Technical and economic analysis of a pump as a turbine for rural electrification

ABSTRACT

Electricity is one of the essential requirements for the economic development of a country. In Ethiopia, more than half of the total population does not have access to electric power. Micro-hydropower (MHP) is one of the most feasible renewable energy options for providing reliable electricity to rural areas. However, in low-income countries such as Ethiopia, the high price of a purpose-made turbine to generate electricity from MHP resources is difficult. This paper presents the feasibility study of a pump as a turbine (PAT) for MHP applications with and without impeller blade modification. The analysis was conducted in terms of initial investment cost, the net present value, payback periods, and the cost of energy. Decreasing blade thickness, blade tip rounding, adjusting blade inlet angle, and blade grooving, then comparing the result with PAT without modification and cross-flow turbine are the modification techniques considered in this research. Based on the projected system lifetime, the equivalent cost of power for the PAT and cross-flow turbines are 0.065 and 0.100 $/kWh respectively. The cross-flow turbine's payback period is 6.04 years, which is significantly longer than the PATs payback period of 3.42 years. From the entire study, it can be concluded that the MHP coupled with PAT provides a lower payback period and cheaper power production. Whereas, impeller blade modification has no significant advantage from the economic point of view. Generally, the impeller modification cost needs to be less than or equal to 25% of the initial cost of the PAT to use the less cost advantage of the PAT.

KEYWORDS:

• Economic analysis
• blade modification
• micro-hydro power
• pump as turbine
• rural electrification

1. Introduction

Energy consumption is directly proportional to the amount of economic growth. In Ethiopia, the energy consumption is 45 kWh/capita which is the lowest when compared to the mean of 578 for Africa and 2752 kWh/capita for the world (Chandrasekharam and Chandrasekhar 2012; Evans 2012). The national electric access rate is also around 51.09% and less than 10% of the rural communities are connected to the national grid (Access to electricity n.d.; Girma 2016). People in rural areas use traditional energy sources such as biomasses and dry cells to fulfil the energy demand causing environmental and economic problems (Getnet Zewde 2016; Gurung et al. 2011). However, the country has large water resources and has a reasonably high-installed capacity of 80 MW of standalone micro and Pico-hydropower plants (Degefu, He, and Zhao 2015). The natural topology of the country is also well suited to create storage reservoirs at relatively low costs and with little environmental and social disruption.

MHP plants are known for their potential to supply rural areas in developing countries with environmentally sound, affordable, and adequate energy, which will lead to an increase in employment opportunities, improvement of the ecological environment, poverty alleviation, improvement of living and cultural standards and economic development (Kengne Signe, Hamandjoda, and Nganhou 2017). Unlike Large hydropower, the reservoirs of MHP do not cover a large amount of space and there is no significant displacement of communities from their original home place. However, the share of MHP in the national energy pool is insignificant. The main reason is the corresponding purpose-made turbines are not affordable (Bozorgi et al. 2013).

Previous studies have focused on performance analysis and performance improvement of the PAT and a few studies are focused on the economic analysis. De Marchis et al. (2016) explored the economic benefit of PATs to produce energy from the fluid line instead of conventional pressure dissipation devices. The result of the analysis showed that the use of PATs can be attractive in economic and energy recovery terms, considering the lower capital cost, when compared to traditional turbines. Motwani, Jain, and Patel (2013) carried out a cost analysis of PAT and Francis turbine as a prime mover to improve the performance characteristics, intended to be compatible with economical way. The comparison is done according to overall efficiency, initial investment cost, life cycle cost analysis, and cost of electricity generation. The output of the study shows the cost of electricity generation for the Francis turbine is more expensive than the PAT.

The cost of electro-mechanical components in MHP plants is relatively higher than the large hydro systems, which varies from 35-40% of the total cost of the plant (Motwani, Jain, and Patel 2013). The cost can be brought down by using PAT instead of purpose-made turbines. Regarding the cost of PAT and generator, different authors have presented different approaches. Ramos, Borga, and Simão (2009) considered the cost of a PAT to vary between 200–400 €/kW for nominal power lower than 40 kW. Carravetta et al. (2013) planned the cost of the PAT and the generator to be 230 and 115 €/kW respectively. De Marchis et al. (2014) used a cost per power unit of 2000 €/kW for PAT plus generator. In the research of (Chacón et al. 2019), a cost model, which estimates the cost per kW of the centrifugal PATs coupled with induction generators with the number of magnetic poles has been used.

