Impact of the Minimum Head on Low-Head Hydropower Plants Energy Production and Proﬁtability

energies

Article Impact of the Minimum Head on Low-Head Hydropower Plants Energy Production and Proﬁtability

Bartosz Ceran 1,* , Jakub Jurasz 2 , Robert Wróblewski 1, Adam Guderski 1, Daria Złotecka 1 and Łukasz Ka´zmierczak 1

1 Institute of Electrical Power Engineering, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan, Poland; [email protected] (R.W.); [email protected] (A.G.); [email protected] (D.Z.); [email protected] (Ł.K.) 2 Department of Engineering Management, Faculty of Management, AGH University of Science and Technology, 30-059 Kraków, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-61-665-2523

Received: 29 October 2020; Accepted: 18 December 2020; Published: 20 December 2020

Abstract: In Poland, existing barrages are characterized by relatively high flow and low head, which is challenging for the effective utilization of theoretical watercourse power. The paper presents the impact of the minimum head of the hydro sets on the annual electricity production of small hydropower plants at low-head locations for two types of water turbines: Archimedes and Kaplan turbines. A developed mathematical model was used to simulate energy yield from Archimedes and Kaplan turbines for a given value of the minimum technical head, depending on the number of installed hydro sets. For economic analysis purposes, the levelized cost of electricity (LCOE) and net present value (NPV) indicators were calculated. The conducted research allowed for comparing Archimedes and Kaplan’s turbine operating conditions and how the minimum head parameter influences their electricity production and utilization time. As concluded in the results, the influence of minimum head in energy production is more distinct for the Archimedes screw technology than for the Kaplan turbine. The research shows that the decrease in energy production associated with the hydro unit’s minimum head parameter is from 0% to 30% for Kaplan, and it is 6% to 52% for Archimedes turbines.

Keywords: small-scale hydropower; Archimedes turbine; Kaplan turbine; minimum head; energy yield

1. Introduction The Polish power system’s generation sector is 70% based on coal-ﬁred power plants [1]. Therefore, the production of 1 kWh of electricity corresponds to the emission of approximately 0.77 kg of carbon dioxide. Increasing environmental restrictions necessitate a transformation of the power sector structure in Poland to increase the share of renewable energy sources in the electricity production process [2]. According to data presented by the Polish transmission system operator (TSO), 5% of the installed capacity in the system are industrial hydropower plants. In comparison, 16% are wind farms and other renewable technologies, including dynamically developing photovoltaics. There is also a massive increase in units operating on gas fuel [3]. In Poland, Europe and worldwide, it is possible to increase the hydropower potential. Hoes et al. [4] estimated the world’s gross theoretical potential of hydropower at 52 PWh/year. Small hydropower plants represent a signiﬁcant part of this potential. In this category, particular attention should be paid

Energies 2020, 13, 6728; doi:10.3390/en13246728 www.mdpi.com/journal/energies Energies 2020, 13, 6728 2 of 21 to small-scale hydropower plants (SHP) operating in low head conditions (below 5 m [5]), the significant potential of which is still not fully recognized. Bódis et al. [6], estimating hydropower resources in Europe, excluded locations with heads below 6 m, which could be utilized in power generation using the currently available technology. Wiemann et al. [7] drew attention to the possibility of managing low heads (from 0.8 m to 2.0 m) in Europe, with the use of hydropower plants with a power of 100–1000 kW. The technical potential of hydropower sources in Poland is estimated at 12–14 TWh per year [8]. This represents about 8% of the annual electricity consumption, which amounted to 170 TWh [3] in 2019. The current use of the aforementioned technical potential is estimated at 12%, a large part of SHPs built next to the existing hydraulic structures (e.g., weirs, dams). According to Punys et al. [9], Poland is the second European country, after France, in terms of the number of hydraulic structures where SHPs can be developed. The estimated total potential of hydropower generation of SHPs in Poland is approximately 1300 GWh/year [9]. Research on the practical use of water potential is the subject of many scientific publications. Zhou et al. [4] included the currently most critical types of turbines in the low head category: propeller turbines, tubular turbines, cross-flow Banki-Michell turbines, open flume Francis turbines, Kaplan turbines, Archimedes screws, and waterwheels. In the research, the last three technologies were given particular attention. Balkhair et al. [5] considered places with an available head below 5 m as low-head locations, while Zhou et al. [10] distinguished the category of even lower heads—from 3 m to 0 m (ultra-low-head). Lavric et al. [11] stated that locations with such small heads often remain unused. Only the development of low-head technologies permits their practical use. In recent years, renewed interest in the already mature technology of waterwheels can be observed, which is reflected in a growing amount of publications on this subject. In [12], the author presented the design of a waterwheel where the maximum power output occurs at a certain wheel speed. In work [13], the authors tested the waterwheel efficiency in run-of-river conditions. In [14], the authors optimized gravity waterwheels. The results showed that the maximum efficiency of overshot and undershot waterwheels was around 85%. In comparison, that of breastshot waterwheels ranged from 75% to 80%, depending on inflow configuration. The aim of the numerical simulations presented in [15] was to show the influence of the immersion depth value on the waterwheel characteristics. In [16], the authors tested the water inflow regulation to undershot waterwheel blades by changing the shape of the end part of the inlet channel. This action is intended to maximize the waterwheel’s efficiency at low and variable flow rates. Hydroelectric power plants based on Archimedes screws [17] began to be used around the year 2000, and they soon became a popular solution for low-head locations. Rohmer et al. [18] conducted the modeling and selecting of the turbine size for the planned flow. The authors examined the effect of excessive filling of the Archimedes screw trough on the occurring energy losses. They compared the theoretical results with experimental results. However, the authors of the work did not mention the occurrence of a minimum head, which is essential for the topic under consideration. In work [19], the authors examined the influence of the angle of inclination of the Archimedes screw turbine on its energy efficiency. Similar to the previously mentioned work, they indicated losses caused by a high level of filling the turbine trough. Moreover, the study distinguishes two optimal inclination angles of the hydro unit, including the local maxima of efficiency, occurring at two different head values. However, as can be deduced from the study, the authors did not investigate the hydro unit’s operation under the conditions of a variable head for the previously specified inclination angle of the Archimedes screw. Such conditions occur in real-life objects. In [20], the authors presented a method for measuring the hydroelectric trough filling height to investigate the overflow of working screws as a function of the trough filling height. The studies did not take into account the variability of the head. On the other hand, the authors of work [21] analyzed the influence of the blade angle and the number of turbine blades on Archimedes hydro unit efficiency, taking into account head changes. Energies 2020, 13, 6728 3 of 21

