2.1. Problem Approach
The model proposed in this work took into account all costs involved in the installation of a PRV and a PAT, as well as the sum of the incomes associated with the operation of both devices during their lifespan. Thus,
NPV (€), which was previously used to determine the economic feasibility of the installation of PATs [
25], was selected in this work to compare both devices:
where
TC (€) is the total installation cost,
t is an index related to year,
L is the lifespan of the device considered, PRV or PAT (assumed as 15 years for both elements in this work).
CS is the total cost saving at year
t (€), and is determined by adding up the water cost saving,
WCS, associated with the reduction of leakage volume after installing these devices and the energy cost saving,
ECS, obtained by the PAT performance.
r is the discount rate. A value of 0.05 for
r was assumed in this work [
33]. No management costs have been considered since the same cost has been assumed for both installation types.
The total installation cost was determined using Equation (2):
where
CPRD is the cost of the pressure reducing device, PRD (PRV or PAT),
CHE the cost of the hydraulic elements required in the installation of each pressure reducing device, and
IC is the installation cost. The determination of each term in Equation (2) is described in the following sections.
The estimation of WCS was carried out by the calculation of the water saving derived from the installation of a PRV or a PAT. When any of these devices is installed in a water supply network, pressure at nodes decreases and hence the leakage flow is reduced.
When the leakage flow at each pipe is known, this value can be assigned to each node and the discharge coefficient,
ci, which relates the leakage flow to pressure can be determined according to Equation (3):
where
qli is the leakage flow at node
i (l s
−1),
β is the emitter exponent which takes into account the pipe material and the shape of the orifice (1.18 has been assumed in this work [
34]) and
Pi is the pressure (m) at node
i. The coefficient
ci was determined by Equation (4):
α is a coefficient (l s
−1 m
−1−β),
j is an index related to pipe,
Kji is the number of pipes connected to node
i, and
Lji is the length of the pipe
j connected to node
i (m). The coefficient
α was determined using EPANET [
35] which enabled the pressure dependent demand analysis. Once the coefficient
α was determined, the effects of the performance of a PRD were evaluated in EPANET and
WCS was estimated by:
where
cw is the water cost (0.3 € m
−3 was assumed in this work [
25]) and
Vl0 and
VlPRD (m
3 day
−1) are the leakage volume in the current situation and after installing the pressure reducing device, respectively.
ndays was the number of days of the year. The leakage volume was obtained by applying Equation (6):
where the term 1/1000 is used to convert units from l s
−1 to m
3 s
−1,
Qlh is the total leakage flow at time
h and ∆
h (s) is the time in which
Qlh (l s
−1) is applied.
However, in most of the cases, the leakage flow of the entire network is the only available data. For these analyses, methodologies to estimate the leakage flow at each node from the total leakage rate have been proposed. In this work, the methodology proposed by Araujo et al. [
36] was used. From the current leakage rate, which is usually estimated as a percentage of the minimum total night flow, an iterative process was carried out to determine the value of
ci which accomplished Equations (3) and (4) using the software EPANET [
35]. This iterative process was required to set the value of
ci at each node and thus determine the leakage flow according to the pressure received at each node [
37]. After that, two types of demand were applied to the nodes, one associated with the human consumption, while the other was pressure-dependent and related to leakage. Therefore, a genetic algorithm was applied to determine the new demand pattern which, multiplied by the base demand and added up the leakage flow, matched with the actual measured hourly demand of the network. A detailed description of the above methodology can be found in [
36]. Once the leakage flow after installing a PRV or a PAT was obtained, the water cost saving was determined by Equation (5).
The procedure to determine the water saving was carried out in MATLAB [
38].
As for the energy cost saving, Equation (7) was used to estimate its value:
where the term 1/1000 is used to convert units from W to kW,
ρ is the water density (kg m
−3),
g the gravity acceleration (m s
−2),
QPAT,h (m
3 s
−1) and
HPAT,h (m) the flow and head provided by the PAT at time
h, respectively.
