# Microturbines at Drinking Water Tanks Fed by Gravity Pipelines: A Method and Excel Tool for Maximizing Annual Energy Generation Based on Historical Tank Outflow Data

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## Abstract

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## 1. Introduction

#### 1.1. Advantages and Characteristics of Potential Drinking Water Hydropower Facilities

- decoupled from uncontrolled downstream water use through a storage tank (“buffered”), or
- determined by uncontrolled water use in the downstream supply zone(s) (“non-buffered”).

#### 1.2. Available Literature and Comparison of Class 1 vs. Class 2 Sites

#### 1.3. Filling a Gap in Currently Available Design Methods for Class 1 Sites

## 2. Materials and Methods

#### 2.1. Design Premise

_{out}) to reflect anticipated future changes), which are further described in Appendix B.3 and Appendix B.4 and the tool itself.

#### 2.2. Determining the Characteristic Site Curve

_{max}, at flow rate = 0) minus the head loss up to the point of interest (h

_{loss}) and the pressure head just downstream of the control valve (h

_{downstream})

_{,}which is necessary for the water to reach the storage tank. Since head loss increases proportionally to the square of flow rate, the curve can be well approximated (Equation (1)) with a downward-facing parabola with its vertex centered on the positive y-axis (flow rate = 0), crossing the positive x-axis at the maximum possible flow rate (pressure exerted on reference point upstream of valve = 0), at which the pressure control valve is completely open and offers no hydraulic resistance (see Figure 8 in Section 3.1 for an example). This is predicated on a simplifying assumption that assumes a constant coefficient of major pipe friction loss (defined in the U.S. as “lambda”, λ), which is known to be flow rate-dependent (e.g., as captured in Moody’s diagram), but is valid for conditions commonly encountered at water supply sites. The resulting second-order polynomial equation takes the following form:

_{loss}is the head loss coefficient, which integrates the major head loss due to pipe friction and minor head loss(es) due to sources of local resistance (e.g., pipe bends, partially opened valves upstream). h

_{loss}as defined in Figure A1 (Appendix A.1) is the central term in Equation (1), the product of K

_{loss}with the square of the flow rate Q. While h

_{max}, K

_{loss}and h

_{downstream}could be determined analytically, the authors found empirical determination to be both more accurate and less labor-intensive. To empirically determine this parabolic curve, two points must be defined, which requires measuring five field data points:

- Q
_{1_inflow}: non-zero inflow rate at control valve, position 1 (e.g., at normal operating flow) - h
_{1_upstream}: pressure head upstream of control valve, position 1 (e.g., at normal operating flow) - h
_{downstream}: pressure head just downstream of the control valve, which is necessary for the water to reach the (frequently somewhat higher) storage tank (e.g., at normal operating flow) - Q
_{2_inflow}: inflow rate at control valve, position 2 (ideally zero flow; i.e., closed valve, but can also be a second, sufficiently different non-zero flow rate than Q_{1}, if closing the valve is not feasible) - h
_{2_upstream}: pressure head upstream of control valve, position 2 (ideally at zero flow; see above)

_{loss}can effectively be considered a constant, it can be determined indirectly by substituting all measured values into Equation (1). Q

_{max}can then be determined simply by setting Equation (1) to zero and solving for Q (Equation (2)).

_{1_upstream}and h

_{2_upstream}will impact the value of h

_{max}, since the pressure measured depends to a small degree on the water level in the upstream tank. Ideally, these measurements should be conducted when the upstream tank is known to be at its typical lowest level, as this will provide a conservative estimate of the pressure that will at a minimum be reliably available to a potential turbine. Furthermore, the flow-dependent head losses between the control valve and storage tank are integrated into the measurement of h

_{downstream}, if performed using a pressure gauge. The change in these losses (and therefore a change in h

_{downstream}) due to a deviation in the turbine flow rate from Q

_{1_inflow}(normal operating flow) is likely negligible, but can also be easily measured by changing the flow rate to the potential future turbine flow rate. The value for h

_{downstream}is usually primarily determined either by the height of the pipe outlet above the turbine (as portrayed in Figure 2) or the water level in the downstream tank (as portrayed in Figure A1), in case the pipe outlet is at the bottom of the downstream tank. Figure 2 provides a visual explanation of some of these terms for the typical case as encountered by the authors in Germany.

#### 2.3. Calculating the Hydraulic Power Available to the Turbine

^{3}), g is gravitational acceleration (m/s

^{2}), Q is the flow rate (m

^{3}/s) and h

_{available}is the available pressure head (m). Since ρ and g can be assumed constant (1000 kg/m

^{3}and 9.81 m/s

^{2}, respectively), the equation can be simplified (Equations (4a) and (4b)) to allow the input of flow rate in more commonly used units of m

^{3}/h or L/min:

_{available}is approximated as a second-order polynomial function of Q (Equation (3)), and this function is multiplied with Q and a constant to compute available hydraulic power, the characteristic curve of hydraulic power available to a turbine can therefore be approximated as a third-order polynomial function of Q (Equation (5)), adjusted by the appropriate constant as per Equation (4):

_{max}occurs can be determined by first taking the derivative of Equation (5) with respect to flow rate Q, resulting in Equation (6):

_{available}to zero leads to Equation (7) for the flow rate corresponding to P

_{max}:

_{P_max}into Equation (5) yields the maximum possible hydraulic power for the given class 1 site. This information becomes relevant upon comparing the results of this method with the method from the 1994 DVGW guidelines [34] (see Section 2.10).

#### 2.4. Consideration of a Bypass Pipeline Parallel to the Turbine

_{bypass}is substantially above the turbine design flow rate Q

_{turbine}, this can maximize total annual energy generation, by enabling Q

_{turbine}to be as low possible, which reduces unnecessary friction losses that would otherwise occur with a higher Q

_{turbine}. This relationship between Q

_{bypass}and Q

_{turbine}should become clearer in the coming sections. The recommended setting is the maximum permissible inflow rate, but this can be freely adjusted by the user.