Moreover, the authors investigated the usefulness of CFD modeling in the implementation of simulation tests. This method brings very reliable results under the conditions mentioned. A specific aspect of these studies was the determining of a different optimal operating angle for turbines with a different number of blades. The authors of [22] described the negative impact of the decreasing head on the efficiency value and the range of achieved rotational speeds of the turbine. The head is adjusted by the level of lower reservoir changes. The paper presents the experimental results of research studies, which indicated a rapid decrease in the hydro unit’s efficiency when increasing the lower reservoir level. Not only does the peak point of the efficiency curve drop, but the curve itself changes shape. What is essential for the analyses is that the authors show the negative impact of the increase in the lower reservoir level on the hydropower plant’s operation. In [23], the authors investigated the efficiency of an Archimedes turbine with a different number of blades using computer simulations in the ANSYS environment. On the other hand, in [24], the authors proved that the average flow and electricity generated by an Archimedes turbine are inversely correlated. The turbine they tested working on a variable flow produces 2% less energy than a constant flow turbine. One of the most efficient technologies in low-head hydropower plants is a tubular turbine with a Kaplan turbine rotor [25]. A large number of scientific publications focus on this type of hydroelectric units. Mulu et al. [26] focused on the experimental studies of flows in the tubular turbine at the point of the highest efficiency and their influence on turbine components. Abeykoon et al. [27] researched the influence of the shape of a Kaplan turbine runner wheel on the hydro unit efficiency. After theoretical calculations, the structure was optimized by simulation in the ANSYS environment, which improved the hydro unit’s efficiency. Abbas et al. [28] focused on the optimal design of a turbine to be used in wastewater treatment plants. According to the manufacturer [29], tubular Kaplan turbines can be currently used from 1.5 m head. Low-head technologies have gained high popularity in recent years, as confirmed by the above-mentioned publications. However, research into low-head technologies focuses mainly on optimizing the design parameters or maximizing the efficiency of converting primary energy into electricity. Only Lavric et al. [11,17,24] considered in their research the shutdown of hydro sets forced by the flow and the concurrent head, showing temporary shutdowns. In spite of very valuable analysis, the authors of these publications do not sufficiently address the impact of the technical minimums of the effective head on the annual production of electricity. Determination of the amount of energy lost due to hydro set shutdowns serves as the starting point for the reduction of such losses. It may inspire numerous scientific research projects to focus on, for example, the analysis of structural alterations in turbines or on modifications of turbine selection procedure at the stage of power plant design. Failure to take into account energy losses resulting from hydro set shutdowns and the lack of research into the impact of the minimum technical value on the production of energy has become a gap in scientific research on this subject matter. Addressing this topic, carrying out calculations leading to the determination of energy lost in this manner, as well as demonstrating the significance of this phenomenon is an innovation presented in this article, and it is intended to bridge the above-mentioned gap. The primary purpose of this study is to investigate the impact of the minimum head of the considered hydro sets on the annual electricity production of small hydropower plants at low-head locations. Archimedes turbines and tubular turbines with Kaplan rotors were used in the case study. Such analyses have not been carried out for Poland so far. The arguments for the selection of the above-mentioned two technologies are the nominal parameters of the considered barrage, falling in the range of application of these technologies [10] and the effectiveness of energy conversion in the range of the analyzed hydrological conditions [11]. Energies 2020, 13, x FOR PEER REVIEW 4 of 20 possible from 1 m head, Zhou et al. [10] considered 10 m as the upper limit, and Rohmer et al. [9] gave the overall applicable head as 1–6.5 m. The efficiency of water energy conversion into mechanical energy received on the shaft is estimated at 80%, and the tendency increases together with increasing turbine diameter [31]. However, the studies in [32] give the highest efficiency value at 89%. The authors quote 4 m as the largest possible Archimedes screw diameter. According to the authors, this value is related to the problem of cracking welds, which connect the shaft with the spiral blades. The initial condition torque Energiesvalues 2020come, 13 ,from 6728 the developed Archimedes turbine model with an assumed water flow rate 4from of 21 0 to 2.7 m3/s [33]; while in [34], the authors assumed the water flow rate from 0.25 to 6.5 m3/s. 2. ProblemThe second Description technology under consideration is a tubular turbine with a Kaplan rotor, one of the Kaplan turbines [35] dedicated to low-head locations. It is a solution with a much more extended periodThe of first application of the considered in the hydropower technologies industry; is the Archimedes however, research turbine. onScientific its imp researchrovement does is still not providecarried out any [26 explicit]. Turbines areas ofwith application unit power for of this up technology. to 1 MW made Elbatran in this et al. technology [30] stated are that mainly its use used was possiblefor heads from of 1 1–1 m7 head,m, while Zhou hydro et al.-sets [10] with considered a higher 10 rated m as thepower upper are limit, applied and for Rohmer higher et head al. [9s] gave[36]. Thethe overallefficiency applicable of Kaplan head turbines as 1–6.5 depends m. on the properties of a given unit [37]. The research in [25] showedThe that efficiency tubular of waterturbine energy efficiency conversion with Kaplan into mechanical rotors might energy exceed received 90% on and the even shaft reach is estimated 91.7%. Theat 80%, diameters and the of tendency classic increasesKaplan turbines together used with in increasing the world turbine exceed diameter 7 m. Units [31 ].with However, such dimensions the studies havein [32 a] giveunit theflow highest of 400 e m3fficiency/s. Simultaneously value at 89%., Thethis authorstechnology quote is 4also m as sui thetable largest for much possible smaller Archimedes flows, evenscrew in diameter. the range Accordingof 0–1.5 m3 to/s [ the38]. authors, this value is related to the problem of cracking welds, whichAs connect a case study, the shaft the withlocation the shown spiral blades.in Figure The 1 was initial adopted, condition with torquea nominal values head come of 1.6 from m. The the 3 exactdeveloped coordinates Archimedes are latitude turbine 52.8648 model and with longitude an assumed 16.0676. water This flow specific rate fromlocation 0 to is 2.7 at mthe/ s170 [33th]; 3 whilekilometer in [34 of], the the Noteć authors River assumed (total length the water of 388 flow km, rate and from a catchment 0.25 to 6.5 area m /s. of 17,330 km2). ThereThe second is a hydrological technology understation consideration at the adjacent is barrage a tubular, measuring turbine with the a flow Kaplan and rotor, water one level of theon theKaplan barrage. turbines There [35 are] dedicated no significant to low-head tributaries locations. between It th isese a solutiontwo stages with, which a much could more significantly extended periodaffect the of applicationwater flow invariation the hydropower passing through industry; the however, two stages. research Therefore, on its improvement these flow values is still will carried be consideredout [26]. Turbines the same with for unit the step power under of up consideration to 1 MW made in the in thisfollowing technology part of are this mainly paper used. At the for Krzyż heads barrage,of 1–17 m, the while following hydro-sets characteristic with a higher flows rated [39] poweroccur: are applied for higher heads [36]. The efficiency of Kaplan turbines depends on the properties of a given unit [37]. The research in [25] showed that 3 tubular average turbine low effi flowciency—26 with m /s Kaplan (SNQ) rotors; might exceed 90% and even reach 91.7%. The diameters 3 of classicaverage Kaplan flow turbines from the used average in the annual world flows exceed— 754 m. m Units/s (SSQ) with; such dimensions have a unit flow 3 of 400average m3/s. Simultaneously, high flow—97 m this/s technology(SWQ). is also suitable for much smaller flows, even in the range 3 of 0–1.5There m /ares [38 several]. similar barrages along the Noteć River, some of which have been developed for powerAs a case generation study, the [40]. location Płaczek shown et al. in [4Figure1] distinguish1 was adopted, four sections with a nominal with different head of terrain 1.6 m. Thecharacteristics. exact coordinates The location are latitude under 52.8648consideration and longitude is placed 16.0676. within the This section specific known location as the is at Canaliz the 170thed 2 Noteć.kilometer of the NotećRiver (total length of 388 km, and a catchment area of 17,330 km ).

Figure 1. Location of the case study. Source: Open Street Map Map..

There is a hydrological station at the adjacent barrage, measuring the flow and water level on the barrage. There are no significant tributaries between these two stages, which could significantly affect the water flow variation passing through the two stages. Therefore, these flow values will be considered the same for the step under consideration in the following part of this paper. At the Krzy˙z barrage, the following characteristic flows [39] occur: average low flow—26 m3/s (SNQ); • Energies 2020, 13, 6728 5 of 21

average flow from the average annual flows—54 m3/s (SSQ); • average high flow—97 m3/s (SWQ). • There are several similar barrages along the NotećRiver, some of which have been developed for power generation [40]. Płaczek et al. [41] distinguish four sections with different terrain characteristics. TheEnergies location 2020, 13 under, x FOR consideration PEER REVIEW is placed within the section known as the Canalized Noteć. 5 of 20

3.3. ModelModel andand MethodMethod DescriptionDescription

3.1.3.1. EstimatingEstimating EnergyEnergy Production—SmallProduction—Small HydropowerHydropower PlantPlant Model Model AccordingAccording to to [ 42[42],], the the nominal nominal head head of of the the Drawsko Drawsko barrage barrage is is 1.6 1.6 m. m. TheThe ManningManning formulaformula waswas usedused forfor uniformuniform flowsflows in in open open flumes flumes (1). (1). ThisThis formulaformula willwill bebe usedused laterlater toto determinedetermine thethe estimatedestimated head-flow relation. head-flow relation. 1 2 3 1 Q = I 2 A R n− , (1) 1 · · h 2· Q = I2 ∙ A ∙ R3 ∙ n−1, (1) where: Q—water flow [m3/s], I—hydraulic gradienth [%], Rh—hydraulic radius [m], n—trough roughnesswhere: Q— coewaterfficient flow [s/m1 [m3/s],/3], A—cross-sectional I—hydraulic gradient area [m [‰],2], Rh—hydraulic radius [m], n—trough roughnessThe water coefficient flumecross-section [s/m1/3], A— areacross (Figure-sectional2) is area defined [m2], by Formula (2): The water flume cross-section area (Figure 2) is defined by Formula (2): A = (b + mh) h, (2) A = (b + mh)·∙ h, (2) where:where: h—fillingh—filling ofof thethe troughtrough [m],[m], b—widthb—width ofof thethe troughtroughbottom bottom [m],[m],m—cotangent m—cotangent ofof inclinationinclination angleangleα α[-][-] ( (αα—the—the slopeslope ofof thethe riverrivertrough) trough)

FigureFigure 2.2. Cross-sectionCross-section ofof thethe Note´criverNoteć river troughtrough modelmodel belowbelow thetheDrawsko Drawskobarrage barrage (own (own study). study).

ThenThen itit isis necessarynecessary to to calculate calculate the the value value of of the the hydraulic hydraulic radius radius Rh Rh according according to to Formula Formula (3): (3):

(b+mh)h R =( b + mh)h h 2, (3) Rh = b+ 2h√1+m , (3) b + 2h √1 + m2 After substituting Formulas (2) and (3) to Formula (1), the relationship Q(h) is obtained as describedAfter substitutingby Formula (4). Formulas (2) and (3) to Formula (1), the relationship Q(h) is obtained as described by Formula (4). 2 1 (b + mh)h 3 2 −1 (4) Q(h) = I ∙ (b + mh) ∙ h ∙ ( !)2 ∙ n b + 2h√1 + m2 3 1 (b + mh)h 1 Q(h) = I 2 (b + mh) h n− (4) The data adopted for the model· are summarized· · b + 2hin √Table1 + m 1.2 Their· accuracy and reliability are crucial for the credibility of the model. The critical parameter that undergoes the most dynamic The data adopted for the model are summarized in Table1. Their accuracy and reliability are changes in the roughness coefficient of the river trough. According to [43], its value depends on, crucial for the credibility of the model. The critical parameter that undergoes the most dynamic changes among other things, the state of riverbed vegetation, which varies together with seasonal changes. in the roughness coeﬃcient of the river trough. According to [43], its value depends on, among other The b parameter was determined based on satellite images. things, the state of riverbed vegetation, which varies together with seasonal changes. The b parameter was determinedTable based 1. Summary on satellite of data images. adopted for the presented calculation methodology [41].

Parameter Data Unit n 0.035 s/m1/3 I 0.002 - b 29.2 m

According to the above model, a curve determining the flume’s filling as a function of flow was obtained, which is shown in Figure 3. It allowed determining the head-flow relation, assuming a constant upper reservoir level. The assumption of a constant upper reservoir level results from the barrage construction and the maintenance of the required shipping parameters on the waterway. The adopted water level in the upper reservoir is directly related to the issued water permit requirements Energies 2020, 13, 6728 6 of 21

Table 1. Summary of data adopted for the presented calculation methodology [41].