Pumps-as-Turbines (PaTs) are investigated as a potential energy recovery and pressure regulating technology in (Rossi et al. 2019), with a case study of the Egna municipality WDN, a city in northern Italy. Based on WDN operating data, a unique analytical approach is used to choose PaTs and forecast machine performance under changing operating situations. For modelling two different set-up configurations and installations, a MATLAB Simulink model is created.

The study in Ali et al. (2023), proposed a novel strategy for developing Pakistan's energy by creating small-hydropower utilising Pump-As-Turbine (PAT), a type of renewable energy with a lower environmental impact that has not previously been used in Pakistan.

The study in Qian et al. (2016) carried out a performance evaluation of an axial-flow pump with adjustable guide vanes in turbine mode. The pump as turbine (PAT) was chosen to replace the conventional turbine to lower the initial capital cost and payback period.

A prototype of an axial pump was developed to assess the pump's parameters, such as head and efficiency, in the pump mode in Zhao et al. (2020), which was used to confirm the simulation approach.

The goal of the work in Kan et al. (2023) is to analyze the energy loss characteristics and flow dynamics of an axial-flow PAT in both pump and turbine operating modes. In order to offer an energy loss intensity model in the cylindrical coordinate system, it employs the numerical simulation approach and makes use of the entropy production theory. This model quantitatively provides the spatial variation pattern for energy losses in pump and turbine operating modes.

A few research works were extensively conducted for the economic analysis of PAT for power-generating applications. Whereas, the economic analysis of PAT with impeller modification is not studied yet. This paper aims to conduct a detailed economic analysis of PAT with and without impeller blade modification for power-generating applications by considering a small village having 23 householders in the base year 2022. The economic analysis is conducted based on initial investment cost, net present value, payback period, and the cost of energy.

The major contributions of this paper are:

1. A comprehensive economic analysis of pump as a turbine (PAT) with and without impeller blade modification for power-generating applications.

2. When the PAT is used instead of a purpose-built turbine, up to 15% of the original investment cost can be saved.

3. The findings of the study show that the MHP coupled with PAT provides a lower payback period and cheaper power production.

4. The proposed PAT has various advantages over the traditional hydro-turbines which include low costs, low complexity, quick delivery, simplicity of replacement of parts, simple installation, availability in a wide range of standard diameters, and mass manufacture for a wide range of heads and flow rates.

2. Materials and method

To prove the economic feasibility of PAT application in MHP development the net present value (NPV), payback periods (PBP), and the cost of energy (Ec) were evaluated. Information, such as initial investment costs (IIC), maintenance costs (Mc), and feed-in tariffs were considered to be able to draw more general conclusions.

Major assumptions made in the economic assessment are: –

• The expected life of the power plant is 30 years (Girma 2016).

• The lifespan of the PAT is considered 15 years (Kramer, Terheiden, and Wieprecht 2018).

• The PAT cost has been calculated according to the BEP of the PAT.

• The maintenance cost of the MHP system is assumed to be 5% of the total capital cost per the project duration, PATs are known for their lower maintenance cost (De Marchis et al. 2016).

• The salvage value of the basic components of the system is 15% of the initial investment cost (Nasir 2019).

• 360 operating days per year (five days are leaving for maintenance work).

• The discount rate was assumed to be 12% (this is the current interest rate of the country),

• Maximum PAT efficiency is considered as 65.5% (Nasir et al. 2022).

2.1. Potential assessment of the candidate sites

According to the mean annual water surplus of the country, the most promising sites are found in the western part of the country, since suitable topographic conditions and constant flows are found most commonly (Meder and Bubenzer 2011). Three sites i.e. Chemoga, Huluka, and Wabi as shown in Figure 1 are found in the western part of the country are selected as candidate sites.

Figure 1. Location of candidate sites.

The recorded mean annual flow presented in Table 1 was analysed using the flow duration curve analysis technique. The probability that a recorded flow will be equalled or exceeded (% of the time) can be calculated using the Weibull plotting position given by Equation (1) (Koteia et al. 2016), this gives a steep curve as shown in Figure 2. (1) $P=100\times \left[M/\left(n+1\right)\right]$(1) where: $P$ = is the Exceedance probability

Figure 2. Flow duration curve of the three sites.