#### 2.5. Using a Numerical Model to Ensure Supply Reliability Based on Historical Flow Data

_{in}must at any point in time be sufficient to meet the demand placed on the storage tank by the water users in the supply zone and cannot endanger the reliability of supply by causing the storage tank to temporarily run below a minimum emergency level (e.g., for fire-fighting reserves). To determine whether this is likely to happen based on a given Q

_{bypass}and Q

_{turbine}, a simple linear, deterministic, dynamic numerical model was incorporated into the tool. The model takes a historical time series of the outflow rate from the storage tank Q

_{out}as input (ideally at a maximum time interval of 15 min) and simulates Q

_{in}through the turbine and bypass as well as the resulting storage tank water level L

_{tank}. The initial condition for L

_{tank}is 75% if no water level time series data are provided along with the time series for Q

_{out}. The basic governing equation (Equation (8)) for L

_{tank}at a given timestamp t+1 is as follows:

_{tank @ t+1}reflects the resulting tank water level at timestamp t+1 at the end of the time step T (between timestamps t and t+1), V

_{in @ T}and V

_{out @ T}are the volume of water entering and leaving the tank during the time step T (between timestamps t and t + 1), respectively, and V

_{tank}is the volume of the storage tank at 100% capacity (m

^{3}). To clarify, “timestamp” t refers to an instantaneous point in time (e.g., 12:00:00 (noon) on 20 June 2019), whereas “time step” T refers to the duration of time passing between the two timestamps t and t+1 (e.g., the 15 min between 12:00:00 and 12:15:00). V

_{out}and V

_{in}are obtained by multiplying the duration of the time step T ([t + 1] − t) with Q

_{out}and Q

_{in}, respectively, to yield a water volume. Q

_{out}is taken from the historical time series provided by the user, whereas Q

_{in}is determined by Equation (9):

_{bypass}is the chosen bypass flow rate, Q

_{turbine}is the chosen turbine flow rate, L

_{2_max shutoff}is the maximum permissible tank water level (% of full), L

_{1_turbine on}is the threshold tank level at which the turbine is operated, L

_{3_bypass on}is the threshold tank level at which the bypass pipe is opened, and the turbine pipe is closed. A further value, L

_{4_min emergency}, signifies the lowest permissible water level. If L

_{tank}falls short of this, the Q

_{turbine}is excluded from the set of feasible solutions. See Figure 2 for a visual representation of these tank levels. For the method to properly function, the following relationships between values must be true (Equations (10a) and (10b)):

_{2_max shutoff}> L

_{1_turbine on}> L

_{3_bypass on}> L

_{4_min emergency}

_{max inflow}≥ Q

_{bypass}≥ Q

_{turbine}

_{max inflow}is the maximum permissible inflow rate into the tank, either legally according to a contract with a long-term water supplier or technically due to pipeline’s natural Q

_{max}(see Appendix A.1 for elaboration) or a limitation on the water source (e.g., a mountain spring). The recommended setting is for Q

_{turbine}to be equal to Q

_{max inflow}.

_{turbine}. Only in cases of high water withdrawal (Q

_{out}) in which the tank level falls very rapidly is the bypass opened (and the turbine pipe closed) to increase the inflow rate to Q

_{bypass}and kept open until the maximum permissible water level is exceeded (tank is full). Then normal operation with the turbine resumes. The number of occasions on which the bypass is opened increases as Q

_{turbine}decreases.

_{in}to exclusively be equal to Q

_{turbine}and Q

_{bypass}, taking into account the impact on L

_{tank}, the tool thus re-defines the inflow regime in such a way that both supply reliability can be guaranteed, and energy generation can be maximized (see Figure 1). This is the step in the tool’s algorithm at which the key advantage of class 1 “buffered” sites is utilized.

#### 2.6. Calculating Total Annual Hydraulic Energy Capture

_{hydraulic}that is applied to the turbine wheel, before being converted to the mechanical energy E

_{mechanical}of the spinning wheel and shaft, and then further converted to electrical energy E

_{electrical}through a generator. E

_{hydraulic}is calculated using Equation (11):

_{in}at each timestamp t (Equation (9)) depends on the outcome of the numerical model described above. This model therefore performs two functions: (1) calculating the energy production for each time step and (2) monitoring whether the water level falls below the minimum permissible level in the storage tank and flagging such solutions as invalid.

#### 2.7. Selection of Microturbines, Global Efficiency Curves and Calculating Total Annual Electric Energy Generation

_{total}at the hydraulic best efficiency point for turbines of varying capacities was plotted relative to P

_{hydraulic}, leading to Figure 3. For each type, AXENT and PAT (two separate models), natural log curves were fitted to the data to generate equations that enabled the estimation of η

_{total}based on the input of P

_{hydraulic}(Equations (12a) and (12b)). The tool can be updated with new data for other types of turbines from other companies, although this cannot currently be easily done by a normal user.

_{total}for a hypothetical range of different turbines, not the characteristic efficiency curve of a single turbine over its operating range. Each turbine also has its own flow-dependent efficiency, such that the operating efficiency will vary from the optimal η

_{total}in the event that it is operated off of its design flow rate, or if a turbine cannot be manufactured to have its peak efficiency precisely at the chosen Q

_{turbine}. For simplicity’s sake, the tool assumes that the turbine is only operated at its optimal η

_{total}, at a single operating point. The flow rate must be high enough to enable the use of a microturbine with a practical size and sufficiently high efficiency, as the efficiency of turbines and generators drops rapidly with declining physical dimensions.

_{electrical}for a given Q

_{turbine}and choice of turbine type is then determined by Equation (13):

#### 2.8. Iteratively Determining the Optimal Turbine Design Parameters

_{out}data provided by the user (see above). Generally speaking, a longer historical time series produces more reliable results by accounting for a wider range of realistic supply scenarios, but a very long time series runs the risk of using obsolete data that does not reflect the expected future supply scenarios and therefore producing sub-optimal results. In the authors’ experience, 12 to 24 months is ideal.

_{turbine}is iteratively run through the numerical model, calculating E

_{electrical}for each value of Q

_{turbine}. This is first done at intervals of 5 m

^{3}/h to determine the approximate optimal Q

_{turbine}, and then again at intervals of 0.5 m

^{3}/h to refine this result. The Q

_{turbine}leading to the greatest E

_{electrical}is declared optimal, and the corresponding h

_{turbine}calculated using Equation (1).

#### 2.9. Estimating Economic Viability

_{total}, the estimation of economic viability is based on available cost data for actual microturbines from the companies Stellba and KSB. These costs are based on past implemented projects, recent price quotes and the experience of collaborating engineers, and include the cost of purchase, installation and commissioning. Table 2 shows the cost items and the ranges for the two different types of turbines incorporated into the tool, as well as the total costs including the 19% value-added tax (VAT) for Germany. The peripheral costs for the AXENT turbine are generally lower, because the design elements required to install it are less complex, and it does not require protection against pressure shocks (water “hammer”), contrary to a typical PAT. Figure 4 shows the specific total cost C

_{specific}data for both types of turbines.

_{specific}are calculated by entering P

_{hydraulic}into Equations (14a) and (14b), and the total costs C

_{total}for a given site and turbine are obtained by multiplying P

_{hydraulic}with C

_{specific}.