Parameter Data Unit n 0.035 s/m1/3 I 0.002 - b 29.2 m

According to the above model, a curve determining the flume’s filling as a function of flow was obtained, which is shown in Figure3. It allowed determining the head-flow relation, assuming a constant upper reservoir level. The assumption of a constant upper reservoir level results from the barrage construction and the maintenance of the required shipping parameters on the waterway. The adopted water level in the upper reservoir is directly related to the issued water permit requirements for the analyzed barrage. The assumed water level in the upper reservoir results from the necessity to maintain the shipping conditions. The data presented in Figure3 were used to calculate the head as a function of flow. The barrage head value at zero flow was obtained by calibrating the model to flow at a nominal head. Nominal head means the difference of water levels on the upper and lower reservoirs at the flow equal to the average of the lowest annual flows (SNQ). For the examined location, it is 26 m3/s [39]. Figure4 compares the model data with empirical data. The model has a mean square error 3 3 Energies(MSE) 2020 of 0.041,, 13, x FOR and PEER in the REVIEW flow range of 50–95 m /s, it is 0.0246. When it comes to the flow of 506 m of 20/s, the value of MSE is less favorable, reaching an error value of 0.065, which will be discussed in the forfollowing the analyzed paragraphs. barrage. The assumed water level in the upper reservoir results from the necessity to maintainThe head-flow the shipping model conditions. takes into account flows in the range of 10–150 m3/s. This is due to the minimumThe data (13.2 presented m3/s), and in Figure maximum 3 were (149 used m3 to/s) calculate flow recorded the head at theas a adjacent function barrageof flow. overThe barrage the last head50 years value [44 at]. zero The appliedflow was model obtained has twoby calibrating simplifying the assumptions. model to flow The at firsta nominal is to assume head. Nominal the flow headbelow means the considered the difference stage of as water a uniform levels flowon the (water upper movement and lower parametersreservoirs at are the constant flow equal along to the averagelength of of the the consideredlowest annual river flows trough). (SNQ). It For is a the slowly examine changingd location, flow (waterit is 26 m3 movement/s [39]. parameters are variable).Figure 4 compares In the case the model of hydraulic data with support empirical by thedata. step The below, model thehas modela mean headsquare value error will (MSE) be ofoverestimated 0.041, and in compared the flow torange the actualof 50–9 values5 m3/s at, it low is 0.0246. flows. TheWhen second it comes simplification to the flow is theof 50 assumption m3/s, the valueof a constant of MSE slope is less of thefavorable, river bed; reaching however, an it error is di ffi valuecult to of indicate 0.065, which the resulting will be negative discussed impact in the of followingthe model. paragraphs.

FigureFigure 3. 3. FFlumelume filling ﬁlling model model as as a a function function of of the the current current volume volume flow. ﬂow.

Figure 4. Comparison of empirical data (red) with the model curve (blue) based on Formula (4).

The head-flow model takes into account flows in the range of 10–150 m3/s. This is due to the minimum (13.2 m3/s), and maximum (149 m3/s) flow recorded at the adjacent barrage over the last 50 years [44]. The applied model has two simplifying assumptions. The first is to assume the flow below the considered stage as a uniform flow (water movement parameters are constant along the length of the considered river trough). It is a slowly changing flow (water movement parameters are variable). In the case of hydraulic support by the step below, the model head value will be overestimated compared to the actual values at low flows. The second simplification is the Energies 2020, 13, x FOR PEER REVIEW 6 of 20

for the analyzed barrage. The assumed water level in the upper reservoir results from the necessity to maintain the shipping conditions. The data presented in Figure 3 were used to calculate the head as a function of flow. The barrage head value at zero flow was obtained by calibrating the model to flow at a nominal head. Nominal head means the difference of water levels on the upper and lower reservoirs at the flow equal to the average of the lowest annual flows (SNQ). For the examined location, it is 26 m3/s [39]. Figure 4 compares the model data with empirical data. The model has a mean square error (MSE) of 0.041, and in the flow range of 50–95 m3/s, it is 0.0246. When it comes to the flow of 50 m3/s, the value of MSE is less favorable, reaching an error value of 0.065, which will be discussed in the following paragraphs.

Energies 2020, 13, 6728 7 of 21 Figure 3. Flume filling model as a function of the current volume flow.

FigureFigure 4.4. Comparison of empiricalempirical datadata (red)(red) withwith thethe modelmodel curvecurve (blue)(blue) basedbased onon FormulaFormula (4).(4).

EmpiricalThe head- dataflow shouldmodel betakes analyzed into account critically flows too. in They the come range from of 10 the–150 period m3/s. between This is Septemberdue to the 2015minimum and October (13.2 m3 2017,/s), and from maximum the summer (149 andm3/s) autumn flow recorded months. at Thisthe adjacent is important barrage because, over the in thelast adopted50 years model,[44]. The a criticalapplied role model is played has two by simplifying the adopted assumptions. roughness coe Tffihecient first n,is theto assume value ofthe which flow changesbelow the with considered the growth stage of theas a bottom uniform river flow trough (water vegetation movement and parameters siltation of are the constant flume, andalong these the parameterslength of the may considered change over river months trough) and. It is years. a slowly changing flow (water movement parameters are variable).For the In created the case model of hydraulicof a hydroelectric support power by the plant step operation, below, the it is model necessary head to adoptvalue awill curve be modelingoverestimated the head-flow compared relation to the with actual a constant values trend. at low It should flows. not The show second sudden simplification changes in the is head the with increasing flow. Therefore, it is appropriate to adopt a simplified model of constant monotonicity.

3.2. Economic Model To further investigate the impact of head and ﬂow variability on the low-head hydropower station performance, the levelized cost of electricity (LCOE) and net present value (NPV) indicators were calculated. Considering the number of uncertain parameters aﬀecting the values of such economic indicators, the Monte Carlo (MC) approach was adopted. This method enables grasping the whole spectrum of potential scenarios where the system under investigation may operate in the future. Table2 summarizes the input data used in the MC simulation. The energy generated annually from the low-head hydropower station of the investment period was obtained from the simulations spanning the period 1971–2018. The detailed procedure is presented in AppendixA. Equations (5) and (6) are used, respectively, to calculate the LCOE and NPV indicators. P I + m At 0 t=1 ( + )t = 1 d LCOE H (5) Pm Et t=1 (1+d)t

H where: I0—investment expenditure [€], At—annual total cost [€], Et —energy generated from hydropower [kWh], d—discount rate [%].

m X R = t NPV t (6) t=1 (1 + r) where: Rt—net cash inﬂows-outﬂows during a single period t [€], r—discount rate [%], t—number of periods. Energies 2020, 13, 6728 8 of 21

Table 2. Input parameters for the Monte Carlo (MC) simulations [45–47].

Parameter Value Comment Assuming continuous Lifetime/investment period 60 years (Carlsson, 2014) maintenance works Typical for RES investment in Return rate/Discount rate 1 5.0% (Paska, 2012) Poland Fixed operational cost (FOM) 1.5% (Carlsson, 2014) Of CAPEX Variable operational cost (VOM) 3% (Carlsson, 2014) Of CAPEX min: 2540, mean: 5600, max 8150. Simulated in MC as a triangular Capital expenditures (CAPEX) All euros/kW. (Carlsson, 2014) distribution. The latest auction won by the Certiﬁcate for hydro generation 120 euros/kWh [47] major hydro producer in Poland Number of MC runs 10,000 Trial and error estimation Kaplan capacity 405 kW Own assumptions Archimedes capacity 398.4 kW Own assumptions 1 regional discount rate. For simplicity, the return rate is assumed to be an equal discount rate.

4. Results

4.1. Estimating Energy Production In the example discussed below, 8 Archimedes hydro units were selected for comparison, based on data provided by one of the manufacturers of this type of solution in Central Europe (GESS-CZ, SRO, [48]). A single hydro unit’s nominal flow rate is 3.75 m3/s, with overload possibility up to 4.5 m3/s. The minimum operating head, which is the critical parameter of the comparison, is 1.2 m. A single hydro unit has a rated power of 49.8 kW. The above-mentioned hydro units were compared with three tubular Kaplan turbines with a horizontal rotor. The data obtained from the manufacturer indicate a rated flow of 11 m3/s for a single turbine, with no overload possibility. This technology has a minimum head of 0.9 m. The rated power of a single hydro unit is 135 kW. Based on the fact that the maximum theoretical power for the tested watercourse in the specific location is approx. 665 kW, the model presented in the article investigated the dependence of annual electricity production on the number of hydro sets installed. The magnitude of the obtained rated power was determined on the basis of the optimal use of the theoretical power of the watercourse. This was confirmed in the further part of the research and illustrated in the diagrams of annual energy production depending on the number of hydro sets installed. Based on model calculations, it was assumed that the installed power for the Archimedes screw is 398.4 kW. For comparison, it is 405 kW for Kaplan turbines. Data from three representative years were selected for detailed analysis. The year 2006 was taken as an example of a year with a lower average annual flow, 2010 was chosen as the average reference year, and 1999 was taken as a year with a higher average flow. In Figure5, where the average annual flow over the years 1971–2018 is presented, the years mentioned above are marked in green. Figure6 shows that the annual electricity production in particular years is compared with the minimum head and without it. Without considering the minimum head, the analyzed power plant operates in the full range of flows occurring at the barrage, i.e., 13.2–149 m3/s. The minimum head for the analysis changes the power plant operation scope depending on the tested technology. The element that binds the head and the flow is the previously modeled head-flow characteristic, which allows for the read of the head occurring on the tested barrage with the known flow or vice versa. The particular value of the minimum head is a parameter appropriate for a given type of hydro unit provided by the manufacturer. It refers to the lowest possible gradient at which the hydro unit can work for a long time. Therefore, each time the value of the current head is reduced below the value adopted by the manufacturer, the hydro unit must be stopped. Energies 2020, 13, x FOR PEER REVIEW 8 of 20

