**4. Results and Discussion**

#### *4.1. Energy Recovery Potential in the WSS of Fribourg*

The algorithm for the evaluation of the available energy in an urban water network (Figure 3) was applied to the case study of Fribourg. The results presented in Table 3 show that there is approximately 170 MWh/year in the network not being used. If accounting for the 430 MWh/year extracted from the WSS by PRVs, a total of approximately 600 MWh/year of available energy exists. The PRV energy contribution represents 72% of the total.

**Table 3.** Results from the evaluation of available energy in the city of Fribourg partitioned by the network, PRVs and the total.


Table 4 shows the pipes of the network where the energy is extracted and Table 5 shows the energy extracted by the PRVs. Some locations in Table 4 show available heads although the corresponding available energy is relatively low. This indicates that these locations are served with low discharges, thus hardly good position for the installation of a turbine.


**Table 4.** Pipes where energy has been extracted.


**Table 5.** Power extracted in RPV.

In pipe 2986, despite the existence of a PRV (Tables 4 and 5), 12.3 m of head is still available which corresponds to an available energy of 102 MWh/year.

### *4.2. Capacity for Generation Using 5BTP Turbine*

The search algorithm was applied to the city of Fribourg network model to obtain the optimal locations for the installation of 1, 2, 3 and 4 turbines. A discount rate of 4% was considered in the calculation of the net present value. Some interesting results were identified. The results for the selling to the grid scheme are presented in Table 6, showing also the 2nd and the 3rd best results in terms of *NPV*20 for each case. These latter options were defined by restricting one of the pipes from the previous best solution.


**Table 6.** Results from the search algorithm applied to the Fribourg network model. The three best solutions in terms of NPV20years are shown.

In an initial phase, whenever the solution includes a location where a PRV concrete chamber already exists, the turbine is assumed to be installed either in line with the valve, or replacing it in the same chamber. Hence, the construction costs (concrete, excavation and earth fill) are omitted. Since these solutions tend to be cheaper than installing in new locations, they were given priority within the search algorithm.

The location in the network of the retained solutions is shown in Figure 8. In Table 6 the annual energy production, turbine runner diameters, average head, average turbinated flow, installed power, net present value after 20 years of operation and respective cost price of the best solutions are shown. No increase in pumping energy was necessary. All the energy generated was representative of excess pressure in the network. As expected from the analysis of Tables 4 and 5, the pipe 2986, with a PRV installed, was the best location to install the energy converters.

Figure 8 shows that the replacement of PRVs is often the best solution. In these, excess pressure is already recognized. Furthermore, the considered exemption of construction costs for existing chambers made these solutions more economically viable.

**Figure 8.** Localization of selected pipes from Table 6 (Zoom A from Figure 4).

The best solutions can extract a considerable quantity of the available energy of the network. One, two, three and four 5BTP turbines would recover approximately 10%, 20%, 22% and 23% of the available energy, respectively. According to these results, it can also be concluded that the installation of three turbines in one pipe represents a smaller increase of energy production from two turbines than the increase of energy production of installing two turbines when compared to one turbine. This is due to the effect of obstruction of flow discharge, in particular when the extracted head is bigger than the original head dissipated in the PRV.

The best and second best solutions, for all the number of turbines, are identical in terms of energy production and of NPV20. Pipes 2896 and 2730 (Figure 8) are presented in the best and second best solutions, respectively. Since they share one node and are inline, the expected production is similar. The differences between both *NPV*20 values are mainly due to the construction costs.

The third best solution has a very small energy production when compared with others, since the discharges and heads are lower. It can be concluded that the pipes where the best and second best solutions are located, upstream from one of the main water tanks, is the most interesting area for hydropower production.

Comparing with the examples of other studies on MHPs in WSSs presented in the introduction, the obtained production in the city of Fribourg is within the same order of magnitude.

Not considering construction costs for the sites where PRVs are located may be optimistic. Hence, a second batch of simulations was carried out considering that additional construction works will be necessary to enlarge and adapt the existing chamber. Site conditions being very varied and coupling old and new chambers being sometimes cumbersome, it was assumed that the construction costs would be equivalent to that of a new chamber. Under these conditions, the best solution from Table 6 became equivalent in terms of NPV20 to the 2nd best solution, since the difference between the two was the construction costs. For the 3rd best solution, no locations were found were it would be feasible to install turbines. The construction costs have hence a considerable weight with respect to the feasibility of these chambers.

### *4.3. Response to Changes in Water Consumption*

Based on the three best solutions previously identified, a 20% decrease in water consumption was imposed on the network. A new energetic equilibrium was computed for these conditions, leading to a new energy production for the network. The results of this sensitivity analysis are presented in Table 7, which can be directly compared with Table 6.


**Table 7.** Previous solutions with 80% of the consumption.

Considering that consumption decreased and that the energy production is highly dependent on the flow discharge, a decrease in energy production was expected. However, the 1st and 2nd best solutions present negligible changes and in the 3rd best solution, there is an increase of energy production. For the best and 2nd best solutions, the MHPs are installed immediately upstream from a regulation water tank. The 20% reduction in the consumption does not strongly influence the flow discharges in this area, which are highly dependent on the levels of the water tank and water source. For the 3rd best solution, the flow discharge increased due to the new network equilibrium. The majority of pipes in the network suffered a decrease in flow discharge with the smaller consumption. However, pipe 2987 was one of the exceptions. These results illustrate the complexity of installing MHPs in urban networks and evoke the need for careful sensitivity analysis with respect to the consumption. Considering the small differences in the results, a sensitivity analysis for a reduction of 10% in the consumption is not shown. Under the actual conditions, the network does not support an increase in the consumption (negative pressures appear in the network even for a slight increase). Thus, an analysis of an increase in the consumption is not presented. However, a complete sensibility analysis should always be envisaged. Also, carrying out long-term simulations is recommended, in order to achieve a robust estimation of the produced energy and economic value of the installation [11].

### **5. Methodology for Expedited Assessment of Energy Recovery**

The obtained results were achieved through an optimization process where a considerable amount of data and also time are needed. Based on the experience gained in the course of this work, an expedited method to preliminarily evaluate the interest of placing one turbine in a given location of a network is provided here. The topography of the network, the maximum discharge in the pipes and the temporal variation of the consumption are assumed to be known.

Since the choice of diameter of the turbine is dependent on the maximum discharge in the pipe, the corresponding head is given by the characteristic curve of the turbine according to the similarity law. Figure 9 presents the variation of head with the maximum pipe discharge, which is obtained considering different runner diameters of the 5BTP. Figure 10 plots investment costs and the installed power as a function of the maximum pipe discharge and, consequently, the diameter of the runner. This figure was obtained considering the unit prices from Table 2 and the existing pipe has a diameter which allows a design velocity of 1 m/s.

**Figure 10.** Variation of average investment cost and installed power of the 5BTP with maximum discharge in the pipe (assuming design head from Figure 9).

The expedite method follows the following steps:


5. Estimate an energy production based on the characteristic curves of the 5BTP [25] and the temporal variation of the consumption. The estimation can be obtained considering the flow data or, if not available, a consumption pattern such as Figure 5.

These steps allow for the preliminary identification of potential locations in the network to install a MHP with one turbine. However, a more detailed simulation, as proposed in the methodology, is required to ensure that the minimum pressure in all nodes is maintained and account for possible discharge variation due to the redundancy of the network, estimating with higher precision both energy production and costs. Combinations with more than one turbine also require detailed simulations.