_{annual}are based on user input on the applicable feed-in tariff or other electricity price at which the generated energy could be sold. In Germany, for example, the legally guaranteed feed-in tariff for turbines below a total capacity of 100 kW commissioned in 2019 is 12.27 ct. €/kWh, for a contract length of 20 years. A site is only eligible for this tariff if the water flows via gravity from its natural source to the turbine. Otherwise, the energy must normally be used on site, replacing electrical energy that would otherwise been purchased from the grid, in Germany at a price of approximately 20 ct. €/kWh. The tool combines the estimated benefits from both of these sources (Equation (15)), which can also complement each other (e.g., if there is a pump set that can be occasionally but not continuously supplied with energy by the turbine, or if the turbine is only able to cover a portion of the energy demand of the pumps).

_{total}, as many projects are hindered by insufficient initial funding.

#### 2.10. DVGW 1994 and 2016 Methods as a Basis of Comparison

_{electrical}in units of kWh/a.

^{3}/h representing the range from 50 to 55 m

^{3}/h) having the greatest energy density (result of Equation (17), applied to each range of flow rates) should be the design turbine flow rate. The resulting Q

_{turbine}is then given as input into the Excel tool to calculate E

_{electrical}assuming the inflow regime is modified as with the tool’s optimization algorithm. In this way, this method is evaluated more generously than if it were applied as intended to class 2 sites, since the flow rates occurring above and below the chosen Q

_{turbine}would not contribute to energy generation, being too high or low to be efficiently processed by the turbine (see Section 3.2 and Table 4 for a concrete example).

_{in}into the tank (approximately representing the “status quo”, if the inflow regime were not modified), and the other based on Q

_{out}from the tank. Historical time series are required for both in order to apply Equation (17).

_{turbine}is given as input into the Excel tool to calculate E

_{electrical}assuming the inflow regime is modified as with the tool’s optimization algorithm. Table 3 offers a concise summary of all methods that are compared in this paper with their corresponding short names.

## 3. Results

#### 3.1. Case Study of Tool Application: Break Pressure Tank (BPT) Rützengrün, Germany

^{3}. Thanks to this storage, BPT Rützengrün is a class 1 site, which permits a degree of flexibility in regulating the inflow and turbine flow rate.

_{bypass}is set equal to the maximum permissible inflow rate, in this case 90 m

^{3}/h.

_{out}from the tank (to the downstream supply zones) ranged from 29.05.2017 to 15.02.2018 and was processed from so-called delta-event (event-based recording) raw data to have a 15-min time interval. These data are necessary to achieve reliable results. While historical time series for water level and tank inflow rate can be used by the tool to infer the storage tank volume (hence the input fields), they were neither available nor necessary, since the volume was known to be 100 m

^{3}. With the information about tank volume and the switching thresholds provided in the first input mask (Figure 6), the tank operation was simulated to determine both acceptable and optimal turbine parameters. This “simulation” consists of a simple numerical model (see Section 2.5), modifying a starting value for the tank level according to the net change in storage volume, as calculated by the difference between the inflow and outflow volumes. The planner must also choose between two types of turbines. In this case, the in-line AXENT turbine was chosen (see Section 2.7 for more details).

_{hydraulic}as well as E

_{electrical}), power (P

_{hydraulic}and P

_{electrical}) and total efficiency η

_{total}for the chosen turbine type at the corresponding P

_{hydraulic}(for the best possible turbine, not the characteristic curve of a single turbine—see Section 2.7) (Figure 7). The optimal parameters (head and flow rate) are also displayed and added to the site curve diagram (Figure 8).

_{annual}are determined based on the information provided. In the same step, the total costs for purchase and installation of the turbine C

_{total}are calculated on the basis of available values from the authors’ experience, to roughly estimate the simple (non-inflation-adjusted) payback period (see Section 2.9 for more information). In the case of BPT Rützengrün for the input data shown here and using the recommended calculation and bypass options, E

_{electrical}is estimated at 26,000 kWh/a (Table 4) and the payback period at 10.0 years. According to the water supply company ZWAV Plauen, if the turbine lifetime can be assumed at 20 years, the payback period must be ≤ 10 years (less than half of the device’s lifetime) to be an acceptable investment. A turbine at this site would therefore be borderline economically viable according to this assessment.

#### 3.2. Assessing the Impact of Quality Control for Input Data

_{annual}(144,000 m

^{3}/a) than was normal in the past and is expected for future operation (252,000 m

^{3}/a), based partially on the multi-year 2-h data. This was corroborated by the ZWAV Plauen staff, who explained that the period captured as 15-min values was unusual due to some maintenance work that was performed on the supply system. To compensate for this, E

_{electrical}and consequently B

_{annual}were linearly increased by multiplication with the ratio between these flow volumes, a factor of 1.75. This adjustment increases E

_{electrical}from 26,000 to 45,600 kWh/a and lowers the payback period from 10.0 to 5.7 years (Table 4), making this project much more economically attractive than would have been the case without a careful analysis of the data. This highlights the fact that the acquisition and handling of data is not always straightforward, and ought to be done with a critical eye.

^{3}, a time interval greater than 15 min led to an unreliable simulation of the tank levels, since the incremental change in storage volume at times exceeded the tank capacity. In this case, only 2-h values were available for a longer time period (Figure 9). As these occasionally exceeded 50 m

^{3}/h, more than 100 m

^{3}would potentially leave the tank in a single time interval. This allows no opportunity for the simulation to react by opening the inflow valve in response to the tank level falling below the switching threshold—the tank would simply be “instantly” emptied. This led the authors to embrace a rule of thumb that 15 min ought to be the maximum time interval between values for Q

_{out}, even if not always strictly necessary, such as for sites with more than 1000 m

^{3}of storage. In general, a longer input time series is better than a shorter one, but as mentioned in Section 2.8 and for reasons made clear here, there is a trade-off between having a sufficiently long dataset for capturing the seasonally varying conditions and accidentally capturing conditions that are obsolete or unlikely to be representative of the future. A period of 12 to 24 months should be sufficient in most cases, but should also be checked for anomalies.

#### 3.3. Comparison of Results Using the Newly Proposed Method with Other Methods

_{out}) range with the highest estimated energy generation. In this case, the Q

_{out}range from 10 to 15 m

^{3}/h is both the most frequent and most promising for highest energy generation. Thus, an average flow rate of 12.5 m

^{3}/h emerges as the design flow rate Q

_{turbine}. It is worth noting that the frequency of occurrence of a range of flow rates does not imply that this range will have the greatest estimated energy generation, due to the other factors that influence energy generation, such as the efficiency of the expected turbine (which declines rapidly with declining power rating), occasionally high demand that reduces energy generation at lower design flow rates (due to the necessity of bypassing more water around the turbine) and the increase in frictional head losses (with increasing flow rate). For example, the flow rate ranges 25 to 30 m

^{3}/h and 30 to 35 m

^{3}/h have nearly the same frequency, but the latter range has a substantially greater expected annual energy generation.