4. Results

4.1. Estimating Energy Production In the example discussed below, 8 Archimedes hydro units were selected for comparison, based on data provided by one of the manufacturers of this type of solution in Central Europe (GESS-CZ, SRO, [48]). A single hydro unit’s nominal flow rate is 3.75 m3/s, with overload possibility up to 4.5 m3/s. The minimum operating head, which is the critical parameter of the comparison, is 1.2 m. A single hydro unit has a rated power of 49.8 kW. The above-mentioned hydro units were compared with three tubular Kaplan turbines with a horizontal rotor. The data obtained from the manufacturer indicate a rated flow of 11 m3/s for a single turbine, with no overload possibility. This technology has a minimum head of 0.9 m. The rated power of a single hydro unit is 135 kW. Based on the fact that the maximum theoretical power for the tested watercourse in the specific location is approx. 665 kW, the model presented in the article investigated the dependence of annual electricity production on the number of hydro sets installed. The magnitude of the obtained rated power was determined on the basis of the optimal use of the theoretical power of the watercourse. This was confirmed in the further part of the research and illustrated in the diagrams of annual energy production depending on the number of hydro sets installed. Based on model calculations, it was assumed that the installed power for the Archimedes screw is 398.4 kW. For comparison, it is 405 kW for Kaplan turbines. Data from three representative years were selected for detailed analysis. The year 2006 was taken as an example of a year with a lower average annual flow, 2010 was chosen as the average reference year, and 1999 was taken as a year with a higher average flow. In Figure 5, where the average annual flow over the years 1971–2018 is presented, the years mentioned above are marked in green. Figure 6 shows that the annual electricity production in particular years is compared with the minimum head and without it. Without considering the minimum head, the analyzed power plant operates in the full range of flows occurring at the barrage, i.e., 13.2–149 m3/s. The minimum head for the analysis changes the power plant operation scope depending on the tested technology. The element that binds the head and the flow is the previously modeled head-flow characteristic, which allows for the read of the head occurring on the tested barrage with the known flow or vice versa. The particular value of the minimum head is a parameter appropriate for a given type of hydro unit provided by the manufacturer. It refers to the lowest possible gradient at which the hydro unit can Energieswork f2020or a, 13long, 6728 time. Therefore, each time the value of the current head is reduced below the value9 of 21 adopted by the manufacturer, the hydro unit must be stopped.

FigureFigure 5.5. Summary of the average annual ﬂowflow in 1971–20181971–2018 (the years analyzedanalyzed inin detaildetail areare markedmarked inin green).green). Energies 2020, 13, x FOR PEER REVIEW 9 of 20

Figure 6.6. Summary of annualannual electricity production. G Greenreen refers to the Kaplan turbine and blue to ArchimedesArchimedes turbine,turbine, takingtaking intointo accountaccount thethe minimumminimum head.head. Both types of turbines are marked with hatching for calculations,calculations, excludingexcluding thethe minimumminimum headhead impact.impact.

The data for the three selectedselected years presented in Figure6 6 should should bebe comparedcompared inin aa broaderbroader view.view. FiguresFigures 77 and and8 8show show that that changes changes in in the the annual annual energy energy production production are are observed, observed, which which are are not proportional to the averageaverage annual flowflow increases.increases. The annual average flow flow in 2010 was 50.5% higher than in 2006, while the energy yield was lower for Kaplan and Archimedes turbines by 6.8% and 38.2%, respectively. For 1999, the observedobserved falls inin productionproduction areare significant.significant. TheyThey are equal to 38.9%38.9% (Kaplan)(Kaplan) andand 29.9% 29.9% (Archimedes) (Archimedes) in in comparison comparison to to 2010, 2010, with with a significant a significant 34.8% 34.8% increase increase in the in averagethe average flow. flow. Comparing Figures 7 and 8, it is possible to notice a much lower annual energy yield with the use of the Archimedes screw technology compared to Kaplan turbines. There are difficulties in using high flows in this technology.

Figure 7. Annual electricity production (red) depending on the number of installed Kaplan turbines compared to the average annual flow (blue). The lowest red line represents one hydro unit, and the highest—eight hydro units. Energies 2020, 13, x FOR PEER REVIEW 9 of 20

Figure 6. Summary of annual electricity production. Green refers to the Kaplan turbine and blue to Archimedes turbine, taking into account the minimum head. Both types of turbines are marked with hatching for calculations, excluding the minimum head impact.

The data for the three selected years presented in Figure 6 should be compared in a broader view. Figures 7 and 8 show that changes in the annual energy production are observed, which are not proportional to the average annual flow increases. The annual average flow in 2010 was 50.5% higher than in 2006, while the energy yield was lower for Kaplan and Archimedes turbines by 6.8% and 38.2%, respectively. For 1999, the observed falls in production are significant. They are equal to 38.9% (Kaplan) and 29.9% (Archimedes) in comparison to 2010, with a significant 34.8% increase in the average flow. Comparing Figures 7 and 8, it is possible to notice a much lower annual energy yield with the Energiesuse of 2020the ,Archimedes13, 6728 screw technology compared to Kaplan turbines. There are difficulties in10 using of 21 high flows in this technology.

FigureFigure 7.7. AnnualAnnual electricityelectricity production (red) dependingdepending on thethe numbernumber ofof installedinstalled KaplanKaplan turbinesturbines comparedcompared toto thethe averageaverage annualannual ﬂowflow (blue).(blue). TheThe lowest red line representsrepresents oneone hydrohydro unit,unit, andand thethe Energieshighest—eighthighest 2020, 13—, eightx FOR hydrohydro PEER units.REVIEWunits. 10 of 20

Figure 8. AnnualAnnual electricity electricity production production (red) depend dependss on the number number of Archimedes Archimedes turbines installed against the average annual ﬂow flow (blue). (blue). The The lowest lowest red red line line represents represents one hydro unit and the highest—fourteenhighest—fourteen units.

ComparingFigures 7 and Figures 8 show7 and that8, it production is possible toincrease notice aslows much down lower after annual the energy 8th Archimedes yield with theturbine use ofwith the an Archimedes installed rated screw flow technology of 36 m3 compared/s and the 3rd to Kaplan Kaplan turbines. turbine, Therewhich are corresponds difficulties to in an using installed high flowsrated flow in this of technology. 33 m3/s. The higher of these values is about 0.7 SSQ (mean flow from average annual flow)Figures and 1.47 SNQand8 (averageshow that low production flow). A increasenominal slows head downis determined. after the 8th Archimedes turbine with an installedTo explain rated the flow differences of 36 m3 /ass and mentioned the 3rd Kaplanabove, Figure turbine,s 9 which, 10 and corresponds 11 are presented. to an installed They consist rated flowof several of 33 msub3/s.-charts. The higher The first of these sub-chart values presents is about the 0.7 power SSQ (mean plant flow’s actual from power average and annual the theoretical flow) and 1.4power SNQ of (average the watercourse low flow). during A nominal the year. head It is results determined. from, among other things, the ordered flow throughTo explain the weir, the i.e. di,ff theerences entire as stream mentioned of water above, in the Figures watercourse9–11 are, presented.which is shown They below consist. Moreover, of several sub-charts.the flow through The first the sub-chart power plant presents is presented the power, which plant’s depends actual on power the number and the theoreticalof running powerhydro units, of the watercoursenever reaching during the thefull year.water It resultsuse in from,the watercourse among other. This things, is due the ordered to the necessity flow through to ensure the weir, an i.e.,environmental the entire stream flow, the of water value inof thewhich watercourse, is specified which in the is water shown permit below. and Moreover, is related the to the flow minimum through theenvironmental power plant requirements is presented, which[49]. For depends the considered on the number barrage, of running the environmental hydro units, flow never is reaching 5 m3/s, themaintained full water throug use inh, theamong watercourse. other things This, a fish is due pass to and the leaks necessity in the to weir. ensure The an last environmental sub-chart presents flow, the number value of of which running is specified turbines in depending the water on permit the current and is head related in tothe the barrage minimum. The environmentaldiscussed sub- requirementsgraphs form a [ 49coherent]. For the whole considered allowing barrage, for analyzing the environmental the barrage flow’s power is 5 m pla3/s,nt maintained operation and through,, in a amongbroader othersense, things, a comparison a fish pass of this and work leaks, in in years the, weir. with different The last average sub-chart flows. presents the number of running turbines depending on the current head in the barrage. The discussed sub-graphs form a coherent whole allowing for analyzing the barrage’s power plant operation and, in a broader sense, a comparison of this work, in years, with different average flows.

Figure 9. Selected operating parameters of Archimedes turbines with an average low flow below mean states (SSQ) (2006). Energies 2020, 13, x FOR PEER REVIEW 10 of 20

Figure 8. Annual electricity production (red) depends on the number of Archimedes turbines installed against the average annual flow (blue). The lowest red line represents one hydro unit and the highest—fourteen units.

Figures 7 and 8 show that production increase slows down after the 8th Archimedes turbine with an installed rated flow of 36 m3/s and the 3rd Kaplan turbine, which corresponds to an installed rated flow of 33 m3/s. The higher of these values is about 0.7 SSQ (mean flow from average annual flow) and 1.4 SNQ (average low flow). A nominal head is determined. To explain the differences as mentioned above, Figures 9, 10 and 11 are presented. They consist of several sub-charts. The first sub-chart presents the power plant’s actual power and the theoretical power of the watercourse during the year. It results from, among other things, the ordered flow through the weir, i.e., the entire stream of water in the watercourse, which is shown below. Moreover, the flow through the power plant is presented, which depends on the number of running hydro units, never reaching the full water use in the watercourse. This is due to the necessity to ensure an environmental flow, the value of which is specified in the water permit and is related to the minimum environmental requirements [49]. For the considered barrage, the environmental flow is 5 m3/s, maintained through, among other things, a fish pass and leaks in the weir. The last sub-chart presents the number of running turbines depending on the current head in the barrage. The discussed sub-

graphs formEnergies a2020 coherent, 13, 6728 whole allowing for analyzing the barrage’s power plant operation11 of 21 and, in a broader sense, a comparison of this work, in years, with different average flows.