Table 1. Mean annual flow descending order of Chemoga, Huluka, and Wabi Rivers.

	Chemoga	Huluka	Wabi
M	Mean FDC (m^3/s)	Mean FDC (m^3/s)	Mean FDC (m^3/s)	P
1	55.7301	7.81183	31.476	9.09
2	55.1178	4.67767	29.064	18.181
3	41.1473	3.11443	28.103	27.272
4	40.7447	2.99392	27.414	36.363
5	39.6815	2.68142	26.215	45.454
6	38.7933	2.4951	23.385	54.545
7	38.1926	2.30392	22.96	63.636
8	5.60417	1.9945	20.179	72.727
9	4.29925	1.8975	15.37	81.818
10	3.54725	1.63655	13.52	90.909

$M$ = is the ordering number, $M=1$ for maximum flow rate.

$n$ = is the number of mean flows (dimensionless).

Among the three candidates, at dry conditions and low flows, the Wabi river is found to be the best one as shown in Figure 2. In addition to these Wabi is selected for practical reasons to visit the field and to meet the respective teams for interviews and discussions, besides, unavailability of electricity is a big problem in the area. The topography is also suitable for hydropower generation. Therefore, the hydraulic data of Wabi river and the topographical information of the place are considered in the research.

2.1.1. Power capacity of the selected site

Accurate measurement of head and flow is very important to calculate the energy potential, the system’s pipeline size, turbine type, rotational speed, and generator size. The net head of the site is determined at the bottom of the penstock, by subtracting friction loss from the gross head using Equation (2). (2) $H_{net}=H_g-H_f$(2) where $h_{net}$ is the actual head available at the inlet of the PAT, $H_g$ is the gross head, and $H_f$ is the total friction loss through the piping system, which is defined as Equation (3). (3) $H_f=H_{ps}+H_{elbow}+H_{gv}+H_u+H_{screen}+H_v$(3) Head loss in the penstock ($H_{ps}$) is the major loss through the pipe and can be calculated from the Darcy-Weisbach equation (Nasir 2019). (4) $H_{ps}=f{\displaystyle \frac{L}{D}{\displaystyle \frac{V^2}{2g}}}$(4) The Darcy friction factor ($f$) can be determined from the standard Moody diagram, or by solving from the Blasius (Equation (5)), Swamee-Jain (Equation (6)), or Haaland equations (Equation (7)) (Brown 2017). (5) $f={\displaystyle \frac{0.316}{R_e^{0.25}}}$(5) (6) $f=0.25[\log \left({\displaystyle \frac{r}{3.7}+{\displaystyle \frac{5.74}{R_e^{0.9}}}}\right){]}^{-2}$(6) (7) ${\displaystyle \frac{1}{\sqrt{f}}=-1.8\mathrm{l}\mathrm{o}\mathrm{g}[\left({\displaystyle \frac{r}{3.7}{)}^{1.11}+{\displaystyle \frac{6.9}{R_e}}}\right]}$(7) where R_e is the Reynolds number. In Equations (6) and (7), r is the relative roughness of the penstock.

The result of the Darcy friction factor solved using the mentioned methodologies is summarised in Table 2.

Table 2. Calculation of Darcy friction factor (f).

	Methodology
	Moody diagram	Blasius equation	Swamee-Jain equation	Haaland equation
f	0.015	0.026	0.025	0.023

The loss coefficient for pipe components (minor loss) (i.e. elbow, valve, and fittings) can be solved by using Equation (8). Screening and velocity losses are also considered using Equation (9). (8) $H_L=K_L{\displaystyle \frac{V^2}{2g}}$(8) (9) $\mathrm{V}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}={\displaystyle \frac{V^2}{2g}}$(9) Now, considering all possible system losses, taking the average Darcy friction factor f = 0.02, friction loss, and net head as a function of flow rate were tabulated in Table 3.

Table 3. Head losses as a function of flow rate.

Q /(m^3/s)	Gross head (m)	Friction loss	Net head (m)
0	27	0	27
0.0013	27	0.4065	26.5934
0.0027	27	1.7041	25.2958
0.0041	27	3.9100	23.0899
0.0055	27	7.0243	19.9756
0.0069	27	11.0468	15.9531
0.0083	27	15.9776	11.0223
0.0097	27	21.8168	5.1831

The working point is the net head flow corresponding to the PAT function, taking into account the head losses in the pipe system. To determine this point, the intersection points of the net head curve with the PAT characteristic curve (Nasir et al. 2022) shown in Figure 3 give the working point of the PAT in the designed system.

