The potential production through DRORs and hydrokinetic turbines in EU was calculated using a Geographic Information System (GIS)-based model, similar to Palla et al. (2016), Bodis et al. (2014), Goyal et al. (2015). The hydropower potential assessment in water mills was carried out using the EU+UK Restor Hydro database (Punys et al. 2019). The potential in WDNs and in WWTPs was calculated by generalizing the results of Mitrovic et al. (2021) to cover the EU+UK area.
DRORs
In DRORs, the hydrological regime of the river is not altered, except for a length L between the point where water is withdrawn, and the point where it is discharged from the turbines, where anyway the EF must be respected. The GIS model computes the annual potential energy production (kWh/y) of a DROR plant at a site (x, y) from the frequency of exceedance of discharges (flow duration curve or FDC) and the river slope according to Eq. (1):
$$E\left(x,y\right)=\gamma \eta H\left(x,y\right)T{\int }_{0}^{1}\mathrm{min}({Q}_{10},\mathrm{max}\left(0,Qnat\left(x,y,\tau \right)-EF\right)d\tau$$
(1)
where:
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\({Q}_{nat}\left(x,y, \tau \right)\) (m3/s) is the river discharge at the site with frequency of exceedance \(\tau\), and T represents the operating annual hours;
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EF is the environmental flow considered (m3/s);
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Q10 is the flow with an exceedance frequency of 10% during the year. This is assumed to be the maximum flow allowed through the turbines;
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\(H\left(x,y\right)\) is the hydraulic head difference (m), assumed independent on the flow (see Eq. (2));
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\(\gamma\), \(\eta\) represent the specific weight of water (9.81 kN m−3) and the overall efficiency of the plant, respectively. The efficiency \(\eta\) depends on the design of the plant, and varies with the flow and head. For the purposes of this assessment we assume it to be a constant equal to 0.65, as in Bódis et al. (2014).
We assumed EF to be a constant discharge each time corresponding to one among the following discharges with a frequency of exceedance of 50% (Q50), 75% (Q75), 90% (Q90), 95% (Q95), 99.7% (Q997), and also 10% of mean annual flow (0.1MAF), 30% of mean annual flow (0.3MAF), and 50% of mean annual flow (0.5MAF).
We estimated the potential energy production of DRORs at a resolution of 100 m using the SRTM digital elevation model (see Vogt et al. 2007). We refer to FDCs interpolated from available measurements as presented in detail in Persiano et al. (2022). The interpolated FDCs refer to the outlet of sub-basins with a drainage area in the range of a few tens to a few hundreds of km2 and we excluded all streams in a non-headwater sub-basin, with a contributing area smaller than 10% of the area at the sub-basin outlet. For the stream network within each sub-basin, we assume the FDC to scale with the ratio MAF(x,y)/MAFbasin(x,y), where MAF(x,y) is the local mean annual flow, and MAFbasin(x,y) is the mean annual flow at the outlet of the sub-basin where the site (x,y) belongs. The MAF used to scale the interpolated FDCs is obtained from the long-term hydrologic surplus (precipitation minus evapotranspiration as an average over an extended period) obtained from the Budyko equation as discussed in Pistocchi et al. (2019) (further details provided in S.M.). We limited our analysis to that part of the European stream network for which hydrologic information on the FDC is available.
A plant is typically located at a site where a head difference is created either by a knickpoint in the stream bed profile, or by an artificial barrier such as a weir. However, the topographic information available at the scale of our analysis does not allow for analysis of these features. In order to estimate the available head difference at each potential site (x,y), we assume that the stream bed follows an exponential graded profile, for which the slope was computed as Pistocchi (2014):
$$J\left(x,y\right)=\theta {Z}_{max}\left(x,y\right)\mathrm{exp}\left(-K\xi \left(x,y\right)\right)$$
(2)
where θ is the exponential profile coefficient, \({Z}_{max}\left(x,y\right)\) (m) is the topographic estimated elevation at the upstream end of the stream segment, placed at a distance \(\xi \left(x,y\right)\) from site (x,y), measured along the stream network. \({H}\left(x,y\right)\) is estimated by multiplying the local stream slope J(x,y) by a representative distance L (m) representing the withdrawal length of the stream, comprising the length of the impoundment upstream of a possible barrier at the plant intake, as well as the distance from the intake to the outfall of the plant (extent of the withdrawal). The procedure to estimate K and J(x,y), following the concepts presented in Pistocchi (2014), is outlined in the S.M section.
