**3. Case Study**

### *3.1. The City of Fribourg*

The proposed methodology for potential analysis and economic value assessment was applied to the case study of the city of Fribourg, Switzerland. The urban water supply network model of Fribourg, which can be seen in Figure 4, has 2972 links and 2805 nodes covering 135 km of pipes and a total elevation difference of 216 m. The network, whose model was provided by the Industrial Services of Fribourg, possesses nine PRVs, seven water tanks and four pumping stations. The population served by the WSN is about 38,000 persons, making this a small sized European city.

**Figure 4.** Water supply network of Fribourg. The nodes are represented by circles with a fill-color representing the elevation of the node.

According to the gathered data, an average daily consumption of Qd,average = 0.108 L/s was associated with each node, and the daily pattern of consumption presented in Figure 5 was applied to obtain an hourly variation.

**Figure 5.** Pattern of hourly variation of consumption along the day, adapted from [21], with the indication of the energy buy-prices which vary within the day.

Six of the water tanks are considered as water sources, with fixed constant levels. The seventh water tank, however, has a known geometry and its level varies along the simulation. In each iteration, the initial level in the seventh water tank was defined in order to have the same initial level at the end of a 24 h cycle. The capacity and elevation of this tank also represents a restriction to the algorithm.

A minimum pressure of 30 m was assumed as a restriction in every consumptive node. According to the Swiss Directive for Water Supply [22], the minimum service pressure in Switzerland is a function of the average number of building stories. The assumed value implies that a 6-story building with 3 m per floor would not require a pump to provide 10 m of water pressure in the upper floor. A restriction of the maximum velocity in the pipes was defined as 2 m/s.

The considered electricity sell-prices is fixed at 0.33 \$/kWh and the considered buy-price depends on the period as indicated in Figure 5. The sell-price is the current feed-in-tariff in Switzerland for this type of power plant [23,24].

The operations of the pumping station for the network consume 250 MWh/year, according to Table 1, assuming a constant efficiency of 60%.


**Table 1.** Operating conditions of the pumping stations and annual energy consumption in the network of Fribourg.

### *3.2. The Micro-Hydropower Technology*

The MHP considered for installation in the city was for a micro-turbine currently under development by the authors [25]. The five blade tubular propeller (5BTP), initially designed under the scope of the EU Project HYLOW (2008–2012), has been recently experimentally tested for the characterization of its performance [25].

It is a suitable turbine for energy recovery in a WSS since it can be installed directly into the pressurized pipe. Furthermore, the operation of the 5BTP is possible with variable flow rates and low heads. The machine consists of a bulb followed by a runner with five fixed blades (Figure 6). It is connected to a rotating axis that leaves the pipe through a 45◦ curve. The rotating axis is connected to the external generator which controls the rotational speed of the turbine. A minimum diameter of 85 mm was considered.

**Figure 6.** Detailed sketch representation of the inline installation of a 5BTP in a pipe.

The installation of the turbine within the network is proposed according to the design presented in Figure 7. It is based on a buried concrete chamber constructed in line with an existing pipe, whose dimensions depend on the diameters of both the existing pipe (DP) and turbine runner (DT). The by-pass is only necessary if the considered branch has no redundancy in its supply, as it has been defined in [18].

**Figure 7.** Sketch of the concrete chamber for the installation of a 5BTP (adapted from [18]). Up to four turbines can be installed with this design.

The choice of diameter of the runner, with a minimum of 85 mm, is a function of the maximum flow rate in the pipe and the experimental characteristic curve [25], which is scaled according to the similarity laws.

Up to four turbines can be installed in the same concrete chamber. The lay-out from Figure 7 is used to estimate the equipment and civil works costs by calculating the main quantities presented in Table 2. A surplus of 25% of this sub-total was added to account for engineering and construction supervision plus 15% for miscellaneous items not quantified at this early phase. The costs for connections to the grid and site access were considered negligible, since the MHPs are installed within urban areas. Savings of 2% were considered for the construction of more than one chamber to take into account group ordering prices. All percentages were applied independently of the number of turbines in the chamber. For the feasibility analysis, a linear cost function was adopted for the electromechanical equipment as a single item. This is justified by the fact that the 5BTP turbine is not ye<sup>t</sup> commercialized, and hence a lumped price based on current technologies for this scale of installed power was considered.


**Table 2.** Unit prices considered for the Fribourg WSS case study.

In the cases of PRV sites, it was assumed that the valve ensures a constant downstream pressure unless the pressure immediately upstream from it is already lower. Since there is a defined minimum pressure throughout the network, it was considered that this constraint was enough to ensure adequate pressure levels in the network. However, in the case of a mandatory constant downstream pressure value, the hydraulic regulation strategy developed by [3] could be adopted. According to this strategy, when the pressure drop needs to be smaller than the head taken by the turbine, a by-pass is opened to divide the flow discharge.
