*2.2. Optimum Site Locations*

Even if potential for hydropower has been recognized in a certain city, the ideal location of turbines within its network is not straightforward. It depends on numerous factors such as the flow rate and respective velocity restrictions which have daily variations, the head which is dependent not only on the minimum service pressures but also on the chosen turbine, and the geometry of the network that conditions the distribution of the flow within its closed network.

To answer this problem, a search algorithm in which a simulated annealing technique was used to optimize the economic value of the installation of micro-hydropower plants (MHP) in a WSS was applied. In the recently developed search algorithm [5,18], in each iteration, a full year is simulated with an hourly time step considering the installation of a given number of turbines in several locations or combined in one location. The produced energy is obtained by coupling the EPANET hydraulic model [20] that calculates the hydraulic state of the network for each time step with the characteristics of the turbines. The position of the turbines in the WSS is changed in each iteration, in the search for the best output. Only the solutions that respect minimum pressure and maximum velocity constraints are accepted.

The best output is given by the objective function that has been defined as the maximization of the net present value of the project annual cash flows over 20 years of operation:

$$f\left(X\right) = \min\left(1/\text{NP}\mathbb{V}\_{\text{20}}\right) \tag{5}$$

where *X* is the solution vector, representing the placement of *N*t turbines, and *NPV*20 is the net present value of the project discounted cash-flows.

In a concise way, the net present value is given by

$$NPV = Rvenues - Capital\,\text{Costs} - Operational\,\text{Costs} -Maintenance\,\text{Costs} \tag{6}$$

where all components are transposed to the year 0 of operation.

In the considered economic model, the capital costs include all investment costs for the construction of the MHPs. The maintenance costs are considered negligible when compared with the maintenance costs of the entire network. The operational costs of a network are given by the electricity bought for pumping operations and the personnel costs for managing the WSS. In this case, since the focus is only on the construction and operation of the turbines, and not the entire network, only the costs for pumping that are superior to the original operational costs are considered. The operational costs are thus given by the electricity buying tariff and the difference between the electrical energy needed for pumping in the situation with the turbines installed and the energy needed for pumping in the initial situation (without turbines).

Two different types of remuneration can be considered depending on the economic model assumed: selling to the grid or self-consumption. When selling to the grid, the revenues are given by the produced energy and the considered sell-tariff. For a self-consumption scheme, it is assumed that the generated energy is consumed in operations within the network. In this case, the gain is in the savings in the electricity bill of the network. To provide an appreciation of the solution, independently of the remuneration type, another economic index, the cost price, is considered:

$$\text{Cost price} = \frac{\text{Capital Costs}}{\frac{(1+r)^{20} - 1}{r \cdot (1+r)^{20}} E\_{annual}} \tag{7}$$

where *r* is the discount rate and *Eanual* is the annual energy production.