_{hydraulic}is also the optimal operating point for a turbine (Table 3). This point can be seen on the green curve of Figure 11, corresponding to a P

_{hydraulic}of 28.2 kW and occurring at a flow rate of 142 m

^{3}/h. A hypothetical turbine suitable for operating at this point would have a pressure drop h

_{turbine}of 72.7 m, as can be seen where the fictive characteristic curve (red curve with triangle markers) of such a turbine crosses the characteristic site curve of the inflow pipeline for BPT Rützengrün.

_{hydraulic}and E

_{electrical}corresponding to each of the turbine operating points. For the 2016 DVGW method “b” (based on inflow rate Q

_{in}), no time series was available, so the single data point used to define the characteristic site curve of the inflow pipeline was taken as the most frequent inflow rate with the highest expected annual energy generation. The corresponding numbers are also summarized in Table 4. The results confirm that the 2018 University of Applied Sciences Dresden (HTWD) method yields the greatest energy generation.

^{3}/h is intentionally “improperly” entered into the HTWD Excel tool, which is built for class 1 “buffered” sites, and modifies the inflow regime to optimize the energy generation. In this way, the only permitted values for Q

_{in}are Q

_{turbine}and Q

_{bypass}—no other inflow rates occur. When properly applied to class 2 sites, this method yields a much lower expected energy generation, since water arriving at all flow rates not falling within a narrow range (e.g., 10 to 15 m

^{3}/h) would be bypassed around the turbine. The energy generation possible within other flow rate ranges (represented by the orange columns in Figure 10) would be lost. Using the HTWD tool for a class 1 site, these other orange columns can be almost entirely and efficiently captured by modifying the inflow rate, which is made possible by the storage tank that decouples the inflow and outflow to and from the site. This is the fundamental advantage of a class 1 site.

^{3}/h, while it would have only 9300 kWh/a if it lacked the 100 m

^{3}storage tank and was therefore a class 2 site—a factor of 2.6 less energy generation.

^{3}/h yields a total energy generation that is 98.3% of that yielded by the 2018 HTWD method—in this case hardly a significant loss. However, it cannot be assumed that this will hold true in every case, as the analysis of further sites in the following section shows. In cases where it does hold true, this method can be used to confirm this truth, which provides the designer and operator with a greater level of confidence in the ultimate design decision.

#### 3.4. Results for Nine Sites in Germany

^{3}/h, whereas the newly proposed design flow rates range from 34 to 84 m

^{3}/h, with an outlier of 300 m

^{3}/h at the newly planned site Rehbocksberg. With the exception of two sites having very small (100 m

^{3}) tanks and one site having a very large (10,000 m

^{3}) tank, the storage capacity ranged from 1000 to 5000 m

^{3}.

^{3}/d. This number was then multiplied with the ratio (taken from the nearby site Chursdorf) between the maximum daily flow volume in the year and the average daily flow volume in the month with the greatest flow volume, which was 1.34. The resulting “worst-case day” had a flow volume of 900 m

^{3}/d, which was assumed to enter the tank over a 24-h period, producing an inflow and turbine design flow rate of 37.5 m

^{3}/h.

_{out}with the highest expected annual energy generation) produced very mixed results, ranging from 53% to 98% of the optimum, with a weighted average of 78%. The 2016 DVGW method “b” (based on Q

_{in}) performed consistently better, ranging from 79% to 100% of the optimum and having a weighted average of 91%.

_{hydraulic}for the highest-capacity turbine (30.0 kW

_{electrical}, Rehbocksberg) to 12,000 €/kW

_{hydraulic}for the lowest-capacity turbine (2.0 kW

_{electrical}, Mittweida), based on past project experience from other sites with similar conditions. The estimated total project costs therefore ranged from approx. 28,000 € to 37,000 €. For the optimal case using the 2018 HTWD method, the annual revenue ranges from 1110 to 22,200 €/a, with simple payback periods from 24.2 to 1.7 years. Of the nine sites, four have payback periods less than 10 years, making them economically viable according to the standards used by the water utility ZWAV Plauen. For the remaining sites, the project costs would have to be reduced in some way to make the installation of a turbine economically viable, for example by reducing the costs of the turbine or other items (see Table 2), or acquiring financial support through state or federal grant funding for renewable energy projects.

## 4. Discussion

#### 4.1. Archetypical Sites: Handling in Excel Tool and Practical Considerations

^{3}) are present, which demands that temporally high-resolution outflow data is available to the Excel tool for determining both acceptable and optimal turbine flow rates. As with these two sites (see Figure 5), these kinds of sites can exist in several stages in series, which can have a simplifying cascade effect, since the downstream BPT regulates the outflow of the upstream BPT.

^{3}/h as the design flow rate for Neundorf, a flow rate of 100 m

^{3}/h or even 150 m

^{3}/h would subtract very little from the total possible energy generation. Both these sites also have high storage capacities of 5000 and 10,000 m

^{3}(although this is not necessarily a property of this archetype), which makes it unlikely that brief periods of high demand would endanger the security of supply by depleting tank levels. Thus, there is also less urgency for having a high-resolution time series of outflow data to verify that the chosen turbine is suitable.

_{electrical}could not be economically fed into the grid. There is also not sufficient energy demand at the site (no pumps or other substantial energy users), such that there is currently no known practical way to use the energy that could be generated with a turbine. Unfortunately, this removes Adorf-Sorge from the list of potential sites.

#### 4.2. Cases in Which the Excel Tool is Not Needed or Appropriate

- There is limited data available for the site and time or other constraints make it undesirable to perform new measurements. In this case the site operator can take the shortcut of using the equivalent of the 2016 DVGW method “b”, and simply select a turbine that operates efficiently at the current typical Q
_{in}. According to the seven sites analyzed here, this leads on average to 10% less energy generation (and annual revenue), with a risk of up to 20% less energy generation. This is the best known alternative method that removes the need for data-based work. - The site in question is a class 2 “non-buffered” site, for which this tool is not appropriate. Using the tool for class 2 sites will lead to gross overestimates of the potential energy generation, as shown in Table 4. This is due to the fact that the tool assumes a complete modification of the Q
_{in}regime, which is not possible at a class 2 site, for which Q_{in}is necessarily equal to Q_{out}.

