, by using a batch size of 64.

In Fig. 4 we compare the actual and forecasted flow and energy values provided by the Indirect Model B and the ML approach, for hydrological year 1971–1972. Surprisingly, while the ML model ensures a much better fitting to the observed flows than the simple regression expression (4), (84 % vs. 63 %), the conversion to energy is rather disappointing. In particular, the classical efficiency metric is only 50.7 %, while the modified efficiency is strongly negative. Furthermore, the derived error properties are clearly non satisfactory (underestimation of the average energy up to 1 MW, quite large standard deviation, and, significant autocorrelation). The poor predictive capacity of the data-driven approach is attributed to the training procedure, in which we ignored the range of operation of the small hydroelectric plant, which is key feature of its management.

Comparison of historical vs. predicted time series obtained by two
forecasting models (indirect B and ML) for

Comparison of different forecasting schemes.

n/a: not applicable

Predictive uncertainty is defined as the probability of occurrence of a
predictand's value (in the particular case, energy production) conditional
upon prior observations and knowledge, as well as on all the information we
have obtained on that specific value from model forecasts (Coccia and
Todini, 2011). A typical means to quantify the predictive uncertainty of a
deterministic simulation model, is to add a random component (noise),

In our case, we use the more robust forecasting scheme (Indirect Model B)
and provide

In order to take advantage of the concept of uncertainty in practice, as would be made in a real-world energy market, we can determine alternative market policies in terms of quantiles. In particular, we can apply the upper, middle and low quantiles as representatives of a risky, mild and conservative forecast of the day-ahead energy, and evaluate them in economic terms, by assigning a unit profit value for delivering the energy produced up to the forecasted value, and a unit penalty for the deviations (i.e., deficits with respect to the forecasted value). For instance, we account for the 90 %, 50 % and 10 % quantiles and apply a fixed profit of EUR 60/MWh and a penalty value of EUR 50/MWh; the aforementioned values are representative of the recent system marginal price and price of deviations, respectively, of the Hellenic Electricity Market. Under this premise, the mild policy ensures a mean annual profit of EUR 0.86 million, the conservative EUR 0.81 million, and the risky EUR 0.43 million. This quick pseudo-financial analysis allows for comparing the different interpretations of a forecasting approach under uncertainty.

Monthly statistical characteristics of residuals derived from the application of Indirect Model B.

Comparison of actual energy production for hydrological year
1972–1973 with three characteristic prediction quantiles (10 %, 50 % and 90 %),
by considering the error process as:

This research aims to revisit the problem of day-ahead power forecasting in the case of small hydropower plants without storage capacity, which has received little attention so far. Taking as an example a typical project of this category, and by using simple yet effective modeling schemes, we attempt to revisit several issues that may have been well-addressed in the generic context of hydrological forecasting, but not in the specific case of SHPPs, namely: (a) the essential information as input to hydropower forecasting; (b) the advantages of the indirect forecasting approach, involving the use of a streamflow forecasting model, against the direct one, that does not account for the inflow input, but relies solely on the energy production data; (c) the importance of past precipitation data as exogenous predictor, providing macroscopic information about the catchment state (e.g. antecedent soil moisture conditions); (d) the training procedure and the skill score to be applied; and (e) the representation of the predictive uncertainty around the point forecast of day-ahead energy; (f) and the use of uncertainty-aware forecasts from the practicians' point-of-view (investors, power engineers, stakeholders).

Our investigations indicated that the proposed flow-based approach is more flexible and physically consistent, since it provides forecasts of the hydropower system's driver, i.e., the inflow arriving at the intake. We also revealed that apart from the inflow data per se, additional information should be introduced within prediction schemes in order to better reflect our hydrological knowledge, in terms of statistical characteristics. In the particular example, these were the mean monthly inflows and the past five-day average values, as representative of the long and short-term regime of the upstream catchment, respectively. However, it is worth mentioning that even a very good prediction of inflows (as quantified in terms of efficiency), does not guarantee an equally good performance in energy prediction (see Fig. 4). Equivalently important is the training procedure and the associated performance measure, where the system's characteristics, i.e., the range of operation of turbines, are embedded as inputs to calibration.

Key outcome of this research was also the quantification of uncertainty, by means of empirical quantiles, which were estimated through a Monte Carlo approach, after fitting a suitable probability distribution to the model residuals. This task, although proved to be simple and effective in its implementation, requires more careful examination, including analysis of the error properties and their seasonal variability, as well as could be benefited from more advanced concepts and tools, such as copulas and conditional non-Gaussian distributions (cf. Tsoukalas, 2018, for a development of this kind). Nevertheless, the interpretation of uncertainty is essential as a guidance for modelling energy market behaviors and providing decision support in the Target model era.

The simulation and forecasting models have been developed in the R environment and they are available at

The
daily inflow and rainfall time series are available at

The methodology was developed in close collaboration of all authors, and all authors contributed to the editing of the paper (mainly KKD, GKS, and AE). KKD employed the literature review, the forecasting analyses, and the development of the source code. GKS prepared the essential data for the case study (design of SHPP, simulation model). IT and PK employed the generation of synthetic data. PK also conducted the analysis with the Deep Feedforward Neural Network. AE supervised the overall research and the preparation of the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the special issue “European Geosciences Union General Assembly 2021, EGU Division Energy, Resources & Environment (ERE)”. It is a result of the EGU General Assembly 2021, 19–30 April 2021.

We are grateful to the Topical Editor, Gregor Giebel, who coordinated the review procedure, and the two anonymous reviewers for their useful comments, which helped substantially in improving the presentation of our work.

This paper was edited by Gregor Giebel and reviewed by two anonymous referees.