Figure 3. Performance characteristics of the Piping system.

After solving the net head of the system, the power capacity in the PAT is given as (Kengne Signe et al. 2017): (10) $P={\eta }_t\times 9.81\times \rho \times Q_t\times H_{net}$(10) where $P$ = Power generated in the PAT’s shaft [$W$], $Q_t$ = the design flow rate [m³/s], $g$ = gravitational acceleration [m/s²], $H_{net}$ = net head [$m$], ${\eta }_t$ = PAT efficiency [%].

2.1.2. Load estimation

Predicting the power demand (generator load) of the consumers connected to the PAT is especially important for isolated operations (Maalawi 2020). A small village with twenty-three householders is considered for this work. The loading table presented in Table 4 shows the total power requirements over the day for lighting, radio, and phone charger.

Table 4. Peak load calculation of power demand.

No.	Appliance	Quantity	Watts in average	Total power (W)	Hours per day	W. hr./day
1	LED bulb	2 × 23 = 46	8.0	368	12 (12-24)	4,416
2	Radio	23	2.5	57.5	17 (1-17)	977.5
3	Phone charger	23	3.0	69.0	14 (1-13)	966
	Sub-total			494.5

The maximum power demand is the sum of the total power of selected devices. The maximum power demand as shown in Table 4 is equals to 494.5 W. An increase in power demand during the lifetime of the project can usually be expected. Considering additional twenty-five percent power demand for future applications and power losses i.e. the total power demand of the area becomes 620.0 W. The demand for electrical power based on the number of populations and their activities can also be determined by using Equation (11) (Kengne Signe et al. 2017): (11) $B_n={\displaystyle \frac{B_m{P}_0{\left(1+\alpha \right)}^n}{m}}$(11) where $B_n$ is future needs of electrical power,$n$ is the lifetime of the project, $B_m$ electrical power needs per household, Po is the current population number of the area, α is the annual growth rate of the population (Population growth (annual %)-Ethiopia, 2020), and m is the average number of persons per household.

2.2. Profitability analysis

Every project needs to profitability evaluation to make sure that it is feasible or not. In addition to the evaluation of initial investment cost the profitability of micro-hydro power using the pump as a turbine is conducted in terms of net present value (NPV) payback period (PBP), and the cost of energy.

2.2.1. Initial investment cost (IIC)

The initial costs are extremely site-specific and can be divided into electromechanical (PAT + generator with the piping system) and civil work. In terms of the civil work, ten percent of the electro-mechanical cost is allocated since the designed plant requires a weir that serves as a waterway. To complete the economic assessment, the profitability analysis is conducted based on the net present value (NPV) and the payback period (PBP) was carried out.

2.2.2. Net present value (NPV)

NPV is the difference between the present value of cash inflows and the present value of cash outflows (represents the investment cost of the project) over a period of time. The present value of cash inflow is defined by Equation (12) by considering the time value of money. (12) $PV=FV/(1+r{)}^n$(12) The mathematical expression of the net present value is expressed in Equation (13). In which, $R_t$ is cash flow (revenues-cost within the specified year), $t$ is the number of periods, $i$ = internal rate of return (interest/discount rate), and $\mathrm{I}\mathrm{I}\mathrm{C}$ is initial investment cost. If $\mathrm{N}\mathrm{P}\mathrm{V}$ is greater than or equal to zero, the project is profitable. From Table 5, the present value of cash inflow is greater than the present value of cash outflow. Therefore, it can be concluded that the proposed project is profitable in terms of the net present value. (13) $\mathrm{N}\mathrm{P}\mathrm{V}=\sum _{t=1}^T{\displaystyle \frac{R_t}{{\left(1+i\right)}^t}\text{–}\mathrm{I}\mathrm{I}\mathrm{C}}$(13)

Table 5. Net cash in/out outflow.