In order to account for a minimum spatial density that must be respected among hydropower plants within a sub-basin, we superimposed a lattice of regular squares with a side of length D to each sub-basin, to explore different plant spatial densities (Erikstad et al., 2020). Within each polygon deriving from the geometric intersection of the lattice and the sub-basin polygons, we selected only one location (x,y) corresponding to the maximum local value of the product MAF(x,y)J(x,y), representing a stream power scale, and for the assumptions made on the calculation of H(x,y), also a hydropower potential scale. For the sake of exploration we considered D = 1 km, D = 5 km, and D = 10 km, meaning that we would admit no more than one hydropower plant every 1 km2, 25 km2, or 100 km2, respectively. While 1 km2 represents an unrealistic scenario (a maximum threshold), 25 km2 and 100 km2 are in line with the measured values reported in Punys et al. (2019) (between 1 plant every 10 km2 and 200 km2, depending on the EU country).
Hydrokinetic Turbines
The kinetic power K (W) in a certain river section can be calculated by Eq. (3):
$$K={^1}/{_2}\rho Q{v}^{2}$$
(3)
where Q (m3/s) is the flow rate, v (m/s) is the flow velocity and ρ is the water density (1,000 kg/m3). Based on the hydraulic geometry relationships presented in Pistocchi and Pennington (2006), we may rewrite Eq. (3) in terms of the river slope and discharge (Eq. (4)).
$$K=4.14\cdot {J}^{0.599}\cdot {Q}^{1.3806}$$
(4)
The stream power resulting from Eqs. (3) and (4) has to be multiplied by the power coefficient Cp = P/K, where P is the mechanical power output, to estimate the power output of the hydrokinetic turbine (HT). Our calculations with Cp = 1 represent the maximum theoretical potential, and results must be scaled by an appropriate Cp reflecting the performance of HTs (Cp affects the potential linearly). At present, we may assume Cp = 0.2 for standard turbines currently available as commercial products, and Cp = 0.4 for available well optimized turbines, e.g. with deflectors or enclosed in hydrodynamic structures. In our assessment we calculated the average power potential using both the average flow and the average of the power duration curve, and then calculated the annual energy potential.
The calculated kinetic power K refers to the power available in 100% of the river section. If only a percentage of the cross section is exploited, results have to be multiplied by the swept area percentage. Although the portion of the exploited cross section strictly depends on local factors, we assumed a constant maximum occupation of 25% of the cross section throughout Europe (e.g. Jenkinson and Bomhof 2014). In our study we considered that the turbine occupies the whole water depth (accepting that it will work partially submerged at low water flows). The potential was calculated at 100 m spatial resolution as per the digital elevation map, although it is known that, in order to avoid wake effects and performance reduction, a minimum longitudinal distance between HT installations must be respected. Usually this distance is estimated as l = 10d (d being a reference HT dimension), so some effect is expected for installations on a scale of 10 m or larger. An assessment of the impacts due to this effect would require a detailed analysis far beyond the scope of this paper, hence we anticipate that our estimated potential is in principle overestimated by neglecting backwater effects and wake effects between installations. An alternate installation on the river banks can mitigate such effects. Within our exploratory intent, we considered HT installations neglecting the presence of barriers and civil structures, and the high kinetic energy at the tail race of hydropower plants.