#### 4.3. Limitations of the Tool

- The tool assumes the selection of a single turbine with a narrow acceptable operating range, and considers neither the possibility of turbines with wide operating ranges nor that of multiple turbines, the latter of which might lead to greater energy generation [25,27]. This was decided partly for simplicity’s sake and partly out of the belief that a single turbine generally represents the most economically viable solution for class 1 sites, which is supported by one of the studies cited above [25]. Furthermore, as indicated in Section 1.2, these studies do take into account the fundamental advantage of class 1 sites, which is the ability to modify the inflow regime, instead using multiple turbines to adapt to the wide range of flow rates occurring based on the current site conditions.
- The tool does not have a sophisticated way to support users with sites for which a feed-in tariff is either not available or not applicable (e.g., in Germany, if the water does not flow 100% via natural gradient). There is an option to enter in the total energy use on site and the percentage of which the user expects to be covered by the turbine. In the future it is planned to implement an algorithm that takes as input a time series of electricity use on site (parallel to the Q
_{out}time series) and estimates how much of this energy use could be covered by the turbine, such that the user does not need to estimate this herself. - There is a lack of decision support in accounting for future changes in water use patterns, which other design methods seem to have accounted for [14,39,40]. However, there is a simplified factor which can be adjusted to account for possible increases or decreases in water use. In this way, an expected future water use pattern can be roughly simulated, and a turbine designed that will still be suitable for this future condition.
- The impact of iteratively varying the threshold tank levels (see Figure 6) to activate and deactivate the turbine and bypass has not been sufficiently assessed. Sitzenfrei and Rauch [14] presented an optimization method that is similar in spirit to the one presented by the authors but applied it to a class 2 site. They pursued an optimization approach by varying parameters in a randomized fashion through 1000 simulations (Monte Carlo simulation), selecting the best solution based on the amount of energy generated over 10 years. The parameters varied in this case are the set-point water levels in the supply tank upstream of the turbine: the overflow level, the level for switching from high to low turbine flow, and the minimum level required for fire-fighting. The HTWD method introduced in this paper could be improved by implementing a similar kind of randomized (e.g., Monte Carlo) variation of the four water level thresholds used to determine when water flows through the turbine, bypass or neither. This might increase the robustness of the solution suggested by the tool and also slightly increase the total annual energy generation predicted by the tool.
- As mentioned in Section 3.2, gaps (i.e., time intervals larger than the smallest time interval; e.g., due to missing data) in the input data time series of Q
_{out}lead to an error in the calculations performed by the tool. Currently, the burden is on the user to ensure that the time series contains no gaps. In the future, this could be improved through an algorithm that automatically checks for and linearly interpolates to fill these gaps. - Currently, the data from only two types of turbines from two manufacturers are incorporated into the tool. This merely reflects the authors’ experience and available data until now and is not intended to imply that there are not further options. No funding links or other conflicts of interest exist between the authors and these two turbine manufacturers.

#### 4.4. Relative Potential of Class 1 vs. Class 2 Sites

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Practical Considerations for Deploying Hydropower in Water Supply Systems

#### Appendix A.1. Origin of Surplus Energy in Gravity-Based Water Supply Systems and Hydraulic Aspects of Their Operation

- kinetic energy of the flowing water (velocity head),
- pressure energy between the water molecules (pressure head) and
- heat (and some sound) due to pipe wall (major) and local (minor) frictional resistance (head “loss”) in reaction to the flowing water.

- Intentionally, because the designer anticipates periods during which nearly the maximum flow rate will be required (e.g., evenings in a dry summer period) or expects the total demand of the supply zone to increase due to population growth and/or increase in commercial or industrial activity, or
- Unintentionally, because the pipeline was chosen with a very generous factor of safety [14], or because demand in the supply zone is decreasing, due to declining population, increasing water use efficiency and/or cessation of commercial and industrial water use.

**Figure A1.**The basic hydraulics of a drinking water hydropower system prior to the installation of a turbine, illustrated under three conditions (no flow, maximum flow, normal flow) using the hydraulic grade line and process diagram (

**a**–

**c**) as well as a diagram of head vs. flow rate (

**d**–

**f**).

#### Appendix A.2. Favorable Site Characteristics for Hydropower

- Nearly constant flow rate, either due to a site being class 1, or because the water use profile in the downstream supply zones do not fluctuate very much in the case of class 2 sites
- Nearly constant pressure conditions
- Existing infrastructure that can be used with only minor modifications to the piping and without any civil construction works (e.g., an easily accessible and enclosed building, control valves and pipe systems with generous amounts of space)
- Local energy needs, such that the energy generated can most economically be used, by replacing the need to purchase energy from the grid (typically the most expensive source)
- Conditions that meet the requirements for receiving a feed-in tariff (e.g., in Germany this is a purely natural gradient, without any pumping upstream of the turbine site)

#### Appendix A.3. Further Characteristics of and Implications for Turbines at Class 1 and Class 2 Sites

#### Appendix A.3.1. Class 1 “Buffered” Sites

#### Appendix A.3.2. Class 2 “Non-Buffered” Sites

#### Appendix A.4. Review of Scientific Literature on Turbine Design Methods for Class 1 and Class 2 Sites

#### Appendix A.4.1. Studies Focusing on Class 2 Sites

^{3}/h) having the greatest energy density (product of total flow volume and hydraulic power) should be the design turbine flow rate.

_{max}(with Q

_{max}defined as the greatest possible flow rate, with no pressure reduction in the pipeline), at which the hydraulic power contained in the flowing water is mathematically at its maximum [37].

#### Appendix A.4.2. Studies Focusing on Class 1 Sites

## Appendix B. User Guidelines for the Excel Tool

#### Appendix B.1. Description of the Tool

- Rough estimate: This sheet estimates the energy generation and economic costs and benefits based on four single input values, making the very optimistic simplifying assumption of a constant flow profile. This allows the user to determine whether it is worthwhile to continue on to the more time-intensive steps of a detailed analysis (the subsequent three sheets).
- Single values: This sheet is for entering between 7 and 14 single values, used for generating the hydraulic site curve, calculating the economic benefits and (optionally) ensuring that the storage tank does not fall below the minimum permissible fill level due to a reduction in the flow rate (which provides the apparent “benefit” of increased energy generation).
- Time series: This sheet is for entering time series (of the past six months to three years), used to iteratively simulate possible turbine parameters with historic data, to determine which parameters provide the greatest energy generation while still providing the daily flow volume required and (optionally) without causing unacceptable reductions in the storage tank level. Up to six time series can be entered, but generally only two are required.x
- Turbine design: This sheet automatically determines the optimal turbine parameters based on the calculation options chosen regarding (a) level of detail and (b) choice of bypass flow. The user may then fine-tune certain design aspects before generating the technical and economic results.
- Results: This sheet contains the results saved using a button on the previous sheet “Turbine design”, providing an overview of the results obtained using various design approaches.

#### Appendix B.2. Data Requirements and Corresponding Quality Criteria for Solutions

- Detailed calculation with time series interval ≤15 min and consideration of storage tank levels using a historical time series of tank levels (to determine the storage capacity by inference)
- (recommended) Detailed calculation with time series interval ≤15 min and consideration of storage tank levels using known or estimated useable storage tank capacity
- Rough calculation with time series interval between 15 min and 1 d and only time series of storage tank outflow
- Rough calculation with partially estimated single values (no time series)

**Table A1.**Data requirements depending on desired quality of results (and corresponding calculation option): “X” = required and “(X)” = optional.