Figure 9.Figure Selected 9. Selected operating operating parameters parameters of of Archimedes Archimedes turbines turbines with an with average an low average ﬂow below low mean flow below Energies 2020, 13states, x FOR (SSQ) PEER (2006). REVIEW 11 of 20 mean states (SSQ) (2006).

Figure 10.Figure Selected 10. Selected operating operating parameters parameters of Archimedes of Archimedes turbines turbines with with anan averageaverage ﬂow flow close close to to SSQ (2010). SSQ (2010).

Figure 11. Selected operating parameters of Archimedes turbines with an average flow above SSQ (1999).

As regards the number of days when turbines were out of service, the operating parameters of Archimedes turbines in 2006 are the most favorable among those in the analyzed period. Each subsequent year, where the average annual flow was higher, the number of shutdowns was higher too. It is highly noticeable in 1999 when the number of days with hydro units working is lower than the number of forced shutdowns. Energies 2020, 13, x FOR PEER REVIEW 11 of 20

EnergiesFigure2020 10., Selected13, 6728 operating parameters of Archimedes turbines with an average flow close to12 SSQ of 21 (2010).

FigureFigure 11. 11.SelectedSelected operating operating parameters of of Archimedes Archimedes turbines turbines with anwith average an average flow above flow SSQ above (1999). SSQ (1999). As regards the number of days when turbines were out of service, the operating parameters of Archimedes turbines in 2006 are the most favorable among those in the analyzed period. As regards the number of days when turbines were out of service, the operating parameters of Each subsequent year, where the average annual flow was higher, the number of shutdowns was Archimedeshigher too. turbines It is highly in noticeable2006 are in the 1999 most when favorable the number among of days those with hydro in the units analyzed working period. is lower Each subsequentthan the year, number where of forced the average shutdowns. annual flow was higher, the number of shutdowns was higher too. It is highlyThere is noticeable a difference in in1999 the when minimum the number head for of both days technologies, with hydroenabling units working the operation is lower of than the numberturbines, of as forced noted atshutdowns. the beginning of the chapter. This results in a significantly different utilization of the theoretical energy of the watercourse. The utilization time of the Archimedes turbine installed capacity in 1999 is 1934.4 h while it is 3581.8 h for the Kaplan turbine. The value of this parameter is 85.2% higher in favor of the Kaplan turbine. It should be noted that the head value at which the hydro unit was stopped was 1.2 m for Archimedes and 0.9 m for Kaplan. Figure 12 shows the average multiyear energy production for three selected years, depending on the number of installed turbines. An interesting and distinctive aspect is the lack of an increase in energy production if the number of Archimedes turbines exceeds twelve, which corresponds to the installed rated flow value of 54 m3/s. Taking into account the environmental flow of 5 m3/s, it gives a flow of 59 m3/s. This value is close to the flow at the minimum head. An analogous phenomenon occurs for Kaplan turbines, as shown in Figure 13. In this case, if the number of installed turbines is higher than six, the increase in electricity production is minimal, i.e., for a flow of 71 m3/s, taking into account the environmental flow. This value is also close to the flow with the minimum head for this technological solution. EnergiesEnergies 20202020,, 1313,, xx FORFOR PEERPEER REVIEWREVIEW 1212 ofof 2020

ThereThere is is a a difference difference in in the the minimumminimum headhead for for both both technologies, technologies, enablingenabling the the operation operation of of turbines,turbines, asas notednoted atat thethe beginningbeginning ofof thethe chapter.chapter. ThisThis resultsresults inin aa significantlysignificantly differentdifferent utilizationutilization ofof thethe theoreticaltheoretical energyenergy ofof thethe watercourse.watercourse. TheThe utilizationutilization timetime ofof thethe ArchimedesArchimedes turbineturbine installedinstalled capacitycapacity inin 19991999 isis 1934.41934.4 hh whilewhile itit isis 3581.83581.8 hh forfor thethe KaplanKaplan turbineturbine.. TheThe valuevalue ofof thisthis parameterparameter isis 85.2%85.2% higherhigher inin favorfavor ofof thethe KaplanKaplan turbine.turbine. ItIt shouldshould bebe notednoted thatthat thethe headhead valuevalue atat whichwhich thethe hydrohydro unitunit waswas stoppedstopped waswas 1.21.2 mm forfor ArchimedesArchimedes andand 0.90.9 mm forfor Kaplan.Kaplan. FigureFigure 1212 showsshows thethe averageaverage multiyearmultiyear eneenergyrgy productionproduction forfor threethree selectedselected yearsyears,, dependingdepending onon thethe numbernumber ofof installedinstalled turbines.turbines. AnAn interestinginteresting andand distinctivedistinctive aspectaspect isis thethe lacklack ofof anan increaseincrease inin energyenergy productionproduction ifif thethe numnumberber ofof ArchimedesArchimedes turbinesturbines exceedsexceeds twelve,twelve, whichwhich correspondscorresponds toto thethe instinstalledalled ratedrated flowflow valuevalue ofof 5454 m3/s.m3/s. TTakingaking intointo accountaccount thethe environmentalenvironmental flowflow ofof 55 m3m3//s,s, itit givesgives aa flowflow ofof 5959 m3m3//s.s. ThisThis valuevalue isis closeclose toto thethe flowflow atat thethe minimumminimum headhead.. AnAn analogousanalogous phenomenonphenomenon occursoccurs forfor KaplanKaplan turbinesturbines,, asas shownshown inin FigureFigure 1313.. InIn thisthis case,case, ifif thethe numbernumber ofof installedinstalled turbinesturbines isis higherhigher thanthan six,six, thethe increaseincrease inin electricityelectricity productionproduction isis minimaminimall,, i.e.i.e.,, forfor aa Energies fflowlow ofof2020 7171, 13 m3m3, 6728//s,s, takingtaking intointo accountaccount thethe environmentalenvironmental flow.flow. ThisThis valuevalue isis alsoalso closeclose toto13 thethe of 21 flowflow withwith thethe minimumminimum headhead fforor thisthis technologicaltechnological solution.solution.

FigureFigureFigure 12.12. AverageAverage 12. Average longlong long-term--termterm productionproduction production ofof of energyenergy energy generate generatedgeneratedd by byby Archimedes ArchimedesArchimedes turbines turbinesturbines with withwith a variable aa variablevariable numbernumbernumber of of installed installedof installed hydro hydro hydro sets. sets. The The The leftmost leftmost leftmost bar bar barrepresents represents represents one hydro one one unit hydro hydro and unitthe unit rightmost—fourteen and and the the rightmost rightmost—— hydro units. fourteenfourteen hydrohydro units.units.

FigureFigureFigure 13.13. AverageAverage 13. Average longlong long-term--termterm productionproduction production ofof of energyenergy energy generatedgeneratedby byby Kaplan KaplanKaplan turbines turbinesturbines with withwith a variable aa variablevariable numbernumbernumber ofof installedinstalled of installed hydrohydro hydro sets.sets. sets. TheThe The leftmostleftmost leftmost barbar bar representsrepresents one oneone hydro hydrohydro unit unitunit and andand the thethe rightmost rightmostrightmost eight eighteight hydro units. hydrohydro units.units. 4.2. Estimating Cost–Eﬃciency Figure 14 shows the economic analysis results according to the methodology described in Section 3.2. Energies 2020, 13, x FOR PEER REVIEW 13 of 20

4.2. Estimating Cost–Efficiency Figure 14 shows the economic analysis results according to the methodology described in Energies 2020, 13, 6728 14 of 21 Section 3.2.

Figure 14. Net present value for investment in two different hydro turbines considering two Figure 14. Net present value for investment in two different hydro turbines considering two simulation methods. simulation methods. Considering the NPV criterion, large variances are noticed in the profitability of investments. AsConsidering shown in Figure the NPV14, assuming criterion, that large the minimum variances head are isnoticed not taken in intothe account,profitability both theof investments. Archimedes As shownand in Kaplan Figure turbines 14, assuming are economically that the minimum justified in head the vast is not majority taken ofinto cases. account For the, both Kaplan the Archimedes turbine and technology,Kaplan turbines the phenomenon are economically of a negative justified NPV in the criterion vast majority (unprofitable of cases. investment) For the isKaplan sporadic. turbine technology,Considering the the phenomenon critical factor of in a the negative analysis, NPV which criterion is the hydro (unprofitable unit’s minimum investment) head parameter, is sporadic. Consideringit leads to the entirely critical di fffactorerent results.in the analysis, Investments which in ais hydropower the hydro unit plant’s minimum based on the head Archimedes parameter, it leadsturbine to entirely technology different are unprofitable results. Invest in virtuallyments in every a hydro inputpower variable plant configuration based on in the the Archimedes models. However, in the case of hydropower plants with Kaplan technology, there are some cases where the turbine technology are unprofitable in virtually every input variable configuration in the models. investment may be profitable. Nevertheless, the NPV indicator clearly shows that an investment in a However, in the case of hydropower plants with Kaplan technology, there are some cases where the hydroelectric power plant of such a capacity, for the assumed input parameters, is unprofitable. investmentConsidering may be profitable. the occurring Nevertheless, parameter of the the NPV hydro indicator unit’s minimum clearly shows head and that its an impact investment on the in a hydroelectricelectricity yieldpower by plant a given of hydrosuch a power capacity, plant for or athe turbine assumed enables input a more parameters, accurate estimationis unprofitable. of the levelizedConsidering cost of the electricity occurring (LCOE). parameter It is a commonly of the hydro accepted unit criterion’s minimum for comparing head and diff itserent impact sources on the electricityof electricity. yield Asby showna given by hydro the results power presented plant inor Figure a turbine 15, the enables unit cost a ofmore electricity accurate from estimat hydropowerion of the levelizedplants c workingost of electricity with Archimedes (LCOE) and. It Kaplanis a commonly turbines (for accepted calculations criterion that for did comparing not consider different the sourcesminimum of electricity. head) is, As consecutively, shown by 175the Euroresults/MWh presented (Archimedes), in Figure and approx.15, the unit 130 Euro cost/MWh of electricity (Kaplan). from hydropowerIn Poland, plants the current working electricity with price Archimedes for household and consumers Kaplan is turbines 137 Euro / (forMWh calculations (including taxes) that [50 did]. not consider the minimum head) is, consecutively, 175 Euro/MWh (Archimedes), and approx. 130 Euro/MWh (Kaplan). In Poland, the current electricity price for household consumers is 137 Euro / MWh (including taxes) [50]. Energies 2020, 13, 6728 15 of 21 Energies 2020, 13, x FOR PEER REVIEW 14 of 20