Water Wheels in Old Mills
The Restor Hydro database includes location, historical use, restorable conditions, expected mean flow and expected head, for historic weirs in EU+UK. Based on the design guidelines reported in S.M, the following design assumptions were made:
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for each site, the water wheel type was chosen depending on flow and head, and can be horizontal axis (four main types: overshot, middle breastshot, high breastshot or backshot, undershot) (Quaranta and Revelli 2018) and vertical axis type (Quaranta et al. 2021b);
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the maximum wheel width was 2 m for horizontal axis type (thus the exploitable flow rate was limited to this width, although installations with more than one wheel in parallel exist). The maximum diameter was fixed at 6 m for horizontal axis type (hence heads above 6 m were limited to 6 m) and 1.5 m for vertical axis type;
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when more wheel types are suitable, the most powerful one was chosen;
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if the flow is not known, it was assumed to be as equal to the flow that the selected wheel type can discharge, for a wheel width of 2 m;
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the overall plant efficiency was chosen based on the wheel type, as detailed in S.M., and typically ranged between 0.65 and 0.70;
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the ratio diameter/head (Dm/H) was chosen as equal to 4 for undershot wheels, 2.1 for middle breastshot wheels, 1.5 for high breastshot wheels and 0.9 for overshot wheels (Quaranta 2020).
Once that we elaborated all mills with available information on flow Q and head H (total data entries = 8,205), the results were generalized for each country by multiplying the average results by the total number of mills defined in moderate or advanced status (17,587 for the EU), including those with unknown characteristics. The analysis could be further extended to the whole recorded mill database (27,749 sites in EU). Mills in moderate condition are those where some visible remnants remain, e.g. a ruin or other historical building. River obstructions may exist that are in need of restoration or re-creation to bring the site back into service. An advanced condition means that in the site there is a complete, or almost complete, weir or other river blockage.
The cost of horizontal axis water wheels was calculated as 24,500 + 3,628 BDm (€) including civil works (7,000- 20,000€), where B (m) is the wheel width and Dm (m) is the diameter; if civil works are excluded, the cost can be quantified as 19,000 + 2,420 BDm (€) (see S.M. for further details). In this work we included civil works. Instead, for vertical axis water wheels, the cost equation proposed in Quaranta et al. (2021b) was used, excluding civil works.
The water wheel technology was chosen as it was present in the analyzed mills in the past (that means that the site is already conceived to host a water wheel) and because of its higher social acceptance and environmental sustainability. Other turbine types could be installed and, eventually, discharge more water.
WDNs and WWTPs
In Mitrovic et al. (2021), the hydropower potential in WDNs and WWTPs was calculated for Ireland, Northern Ireland, Scotland, Wales, Portugal and Spain, on the basis of site-specific data from more than 8,800 locations. These included pressure reducing values, wastewater treatment plants and other locations within these systems suitable for hydropower installation. The plant efficiency was considered as equal to 50%.
The hydropower potential from WDNs was found to be 2.89 kW per 1000 people in Scotland and 0.29 ± 0.12 kW per 1000 people in the other countries (excluding sites < 2 kW). This may be attributed to the fact that the Scotland territory is highly mountainous. Therefore, the meta-models represented by Eqs. (5) and (6) were derived and used in our analysis:
$${P}_{w}=0.29\ \mathrm{if}\ e<700\ \mathrm{m\ a}.\mathrm{s}.\mathrm{l}.\ \mathrm{or}\ 2.89\ \mathrm{if}\ e>700\ \mathrm{m}$$
(5)
where Pw is the power potential from WDNs for every 1000 people (kW/people), Pww is the power potential from WWTPs (kW), p is the served population (million), and e is the elevation range of each Functional Urban Areas (FUA). A FUA consists of a densely inhabited city and of a surrounding area whose labour market is highly integrated with the city. The largest 671 FUAs in EU + UK were considered, with known population, representing half of the EU + UK population. The elevation e is defined as the difference between the maximum elevation and the minimum one (the Scottish FUAs of Glasgow and Edinburgh value is 751 m and 665 m, respectively). The annual energy generation was calculated multiplying the potential by 8,760 annual hours to obtain a maximum potential. Pumps as Turbines (PATs) are considered the most compact and cost-effective technology in this context (Novara et al. 2019). Furthermore, it must be noted that Eq. (6) refers to regions in non-alpine environment, and the coefficient would be 353 instead of 44.2 to well reproduce the Switzerland estimate of 9.3 GWh/y (9.3 GWh/y corresponds to 8760 h and 35% of average capacity factor, see Discussion section). Therefore, similarly to Eq. (5), these two coefficients were used based on the elevation range (Bousquet et al. 2017).