Data Type | Unit | (1) Detailed Calc., Tank Level Check via Time Series | (2) Detailed Calc., Tank Level Check via Storage Volume | (3) Rough Calc., Only Outflow Time Series | (4) Rough Calc., Estimated Single Values |
---|---|---|---|---|---|

Single values (sheet 2) | |||||

Inflow rate (Q_{in}) at control valve, position 1 (e.g., at normal flow) | m^{3}/h | X | X | X | X |

Upstream pressure (h_{1_upstream}) at control valve, position 1 | m; bar | X | X | X | X |

Q_{in} at control valve, position 2 (e.g., at zero flow) | m^{3}/h | X | X | X | X |

h_{2_upstream} at control valve, position 2 | m; bar | X | X | X | X |

h_{downstream} at control valve (worst case) | m; bar | X | X | X | X |

Eligible for feed-in tariff? (yes/no) | --- | X | X | X | X |

Max. permissible Q_{in} (e.g., by contract), Q_{max inflow} | m^{3}/h | X | X | (X) | |

Min. tank level (L_{tank}) in normal operation, L_{1_turbine on} | % | X | X | ||

Max. permissible tank level, L_{2_max shutoff} | % | X | X | ||

Threshold for opening bypass, L_{3_bypass on} | % | X | X | ||

Min. tank level in an emergency, L_{4_min emergency} | % | X | X | ||

Useable storage volume, V_{tank} | m^{3} | X | |||

Electricity price on site | €/kWh | X | X | X | X |

Feed-in tariff (if relevant) | €/kWh | (X) | (X) | (X) | (X) |

Time series (sheet 3)—for the previous six months to three years | |||||

Timestamp for data time series (in format TT.MM.YYYY HH:mm:ss) | --- | X | X | X | |

Q_{out}, from storage tank | m^{3}/h | X | X | X | |

Storage tank level, L_{tank} | % | X | |||

Q_{in}, to storage tank | m^{3}/h | X | (X) | ||

Timestamp for Q_{in} | --- | (X) | (X) | ||

Energy usage on site | kWh | (X) | (X) |

**Table A2.**Quality criteria for solutions provided by the Excel tool, depending on the chosen calculation option, where 1 = lowest and 5 = highest.

Calculation Option | Rough Estimate (Sheet 1) | (1) Detailed Calc., Tank Level Check via Time Series | (2) Detailed Calc., Tank Level Check via Storage Volume | (3) Rough Calc., Only Outflow Time Series | (4) Rough Calc., Estimated Single Values | |
---|---|---|---|---|---|---|

Quality Criteria for Solution | ||||||

Time needed for gathering and quality-checking data (per site) | 30 min. to 2 h | 8 to 24 h | 8 to 24 h | 4 to 16 h | 2 to 4 h | |

Confidence that tank level does not fall below min. permissible level | 1 | 5 | 4 | 2 | 1 | |

Accuracy in estimating energy generation | 1 | 5 | 5 | 3 | 2 | |

Robustness against high variation in tank outflow | 1 | 5 | 5 | 3 | 1 | |

Main advantages | Quick feedback | Best all-around solution | Faster, sometimes reliable | Small step up from rough estimate | ||

Main disadvantages | Not reliable | Takes most time and effort | Tank levels uncertain; energy generation estimates based on daily flow volumes |

#### Appendix B.3. Choice of Bypass Flow

- Smallest possible bypass flow (minor reduction in energy generation, but smaller difference between turbine and bypass flow, which is preferable to some water supply system operators),
- (recommended) Maximum permissible bypass flow (based on the user input, implies larger difference between turbine and bypass flow, but maximum energy generation and greater supply reliability) and
- Choose the turbine flow such that in a typical situation no bypass is required (moderate reduction in energy generation, but greatest supply reliability and possibly lowest investment costs, as there is no need for electronically automated bypass valve regulation).

#### Appendix B.4. Assumptions/Limitations/Remarks

- Historic water use patterns are a reliable proxy for the future. While the tool allows for some adjustment factors to account for possible future changes in both quantity and variation of user water demand, these do not aid in predicting major future trends. Therefore, it behooves the water supplier to have sufficient safeguards in place to enable manual interventions in the case that storage tank levels unexpectedly fall below permissible levels.
- Insofar as it is not already the case, the inflow rate can be kept constant during the operation of a turbine. This assumes that there are no restrictions on the inflow side, such as any put in place by the third-party operator of the reservoir or long-range supply pipeline.

- If time series are used, as recommended, having any gaps (for example, a 120-min gap in a series with otherwise 15-min intervals) leads to a false result and must be avoided by quality-checking the data.
- Only one time interval is currently possible for all data types (e.g., 15 min for both outflow and storage tank level, with the exception of the inflow rate, which has the option of a different time interval).

- The diameter of the pipeline plays an essential role in the availability of excess energy for hydropower generation. However, the exact diameter is not normally essential information regarding the selection of a turbine. The most reliable basis for turbine selection is the actual characteristic hydraulic site curve, derived from measurements at the storage tank flow. The turbine can normally be flexibly integrated into most pipeline systems with suitably tapered reducer and expander joints. The pipelines leading to the sites described here ranged in diameter from 150 mm at the smallest to 600 mm at the largest (for a supply main from a long-distance regional water supplier), while the pipelines in the immediate run-up to the tank typically ranged from 150 mm to 350 mm.
- When measuring pressure at field sites, one should be aware that manometers sometimes exhibit drift after years of use, such that the manometer should be separated from the water pressure and exposed to atmospheric pressure (for example, using an aeration valve) to obtain a reliable reference value corresponding to a relative pressure of 0 bar. This value can then simply be deducted from the value read when the manometer is again fully exposed to water pressure.
- Some supervisory control and data acquisition (SCADA) systems provide an option to convert the time interval of the collected data from e.g., delta-event (random, event-based time interval) to a fixed 15-min interval. If this is a feasible and reliable option, this should be used. Alternatively, the authors have developed a further Excel tool solely for the purpose of converting such delta-event time series into time series with a fixed, regular time interval. This tool can be made freely available upon request.

- The flow rate must at any point in time be sufficient to meet the demand placed on the storage tank by the water users in the supply zone, and cannot endanger the reliability of supply (e.g., by causing the storage tank to temporarily run empty). The bypass can, for example, be set at a higher flow rate than the turbine flow rate, in order to enable rapid filling in periods of high water withdrawal from the tank.
- The flow rate must be high enough to enable the use of a microturbine with a practical size and sufficiently high efficiency, as the efficiency of turbines and generators drops rapidly with declining physical dimensions, and the turbine should fit into the existing infrastructure without making large structural changes in the piping network.