Figure 15. Levelized cost of electricity for two different turbines and simulation approaches. Figure 15. Levelized cost of electricity for two different turbines and simulation approaches. It should also be borne in mind that the use of renewable energy resources based on watercourse bringsIt should a number also be of borne benefits, in mind particularly that the the use introduction of renewable of very energy low-emission resources electricity based on (in watercourse terms bringsof CO2)a number into the of powerbenefits, system particularly and a positive the introduction effect on low of retention. very low These-emission benefits electricity are difficult (in to terms of COquantify2) into and the express power in system monetary and values; a positive therefore, effect they on are low not retention. included in These the LCOE benefits or NPV are analyses. difficult to quantify5. Discussion and express in monetary values; therefore, they are not included in the LCOE or NPV analyses. The parameters on the barrage, i.e., a relatively high flow and nominal head below 1.7 m, pose an 5. Discussionenormous challenge to the effective use of the theoretical watercourse power. Such conditions are the reality of the Polish hydropower landscape. For natural reasons, the locations with the most favorable hydrologicalThe parameters conditions on the were barrage, utilized i.e. first., a relatively That is why high the locationsflow and that nominal remain head under below development 1.7 m, pose an enormousare a great challenge technological to the challenge. effective use of the theoretical watercourse power. Such conditions are the realityLow-head of the Polish locations hydropower are plentiful landscape. in Poland For and, natural taking reasons, into account the locations the aforementioned with the most favorablephenomena, hydrological it causes conditions much pressure were on utilized hydro-set first manufacturers. That is why to the improve locations low-head that remain solutions. under developmentThe main desirableare a great features technological are the abilitychallenge. to use increasingly lower heads with non-increasing unit costs and simultaneously retaining the required maintenance-free operation. One of the most Low-head locations are plentiful in Poland and, taking into account the aforementioned popular small-scale hydropower development directions is tubular turbines with Kaplan rotors and phenomena, it causes much pressure on hydro-set manufacturers to improve low-head solutions. The Archimedes screws. main desirableProducers features of the are technologies, the ability as to mentioned use increasingly above, compete lower heads vigorously with fornon the-increasing customer unit who costs and needs simultaneously to choose the retaining most promising the req technologyuired maintenance given the limited-free information operation. available—looking One of the most more popular smallat-scale a given hydropower technology than development just the performance directions characteristics is tubular could turbines help in making with Kaplan the right rotors choice. and ArchimeThe firstdes step screw showings. the essence of taking into account the minimum head is its impact on the annual electricityProducers production of the technologies, (Figure6). The as figure mentioned compares above, the annual compete energy vigorously production for results the customer for both who needstechnologies, to choose showing the most the promis significanting impacttechnology of the minimumgiven the head limited on this information value. This aspectavailable has— beenlooking morepreviously at a given omitted technology in research than performed just the performance by most of the characteristics authors cited in thecould introduction help in making to this study. the right choice. TheThe first minimum step showing head value the also essence significantly of taking influences into account the obtained the minimum energy yields head as theis its number impact on of installed hydro sets increases (Figure 12, Figure 13). We can observe the negligible sense of investing the annual electricity production (Figure 6). The figure compares the annual energy production results for both technologies, showing the significant impact of the minimum head on this value. This aspect has been previously omitted in research performed by most of the authors cited in the introduction to this study. The minimum head value also significantly influences the obtained energy yields as the number of installed hydro sets increases (Figure 12, Figure 13). We can observe the negligible sense of investing in additional hydro units above a particular value of the installed rated flow. The first of Energies 2020, 13, 6728 16 of 21 in additional hydro units above a particular value of the installed rated flow. The first of these limits is the flow that occurs at the minimum head. Exceeding the installed flow by this value will not increase the energy produced during the year. This is due to the need to stop the operation of hydro sets above that flow. The phenomenon, as mentioned above, is illustrated in Figure9 to Figure 11. The relationship between flow increase, head decrease on the barrage, and the number of operating hydro sets is clearly visible. For the sake of simplification in the model, the head at the weir and the power plant stand was assumed as one identical value. The modeled power plant works with water discharge into the power channel in the considered location, connecting to the river mainstream several hundred meters below the dam. It is possible that the operation of the hydro sets with the head close to the minimum parameters could be kept thanks to the limitation of the flow through the power plant and thus switching off other hydro sets. However, these considerations require further simulations and, if possible, real tests. Another assumption is that the flow in a watercourse is uniform, while in reality, it should be slowly variable. The results of the studied model were compared with the empirical data and considered sufficiently accurate. The number of running hydro sets was also determined based on their rated flow ranges to force their operation in the optimal range of the efficiency characteristics. Furthermore, no online algorithm was performed to search for the maximum efficiency point. It should also be borne in mind that a hydropower plant’s construction with an existing barrage may change the flow drop characteristics. Earlier in this paper, Figures 12 and 13 outline the issue of determining the installed flow of low-head power plants. It seems that these values could depend on a particular multiplicity of the average low flow (SNQ), i.e., the parameter at which the nominal head occurs, and of the average flow from the mean states (SSQ). The former flow value would be the lower limit of the proposed range, and the latter would be the upper limit. This issue also requires further research, taking into account a more comprehensive range of representative river types and barrage head characteristics occurring in these watercourses.

6. Conclusions The main topic of the work is to investigate the influence of the minimum head parameter on the operations of low-head hydropower plants. By modeling and analyzing the SHP at the Drawski Młyn water barrage, it has been shown that this parameter influences electricity production. This effect is more distinct for the Archimedes screw technology than for the Kaplan turbine. The decrease in energy production associated with the hydro unit minimum head parameter for Kaplan is from 0% to 30%, and from 6% to 52% for Archimedes turbines, for the years considered in Figure6. Then, there are significant discrepancies in the economic analysis results for both types of hydro sets. At the same time, it should be pointed out that the recommended installed flow rate for low-head locations should be specified in detail because the criteria adopted so far seem to be inadequate. The rapid development of low-head technologies should be observed, as they may be devoid of the indicated shortcomings in the future. The development should be aimed at improving the minimum head parameter.

Author Contributions: Conceptualization, J.J., B.C. and A.G.; methodology, J.J. and A.G.; software, A.G. and Ł.K.; validation, J.J.; formal analysis, R.W.; investigation, J.J. and R.W.; resources, A.G. and Ł.K.; data curation, A.G. and Ł.K.; writing—original draft preparation, A.G. and Ł.K.; writing—review and editing, B.C., J.J. and D.Z.; visualization, D.Z.; supervision, R.W.; project administration, B.C.; funding acquisition, B.C. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Higher Education, grant number 0711/SBAD/4468. Acknowledgments: We thank Egidijus Kasiulis and Alban Kuriqi for their help and meaningful comments, which they have provided us during the revision of our paper. Conﬂicts of Interest: The authors declare no conﬂict of interest. Energies 2020, 13, x FOR PEER REVIEW 16 of 20

Abbreviations Energies 2020, 13, 6728 17 of 21 CAPEX capital expenditures FOM fixed operational cost Abbreviations LCOE levelized cost of electricity CAPEXMC Monte capital expendituresCarlo simulation FOMNPV net fixed present operational value cost LCOESHP small levelized-scale cost hydropower of electricity MCSNQ average Monte Carlo low simulation flow NPVSSQ average net present flow value from the average flows SHP small-scale hydropower SWR average high flow SNQ average low flow TSO transmission system operator SSQ average flow from the average flows SWRVOM variable average high operational flow cost TSO transmission system operator VOMAppendix A variable operational cost The simulated energy generation from hydro turbines over 1974–2018 did not fit any standard Appendixstatistical distribution. A Considering the above, the procedure applied was to generate random energy generationThe simulated values whil energye maintaining generation from the hydrosimulated turbines time over series 1974–2018 of statistical did not parameter fit any standards. The statisticalfirst step distribution. Considering the above, the procedure applied was to generate random energy generation values whileinvolved maintaining creating the a histogram simulated time (Figure series A of1) statistical, which would parameters. show The how first the step energy involved was creating generated, a histogram on an (Figureannual A1 basis), which, over would that showperiod. how In the this energy case, was the generated, bins’ width on anwas annual selected basis, as over 100 that MWh period., but In it this can case, be theadjusted bins’ width according was selected to the asdesired 100 MWh, granularity. but it can be adjusted according to the desired granularity.

Figure A1. Histogram of energy generation over the period 1974–2018.1974–2018.

The next step in generating random values from their historical distribution involved calculating the probabilityThe next of energy step in generation generating within random each binvalues range. from The their calculated historical probabilities distribution are presented involved in calculating Table A1. the probability of energy generation within each bin range. The calculated probabilities are presented in Table A1. Table A1. Probability of energy generation from a given range.