ηh was the efficiency of the PAT and
ep the savings from displaced electricity costs (0.17 € kWh
−1 has been assumed in this work, [
39]).
Different methodologies to estimate the friction losses in a PAT have been developed [
40,
41]. A simplified approach similar to the one proposed by [
23] was considered in this work. According to [
42], the maximum PAT efficiency, i.e., the efficiency of a PAT at the Best Efficiency Point (BEP) is achieved when the flow at the PAT is 75% of the maximum flow, considering 0% as the minimum flow rate through a PAT and 100% as the maximum flow at the same speed. Therefore, two considerations were assumed in this work: (1)
QPAT,h was
QBEP when the input flow was higher than
QBEP and
ηh matched with the maximum PAT flow-to-wire efficiency,
ηmax, assumed here as 0.65 [
18,
25]. In this case, the rest of the flow was bypassed; (2)
QPAT,h matched with the input flow when it was lower than
QBEP and the
ηh was determined according to the methodology proposed by [
42], in which they evaluated the performance of 113 PATs by characterising the relationship between head and specific speed. The 113 PATs performance database was included in EPANET, to estimate the hydropower potential according to the instant flow and head at a certain site.
A flow chart with a summary of the methodology above described is shown in
Figure 1.
2.3. PAT Total Installation Cost
The cost in the European context of a centrifugal PAT with a connected four-pole asynchronous motor used as a generator can be estimated as function of its nominal flow and head working conditions at the Best Efficiency Point (BEP) through a set of linear correlations [
53]:
The above equation was determined from a database of 343 commercially available pumps and 286 generators [
53]. Only asynchronous induction motors which can efficiently work as generators and are commonly sold as standard prime movers of hydraulic pumps were selected. More specifically, four-pole asynchronous motors have been considered as their moderate nominal speed of about 1500 RPM prevents PATs from reaching an excessive speed under runaway conditions, compared to two-poles units.
Apart from the purchase of the turbine and the generator, the final cost of a typical Micro-Hydropower (MHP) scheme includes additional contributions (see
Figure 2b) which can be grouped as follows:
- -
Civil works and hydraulic equipment, including:
- ○
a bypass pipe;
- ○
a set of actuated or manually operated control and sectioning valves;
- ○
a PRV (in certain installations). The necessity of installing this device depends on whether the PAT will operate far from its BEP at a given site, and the capability of the actuated valves to control the pressure received at downstream nodes. If the pressure is too high to be controlled by the actuated control valves, a PRV installed in the bypass is required.
- ○
a Y-strainer;
- ○
a powerhouse hosting the equipment.
- -
Electric cabinet and control system
- -
Grid connection fee
- -
Commissioning
- -
Other project costs (including consultancy)
The cost of the above elements in PAT energy recovery installations is unclear, since no comprehensive study has provided a cost breakdown of PAT-based MHP schemes embedded in water infrastructures to date. Some authors have suggested that the contribution given by the purchase of a conventional turbine and generator may account typically for the 35% [
54] up to a maximum of 70% of the final cost figure of a MHP scheme [
18]. However, such figures are not directly applicable to the context of this research since their authors did not consider the use of PATs, which allows for a considerable reduction of the turbine purchase price (5 to 20 times less expensive). In addition, they did not refer specifically to hydropower stations within water distribution networks.
In order to evaluate more accurately the cost of such plants, data from 9 energy recovery schemes in water networks from different countries have been compiled [
24,
55,
56,
57]. All of the selected plants adopted a PAT as a generating device, and had nominal powers ranging from 9 to 120 kW. The location and power rating of all 9 schemes is displayed in
Figure 3. According to the available information, it was possible to sub-divide the total cost of the installation into single components:
- -
turbogenerator alone;
- -
turbogenerator and control system;
- -
commissioning;
- -
civil works and hydraulic equipment;
- -
grid connection;
- -
other project costs.
From the purchase price of a PAT and a generator by means of Equation (8), the resulting cost breakdown allowed the realistic quantification of the total expected cost of a PAT-based MHP plant in water infrastructures from its nominal values of flow rate and hydraulic head.