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**Figure 1.**Key difference between class 1 (“buffered”) and class 2 (“non-buffered”) sites, based on data from 27 April 2017 from the class 1 site “Voigtsgrün” in Saxony, Germany (the isolated, very high peaks occurring between 00:00 and 04:00 and at 18:00 are due to a beer brewery). *This illustration only intends to show the turbine in parallel to the control valve; the turbine does not need to be located above the control valve and is typically located at nearly the same elevation.

**Figure 2.**Visual explanation of some key parameters used in the method, as introduced in Section 2.2 and Section 2.5. * Note that h

_{max}depends on the current water level in the upstream tank, which is why the measurement of h

_{1_upstream}and h

_{2_upstream}should be conducted when the upstream tank is known to be at its typical lowest level.

**Figure 3.**Global efficiency data for AXENT and pumps-as-turbines (PAT) microturbines, with best-fit natural log curves.

**Figure 5.**Diagram of the Carlsfeld supply system, with break pressure tank (BPT) Vogelsgrün and BPT Rützengrün. As illustrated in Figure 1, the potential turbines would be positioned in parallel with the existing pressure control valves.

**Figure 7.**Calculated performance parameters of hypothetical turbines (at best efficiency point) with iteratively varied design flow rates (here from 5 to 245 m

^{3}/h), with values for BPT Rützengrün.

**Figure 8.**Site curve of BPT Rützengrün with characteristic curves of the corresponding hydraulic power as well as the (hypothetical) turbine with optimal operating parameters. 1 bar = 10.19 m of head.

**Figure 9.**Outflow data series available for BPT Rützengrün, with the data used in the Excel tool highlighted in orange.

**Figure 10.**Frequency distribution of outflow rates and corresponding estimated annual electrical energy generation per flow rate class, at 15-min intervals for BPT Rützengrün.

**Figure 11.**Site curve of BPT Rützengrün, hypothetical turbine curves for design results of all four methods, and corresponding hydraulic power as well as estimated annual electrical energy generation at each operating point.

**Table 1.**Matrix of consequences for drinking water hydropower development, depending on the type of gravity pipeline and site.

Water Supply Site | with Storage Tank (Class 1, “Buffered“) | without Storage Tank (Class 2, “Non-Buffered”) | |
---|---|---|---|

Gravity Pipeline | |||

with pressure control | Hydropower is very practical, as the storage tank provides flexibility in re-defining the inflow regime | Hydropower is possible, but may require a complex design to accommodate high variability in flow rate and pressure due to uncontrolled downstream water use | |

without pressure control | Hydropower is theoretically possible, but would reduce inflow rate if installed at outlet of existing pipeline, which may negatively affect supply reliability |

Cost Parameter | Purchase Cost (Turbine and Generator) | Installation | Pipe Modi-fications | Electromechanical Control Systems | Total Incl. 19% Value-Added Tax (VAT) | |
---|---|---|---|---|---|---|

Turbine Type | ||||||

AXENT (Stellba) | 27,500–65,000 € | 2500–4000 € | 1500–3000 € | 1000 € | 40,500–85,700 € | |

PAT (KSB): Multitec and Etanorm | 4400–15,700 € | 5000–8000 € | 5000 € | 10,000 € | 29,100–46,100 € | |

Data source (year) | Past invoice and recent price quotes (2016–2018) | Past projects (2011–2016) and engineering estimates (2016–2018) |

Turbine Design | (1) HTWD ^{1} 2018 | (2) DVGW ^{2} 1994 | (3) DVGW 2016, a ^{3} | (4) DVGW 2016, b ^{4} | |
---|---|---|---|---|---|

Method Characteristics | |||||

Basis for design | Diverse data to determine the flow rate with the maximum annual energy generation | Q with max. hydraulic power (see Equation (18)) | Q_{out} | Q_{in} | |

with historically greatest energy density (see Equation (17)) | |||||

Data requirements | Medium to high | Lowest | Medium | ||

Confidence of achieving max. energy generation | Highest (with high data reqs.) | Lowest | Low to medium |

^{1}HTWD — Hochschule für Technik und Wirtschaft Dresden (University of Applied Sciences), the authors’ home institute;

^{2}DVGW — Deutscher Verein des Gas- und Wasserfaches (German Technical and Scientific Association for Gas and Water), publisher of guidelines on drinking water hydropower;

^{3}

**a**—variant of the DVGW method based on tank outflow;

^{4}

**b**—variant of the DVGW method based on tank inflow

**Table 4.**Summary of the results for BPT Rützengrün using all four methods described in this article.

Method | (1) HTWD 2018 | (2) DVGW 1994 | (3i) DVGW 2016, a ^{1} | (3ii) DVGW 2016, a ^{2} | (4) DVGW 2016, b | |
---|---|---|---|---|---|---|

Parameter | ||||||

Flow rate Q_{turbine} (m^{3}/h) | 41.0 | 142 | 12.5 | 63.1 | ||

Pressure drop h_{turbine} (m) | 106 | 72.7 | 109 | 102 | ||

Hydraulic power P_{hydraulic} (kW) | 11.8 | 28.2 | 3.7 | 17.5 | ||

Annual energy generation E_{electrical}, nominal (kWh/a) | 26,000 | 18,500 | 13,700 | 5300 | 25,600 | |

Annual electrical energy generation E_{electrical}, corrected for flow volume (kWh/a) ^{3} | 45,700 | 32,500 | 24,000 | 9300 | 44,800 | |

Annual electrical energy generation E_{electrical}, corrected (% of result via HTWD method) | 100% | 71.2% | 52.7% | 20.4% | 98.3% |

^{1}Method applied improperly, as if class 1 site (see Section 2.10 for elaboration);

^{2}method applied properly, as if class 2 site;

^{3}increased by a factor of 1.75 to account for expected future flow volumes (see Figure 9 and preceding discussion).