Table A1. ProbabilityRange [MWh] of energy generation % Probability from a given range. (1000–1100> 4.17% (1100–1200Range [MWh]> % Probability0.00% (1200–1300(1000–1100> > 4.17%0.00% (1300–1400(1100–1200> > 0.00%4.17% (1400–1500(1200–1300> > 0.00%8.33% (1500–1600> 10.42% (1300–1400> 4.17% (1600–1700> 14.58% (1700–1800(1400–1500> > 8.33%25.00% (1800–1900(1500–1600> > 10.42%33.33% (1600–1700> 14.58% In the third step, the cumulative probability(1700–1800 is calculated> 25.00% (Table A2). Energies 2020, 13, 6728 18 of 21

Table A2. Cumulative probability.

Cumulative Range [MWh] probability (1000–1100> 4.17% (1100–1200> 4.17% (1200–1300> 4.17% (1300–1400> 8.33% (1400–1500> 16.67% (1500–1600> 27.08% (1600–1700> 41.67% (1700–1800> 66.67% (1800–1900> 100.00%

Finally, the energy generation time series can be replicated by applying the following approach: Step 1. Generate random numbers p(1) from a uniform distribution ranging from 0 to 1; Step 2. For the generated number, check if it is less than the cumulative probability for the first range (1000–1100 MWh). For example, if that is the case, the random number p(1) was 0.02, proceed to Step 3; if not, proceed to Step 4; Step 3. For the range for which the p number was smaller than the cumulative probability, generate another number from a uniform distribution in which minimum and maximum values are, as in the range boundaries, for the case that would mean generating a number from a uniform distribution ranging from 1000 to 1100 MWh. The generated number is then the first simulated energy generation value. Proceed to Step 1 to generate the following energy generation values; Step 4. In this step, move to the next range and its cumulative probability values. If the cumulative probability values are similar for two or more ranges, remove the subsequent ones and keep only the first one. In Table A2, the range 1000–1100 would be kept only, while 1100–1200, 1200–1300 would have to be removed. Select the first range for which the p number is smaller than its cumulative probability value. For example, for p equal to 0.25, it would be range 1500–1600. For p equal to 0.6, it would be 1700–1800. Repeat this step until the p-value is assigned to the range. If found, proceed to step 1; Step 5. The simulation ends when the desired number of energy generation numbers has been reached. To assess the usefulness of the proposed approach, we have generated 3000 energy generation numbers whose distribution should follow the historical data obtained from simulations over the period 1974–2018. The chart in Figure A2 compares the simulation results from historical data and after applying the procedure proposed above. Energies 2020The, 13 proposed, x FOR methodPEER REVIEW enables a perfect fit with the original distribution. 18 of 20

Figure A2.Figure The A2. probabilityThe probability of energy of energy distribution distribution from didifferentﬀerent ranges ranges is based is based on historical on historical data data simulations and recreating the distribution based on the proposed method. simulations and recreating the distribution based on the proposed method. References References 1. Ceran, B. Inﬂuence of the CO2 emission factor value on the result of the load distribution analysis between the hybrid PV/WT/FC system and the electric power system. E3S Web Conf. 2019, 108, 01016. [CrossRef] 1. Ceran, B. Influence of the CO2 emission factor value on the result of the load distribution analysis between the hybrid PV/WT/FC system and the electric power system. E3S Web Conf. 2019, 108, 01016, doi:10.1051/e3sconf/201910801016. 2. Szczerbowski, R.; Ceran, B. Development perspectives of the Polish power generation sector according to the climate preservation conference COP21 policies. E3S Web Conf. 2017, 14, 01003, doi:10.1051/e3sconf/20171401003. 3. Polish Power Networks (In Polish: Polskie Sieci Elektroenergetyczne). Available online: https://www.pse.pl/web/pse-eng (accessed on 20 May 2020). 4. Hoes, O.; Meijer, L.; van der Ent, R.; van de Giesen, N. Systematic high-resolution assessment of global hydropower potential. PLoS ONE 2017, 12, doi:10.1371/journal.pone.0171844. 5. Balkhair, K.S.; Ur Rahman, K. Sustainable and economical small-scale and low-head hydropower generation: A promising alternative potential solution for energy generation at local and regional scale. Appl. Energy 2017, 188, 378–391, doi:10.1016/j.apenergy.2016.12.012. 6. Bódis, K.; Monforti, F.; Szabó, S. Could Europe have more mini hydro sites? A suitability analysis based on continentally harmonized geographical and hydrological data. Renew. Sustain. Energy Rev. 2014, 37, 794– 808, doi:10.1016/j.rser.2014.05.071. 7. Wiemann, P.; Muller, G.; Senior, J. Review of current developments in low head, small hydropower. In Proceedings of the 32nd IAHR Conference 2007, Venice, Italy, 1–6 July 2007. 8. Kowalczyk, K.; Cieśliński R. Analysis of the hydroelectric potential and the possibilities of its use in the Pomeranian voivodeship. Woda-Środowisko-ObszaryWiejskie 2018, 18, 69–86. 9. Punys, P.; Kvaraciejus, A.; Dumbrauskas, A.; Šilinis, L.; Popa, B. An assessment of micro-hydropower potential at historic watermill, weir, and non-powered dam sites in selected EU countries. Renew. Energy 2019, 133, 1108–1123, doi:10.1016/j.renene.2018.10.086. 10. Zhou, D.; Deng, Z.D. Ultra-low-head hydroelectric technology: A review. Renew. Sustain. Energy Rev. 2017, 78, 23–30, doi:10.1016/j.rser.2017.04.086. 11. Lavrič, H.; Rihar, A.; Fišer, R. Assessment of electrical energy production in small hydropower plant with ultra-low head. In Proceedings of the 2013 International Conference-Workshop Compatibility and Power Electronics, Ljubljana, Slovenia, 5–7 June 2013; doi:10.1109/CPE.2013.6601137. 12. Quaranta, E. Stream water wheels as renewable energy supply in flowing water: Theoretical considerations, performance assessment and design recommendations. Energy Sustain. Dev. 2018, 45, 96– 109, doi:10.1016/j.esd.2018.05.002. 13. Budiarso, B.; Helmizar, H.; Warjito; Nuramal, A.; Ramadhanu, W.; Adanta, D. Performance of breastshot waterwheel in run of river conditions. In AIP Conference Proceedings; AIP Publishing LLC: New York, NY, USA, 2020; Volume 2227, p. 020014, doi:10.1063/5.0000940. 14. Quarantaa, E.; Revelli, R. Gravity water wheels as a micro hydropower energy source: A review based on historic data, design methods, efficiencies and modern optimizations. Renew. Sustain. Energy Rev. 2018, 97, 414–427, doi:10.1016/j.rser.2018.08.033. Energies 2020, 13, 6728 19 of 21

2. Szczerbowski, R.; Ceran, B. Development perspectives of the Polish power generation sector according to the climate preservation conference COP21 policies. E3S Web Conf. 2017, 14, 01003. [CrossRef] 3. Polish Power Networks (In Polish: Polskie Sieci Elektroenergetyczne). Available online: https://www.pse.pl/ web/pse-eng (accessed on 20 May 2020). 4. Hoes, O.; Meijer, L.; van der Ent, R.; van de Giesen, N. Systematic high-resolution assessment of global hydropower potential. PLoS ONE 2017, 12.[CrossRef][PubMed] 5. Balkhair, K.S.; Ur Rahman, K. Sustainable and economical small-scale and low-head hydropower generation: A promising alternative potential solution for energy generation at local and regional scale. Appl. Energy 2017, 188, 378–391. [CrossRef] 6. Bódis, K.; Monforti, F.; Szabó, S. Could Europe have more mini hydro sites? A suitability analysis based on continentally harmonized geographical and hydrological data. Renew. Sustain. Energy Rev. 2014, 37, 794–808. [CrossRef] 7. Wiemann, P.; Muller, G.; Senior, J. Review of current developments in low head, small hydropower. In Proceedings of the 32nd IAHR Conference 2007, Venice, Italy, 1–6 July 2007. 8. Kowalczyk, K.; Cie´sliński,R. Analysis of the hydroelectric potential and the possibilities of its use in the Pomeranian voivodeship. Woda-Srodowisko-ObszaryWiejskie´ 2018, 18, 69–86. 9. Punys, P.; Kvaraciejus, A.; Dumbrauskas, A.; Šilinis, L.; Popa, B. An assessment of micro-hydropower potential at historic watermill, weir, and non-powered dam sites in selected EU countries. Renew. Energy 2019, 133, 1108–1123. [CrossRef] 10. Zhou, D.; Deng, Z.D. Ultra-low-head hydroelectric technology: A review. Renew. Sustain. Energy Rev. 2017, 78, 23–30. [CrossRef] 11. Lavriˇc,H.; Rihar, A.; Fišer, R. Assessment of electrical energy production in small hydropower plant with ultra-low head. In Proceedings of the 2013 International Conference-Workshop Compatibility and Power Electronics, Ljubljana, Slovenia, 5–7 June 2013. [CrossRef] 12. Quaranta, E. Stream water wheels as renewable energy supply in flowing water: Theoretical considerations, performance assessment and design recommendations. Energy Sustain. Dev. 2018, 45, 96–109. [CrossRef] 13. Budiarso, B.; Helmizar, H.; Warjito; Nuramal, A.; Ramadhanu, W.; Adanta, D. Performance of breastshot waterwheel in run of river conditions. In AIP Conference Proceedings; AIP Publishing LLC: New York, NY, USA, 2020; Volume 2227, p. 020014. [CrossRef] 14. Quarantaa, E.; Revelli, R. Gravity water wheels as a micro hydropower energy source: A review based on historic data, design methods, efficiencies and modern optimizations. Renew. Sustain. Energy Rev. 2018, 97, 414–427. [CrossRef] 15. Zhao, M.; Zheng, Y.; Yang, C.; Zhang, Y.; Tang, Q. Performance Investigation of the Immersed Depth Effects on a Water Wheel Using Experimental and Numerical Analyses. Water 2020, 12, 982. [CrossRef] 16. Quaranta, E.; Müller, G. Optimization of undershot water wheels in very low and variable flow rate applications. J. Hydraul. Res. 2019, 1–5. [CrossRef] 17. Lavriˇc,H.; Rihar, A.; Fišer, R. Influence of equipment size and installation height on electricity production in an Archimedes screw-based ultra-low head small hydropower plant and its economic feasibility. Renew. Energy 2019, 142, 468–477. [CrossRef] 18. Rohmer, J.; Knittel, D.; Sturtzer, G.; Flieller, D.; Renaud, J. Modeling and experimental results of an Archimedes screw turbine. Renew. Energy 2016, 94, 136–146. [CrossRef] 19. Siswantara, A.I.; Siswantara, A.I.; Warjito; Budiarso, B.; Harmadi, R.; Syafei, M.H.; Adanta, D. Investigation of the α angle’s effect on the performance of an Archimedes turbine. Energy Procedia 2017, 156, 458–462. [CrossRef] 20. Songin, K.; Lubitz, W. Measurement of fill level and effects of overflow in power-generating Archimedes screws. J. Hydraul. Res. 2019, 57, 635–646. [CrossRef] 21. Dellinger, G.; Simmons, S.; Lubitz, W.D.; Garambois, P.; Dellinger, N. Effect of slope and number of blades on Archimedes screw generator power output. Renew. Energy 2019, 136, 896–908. [CrossRef] 22. Lubitz, W.D.; Lyons, M. Archimedes Screws for Microhydro Power Generation. In Proceedings of the ASME 2013 7th International Conference on Energy Sustainability, Minneapolis, MN, USA, 14–19 July 2013. [CrossRef] Energies 2020, 13, 6728 20 of 21