**Table 5.**Summary of the site characteristics, with selected design results obtained using the 2018 HTWD method.

Site | V_{tank} (m^{3}) | V_{annual} (m^{3}/a) | Q_{in} and h_{available} before Turbine (Typical Operating Point) | Q_{in} and h_{turbine} with Turbine | P_{electrical} (kW) | Q_{bypass} (m^{3}/h) | Confidence in Results |
---|---|---|---|---|---|---|---|

Adorf-Sorge | 1000 | 328,000 | 145 m^{3}/h117 m | 84 m^{3}/h139 m | 20.7 | 150 | High |

Rützengrün | 100 | 252,000 ^{1} | 63.1 m^{3}/h102 m | 41.0 m^{3}/h106 m | 7.5 | 90 | High |

Vogelsgrün | 100 | 158,000 | 58.3 m^{3}/h71.3 m | 43.5 m^{3}/h74.9 m | 5.6 | 90 | High |

Voigtsgrün | 4000 | 255,000 | 58.8 m^{3}/h45.3 m | 39 m^{3}/h47.6 m | 3.1 | 100 | High |

Chursdorf | 4000 | 220,000 | 24 m^{3}/h98.3 m | 32.5 m^{3}/h97.6 m | 5.4 | 65 | High |

Mittweida | 1500 | 260,000 | 55 m^{3}/h19.6 m | 34 m^{3}/h21.8 m | 2.0 | 150 | Med. |

Rochlitz | 5000 | 207,000 | 61 m^{3}/h63.2 m | 37.5 m^{3}/h68.9 m | 4.4 | 72 | Low |

Neundorf | 4000 | 292,000 | 100 m^{3}/h39.5 m | 50 m^{3}/h40.4 m | 3.4 | 130 | High |

Rehbocksberg | 10,000 | 1,800,000 | N.A. (new site) | 300 m^{3}/h55.7 m | 30.0 | 360 | High |

^{1}Corrected based on long-term data (see Figure 9 and preceding discussion).

**Table 6.**Comparison of the estimated E

_{electrical}(in kWh/a) achieved by four different turbine design methods, in italics as percentages of the value given by method 1.

Site | (1) HTWD 2018 (New Method) | (2) DVGW 1994 kWh/a | (3) DVGW 2016, a kWh/a | (4) DVGW 2016, b kWh/a | ||
---|---|---|---|---|---|---|

Data Basis: Start Date (Nr. of Days) | Calculation and Bypass Options Used | kWh/a | ||||

Adorf-Sorge | 27 April 2017 (179) | Calc. 2 Bypass 2 | 80,900 | 59,100 | 78,200 | 69,800 |

100% | 73% | 97% | 86% | |||

Rützengrün | 29 May 2018 (256) | Calc. 2 Bypass 2 | 45,700 | 32,500 | 24,100 | 44,800 |

100% | 71% | 53% | 98% | |||

Vogelsgrün | 29 May 2018 (256) | Calc. 2 Bypass 2 | 20,000 | 14,600 | 19,500 | 19,100 |

100% | 73% | 98% | 96% | |||

Voigtsgrün | 27 April 2017 (179) | Calc. 2 Bypass 2 | 20,300 | 14,400 | 11,000 | 19,100 |

100% | 71% | 54% | 94% | |||

Chursdorf | 28 October 2017 (338) | Calc. 2 Bypass 2 | 36,700 | 23,300 | 32,900 | 29,100 |

100% | 63% | 90% | 79% | |||

Mittweida | 20 July 2013 (1714) | Calc. 3 Bypass 2 | 8980 | 6610 | No data | 7450 |

100% | 74% | 83% | ||||

Rochlitz | Single values, estimates ^{1} | Calc. 4 | 24,100 | 17,200 | No data | 22,400 |

100% | 72% | 93% | ||||

Neundorf | Single values, future plans | Calc. 4 | 19,800 | 14,000 | No data | 19,800 100% |

100% | 71% | |||||

Rehbocksberg | Single values, future plans | Calc. 4 | 180,000 | 126,000 | No data—new storage tank | |

100% | 70% | |||||

Arithmetic mean | --- | --- | 48,500 100% | 34,000 70% | 36,500 86% | 28,900 91% |

Weighted mean | --- | --- | 48,500 100% | 34,200 71% | 33,100 78% | 28,800 91% |

^{1}Based on the estimated maximum daily flow volume in any given year (see preceding text for clarification).

**Table 7.**Comparison of the estimated annual revenue (in €/a) and simple payback period (in a) for the turbine parameters determined using the four different turbine design methods.

Site | (1) HTWD 2018 | (2) DVGW 1994 | (3) DVGW 2016, a | (4) DVGW 2016, b |
---|---|---|---|---|

Adorf-Sorge | 9980 €/a | 7280 €/a | 9650 €/a | 8600 €/a |

3.6 a | 5.1 a | 3.8 a | 4.3 a | |

Rützengrün | 5630 €/a | 4010 €/a | 2970 €/a | 5530 €/a |

5.7 a | 8.8 a | 9.6 a | 6.1 a | |

Vogelsgrün | 2470 €/a | 1800 €/a | 2410 €/a | 2360 €/a |

12.7 a | 18.4 a | 12.9 a | 13.7 a | |

Voigtsgrün | 2510 €/a | 1780 €/a | 1350 €/a | 2360 €/a |

11.8 a | 17.9 a | 20.7 a | 13.2 a | |

Chursdorf | 4520 €/a | 2870 €/a | 4060 €/a | 3590 €/a |

6.9 a | 12.3 a | 7.9 a | 8.4 a | |

Mittweida | 1110 €/a | 815 €/a | No data | 919 €/a |

24.2 a | 34.8 a | 30.7 a | ||

Rochlitz | 2980 €/a | 2130 €/a | No data | 2770 €/a |

10.3 a | 15.3 a | 11.5 a | ||

Neundorf | 2450 €/a | 1720 €/a | No data | 2450 13.1 a |

12.2 a | 20.3 a | |||

Rehbocksberg | 22,200 €/a | 15,500 €/a | No data—new storage tank | |

1.7 a | 2.8 a | |||

Arithmetic mean | 5980 €/a 9.9 a | 4120 €a 15.1 a | 4090 €/a 11.0 a | 3570 €/a 12.6 a |

Weighted mean | 3200 €/a 5.3 a | 2300€a 8.2 a | 2850 €/a 7.6 a | 2540 €/a 9.0 a |

© 2019 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/).

## Share and Cite

**MDPI and ACS Style**

Voltz, T.J.; Grischek, T.
Microturbines at Drinking Water Tanks Fed by Gravity Pipelines: A Method and Excel Tool for Maximizing Annual Energy Generation Based on Historical Tank Outflow Data. *Water* **2019**, *11*, 1403.
https://doi.org/10.3390/w11071403

**AMA Style**

Voltz TJ, Grischek T.
Microturbines at Drinking Water Tanks Fed by Gravity Pipelines: A Method and Excel Tool for Maximizing Annual Energy Generation Based on Historical Tank Outflow Data. *Water*. 2019; 11(7):1403.
https://doi.org/10.3390/w11071403

**Chicago/Turabian Style**

Voltz, Thomas John, and Thomas Grischek.
2019. "Microturbines at Drinking Water Tanks Fed by Gravity Pipelines: A Method and Excel Tool for Maximizing Annual Energy Generation Based on Historical Tank Outflow Data" *Water* 11, no. 7: 1403.
https://doi.org/10.3390/w11071403