23. Khan, A.; Khattak, A.; Ulasyar, A.; Imran, K.; Munir, M.A. Investigation of Archimedes Screw Turbine for Optimal Power Output by Varying Number of Blades. In Proceedings of the 2019 International Conference on Electrical, Communication, and Computer Engineering (ICECCE), Swat, Pakistan, 24–25 July 2019; pp. 1–6. [CrossRef] 24. Lavriˇc,H.; Rihar, A.; Fišer, R. Simulation of electrical energy production in Archimedes screw-based ultra-low head small hydropower plant considering environment protection conditions and technical limitations. Energy 2018, 164, 87–98. [CrossRef] 25. Zhu, L.; Zhang, H.P.; Zhang, J.G.; Meng, X.C.; Lu, L. Performance of a bulb turbine suitable for low prototype head: Model test and transient numerical simulation. Conf. Ser. Earth Environ. Sci. 2012, 15, 042032. [CrossRef] 26. Mulu, B.G.; Jonsson, P.P.; Cervantes, M.J. Experimental investigation of a Kaplan draft tube—Part I: Best efficiency point. Appl. Energy 2012, 93, 695–706. [CrossRef] 27. Abeykoon, C.; Hantsch, T. Design and Analysis of a Kaplan Turbine Runner Wheel. In Proceedings of the 3rd World Congress on Mechanical, Chemical, and Material Engineering (MCM’17), Rome, Italy, 8–10 June 2017. HTFF 151/1-16. [CrossRef] 28. Abbas, A.; Qandil, M.; Al-Haddad, M.; Amano, R.S. Performance Investigation of Very-Low-Head Kaplan Hydro-Turbines. In Proceedings of the AIAA SciTech 2019 Forum, San Diego, CA, USA, 7–11 January 2019. [CrossRef] 29. Water Turbines Works—Poland. Available online: https://www.wtw-poland.com/en/offer (accessed on 7 April 2020). 30. Elbatran, A.H.; Yaakob, O.B.; Ahmed, Y.M.; Shabara, H.M. Operation, performance and economic analysis of low head micro-hydropower turbines for rural and remote areas: A review. Renew. Sustain. Energy Rev. 2015, 43, 40–50. [CrossRef] 31. Nuernbergk, D.M.; Rorres, C. Analytical Model for Water Inflow of an Archimedes Screw Used in Hydropower Generation. J. Hydraul. Eng. 2013, 139, 213–220. [CrossRef] 32. Saroinsong, T.; Soenoko, R.; Wahyudi, S.; Wahyudi, S. Fluid Flow Phenomenon in a Three-Bladed Power-Generating Archimedes Screw Turbine. J. Eng. Sci. Technol. Rev. 2016, 9, 72–79. [CrossRef] 33. Raza, A.; Xu, D.; Mian, M.S.; Ahmed, J. A micro hydro power plant for distributed generation using municipal water waste with Archimedes screw. In Proceedings of the 2013 16th International Multi Topic Conference, Lahore, Pakistan, 19–20 December 2013; pp. 66–71. [CrossRef] 34. Rohmer, J.; Sturtzer, G.; Knittel, D.; Flieller, D.; Renaud, J. Dynamic model of small hydro plant using Archimedes screw. In Proceedings of the 2015 IEEE International Conference on Industrial Technology (ICIT), Seville, Spain, 17–19 March 2015; pp. 987–992. [CrossRef] 35. Breeze, P. Hydropower. In Power Generation Technologies, 3rd ed.; Breeze, P., Ed.; Newnes: Oxford, UK, 2019; pp. 173–201. [CrossRef] 36. Quaranta, E. Optimal Rotational Speed of Kaplan and Francis Turbines with Focus on Low-Head Hydropower Applications and Dataset Collection. J. Hydraul. Eng. 2019, 145.[CrossRef] 37. Kim, H.-H.; Rakibuzzaman, M.; Kim, K.; Suh, S.-H. Flow and Fast Fourier Transform Analyses for Tip Clearance Effect in an Operating Kaplan Turbine. Energies 2019, 12, 264. [CrossRef] 38. Yang, W.; Wu, Y.; Liu, S. A modification method on runner blades in a Bulb turbine. Iop Conference Series: Earth and Environmental Science 2010, 12, 012003. [CrossRef] 39. Report on Preparing Flood Danger Maps and Flood Risk Map (In Polish: Raport z Wykonania Map Zagro˙zeniaPowodziowego i Map Ryzyka Powodziowego). Available online: https://www.kzgw.gov.pl/files/ mzp-mrp/zal1.pdf (accessed on 10 July 2020). 40. Electricity Generation from Renewable Energy Sources in Poland—The Presidents of the Energy Regulatory Office Report in 2019 (In Polish: Wytwarzanie energii elektrycznej w Polsce w małych instalacjach OZE—RaportPrezesa URE za 2019 rok). Available online: https://bip.ure.gov.pl/bip/o-urzedzie/zadania-prezesa-ure/raport-oze-art- 17-ustaw/3556,Raport-zbiorcze-informacje-dotyczace-wytwarzania-energii-elektrycznej-z-odnawial.html (accessed on 10 July 2020). 41. Płaczek, J.; Dysarz, T.; Wicher-Dysarz, J. Analysis of selected dams operation in the reach of the NotećBystra during the flood hazard conditions. Acta Scientiarum Polonorum. Formatio Circumiectus 2016, 15, 295–307. [CrossRef] Energies 2020, 13, 6728 21 of 21

42. The Inventory of the Constituent Parts of Inland Waterways of Special Transport Significance (In Polish: Inwentaryzacja cz˛e´sciSkładowych Sr´ ódl ˛adowychdróg Wodnych o Szczególnym Znaczeniu transportowym). Available online: https://mgm.gov.pl/wp-content/uploads/2017/11/inwentaryzacja-czesci-skladowych- srodladowych-drog-wodnych-o-szczegolnym-znaczeniu-transportowym.pdf (accessed on 10 July 2020). 43. Manning’s Equation—Manning’s n Values. Available online: http://www.fsl.orst.edu/geowater/FX3/help/8_ Hydraulic_Reference/Mannings_n_Tables.htm (accessed on 10 July 2020). 44. Institute of Meteorology and Water Management National Research Institute—Hydrological data (In Polish: Instytut Meteorologii i Gospodarki Wodnej PaństwowyInstytut Badawczy—Dane hydrologiczne). Available online: https://dane.imgw.pl/data/dane_pomiarowo_obserwacyjne/dane_hydrologiczne/ (accessed on 10 July 2020). 45. Carlsson, J.; Fortes, M.D.M.P.; de Marco, G.; Giuntoli, J.; Jakubcionis, M.; Jäger-Waldau, A.; Sigfusson, B. ETRI 2014-Energy Technology Reference Indicator Projections for 2010–2050; European Commission, Joint Research Centre, Institute for Energy and Transport; Publications Office of the European Union: Luxembourg, 2014. 46. Paska, J. Assessment methodology for costs of electricity generation. Rynek Energii 2012, 2, 24–28. 47. TAURON Polska Energia, S.A. Available online: https://media.tauron.pl/pr/360947/elektrownie-wodne- tauron-zwyciezcami-aukcji-oze (accessed on 10 July 2020). 48. Archimedes screw distributor’s page. Available online: http://dobraenergia.info/ (accessed on 10 July 2020). 49. Kuriqi, A.; Pinheiro, A.N.; Sordo-Ward, A.; Garrote, L. Water-energy-ecosystem nexus: Balancing competing interests at a run-of-river hydropower plant coupling a hydrologic–ecohydraulic approach. Energy Convers. Manag. 2020, 223, 113267. [CrossRef] 50. Eurostat—Electricity Price Statistics. Available online: https://ec.europa.eu/eurostat/statistics-explained/ index.php/Electricity_price_statistics (accessed on 10 July 2020).

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional aﬃliations.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).