Year	Cash flow ($)	Year	PV ($)	Year	PV ($)	Year	PV ($)
0	−2241.12	8	2,986.33	16	8,223.93	24	13,461.53
1	−1,596.57	9	3,641.03	17	8,878.63	25	14,116.23
2	−941.87	10	4,295.73	18	9,533.33	26	14,770.93
3	−287.17	11	4,950.43	19	10,188.03	27	15,425.63
4	367.53	12	5,605.13	20	10,842.73	28	16,080.33
5	1,022.23	13	6,259.83	21	11,497.43	29	16,735.03
6	1,676.93	14	6,914.53	22	12,152.13	30	17,389.73
7	2,331.63	15	7,569.23	23	12,806.83

According to the information from the Ethiopian Electric Utility (EEU), the current tariff for electricity is $0.06/kWh which includes all components of the electricity bill such as the cost of power, distribution, and taxes. The Annual revenue expressed in $/year can be calculated as the product of the energy cost and the yearly energy production (YEP) subtracting the maintenance cost ($M_C$) (see Equation 14). Considering a continuous service for 360 days per year the annual revenue is 654.70 USD. (14) $A_R=\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\times YEP-M_C$(14)

2.2.3. Payback period (PBP)

The payback Period (PBP) was used in this study to determine the period needed to recover the initial investment cost (Chacón et al. 2019). To estimate the payback period of the project, net present value curves are determined with a discount rate of $i$ = 12%. This is the intersection of NPV curve and abscissa as shown in Figure 4. The exact value of PBP can be calculated as the ratio between the total installation cost and annual revenue using Equation (15). It has to be highlighted that for MHP projects, the PBP has to be lower than 10 years to be considered economically viable if it is greater than or equal to 10 years the project were discarded (Chacón et al. 2019; De Marchis et al. 2014). The results of the payback period evaluation presented in Table 6 shows the economic benefits of the project, with an attractive payback period of approximately 3.42 years. (15) $\mathrm{P}\mathrm{B}\mathrm{P}={\displaystyle \frac{\mathrm{E}\mathrm{M}\mathrm{C}+CW}{A_R}}$(15)

Figure 4. Payback period of the project.

Table 6. Economic feasibility of PAT: Cost and payback analysis.

$\mathrm{I}\mathrm{I}\mathrm{C}\left(\mathrm{\$}\right)$	${\mathrm{M}}_{\mathrm{C}}\left(\mathrm{\$}\right)$	${\mathrm{A}}_{\mathrm{R}}=\left(\mathrm{\$}/\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\right)$	$\mathrm{P}\mathrm{B}\mathrm{P}\left(\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\right)$	Cost of energy ($/kWh)
2,241.12	101.87	654.70	3.42	0.0642

2.3. Cost of impeller modification

In this study, decreasing blade thickness, blade tip rounding, adjusting blade inlet angle, and blade grooving modification techniques with respective efficiency of 66.89%, 68.34%, 69.58%, and 70.06% are analysed, and then compare the result with the initial PAT (pump without modification) (Nasir et al. 2022). Intuition, comparison, analogical, parametric, and analytical methods are the main techniques that serve for estimating the cost of impeller modifications. Among the five listed methods, the analytical method is found to be the most accurate one. In which both direct and indirect costs are considered. The cost of materials, cost of labour, and cost of the machinery (including tool and energy costs) are used to calculate the total cost to improve performance (Vijayaramanath et al. 2009).

The listed modification techniques do not charge the material cost, since the modification is done on the initial blades. So, labour and machinery costs are calculated to estimate the total cost.

Face milling and slotting are used to decrease blade thickness and grooving respectively. The labour cost for machining can be calculated by using Equation (16) (Adithan 2007). Regarding the machinery cost, the cost of multi-axis machinery (including tax, tool cost, and power cost) is in the range of $75-$120 per hour (CNC Machining Cost Calculation, (n.d.). (16) $C_L=T_t\times \mathrm{l}\mathrm{a}\mathrm{b}\mathrm{o}\mathrm{r}\mathrm{w}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}$(16) where $T_t$ is total operation time, the sum of basic machining time and allowances.

The basic formula used for determining the machining time (T) is: (17) $T={\displaystyle \frac{L}{\mathrm{f}\mathrm{e}\mathrm{e}\mathrm{d}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{v}.\times N}}$(17) where L = length of total tool travel in mm, it is the sum of the length of the job and added table travel. (18) $\mathrm{A}\mathrm{d}\mathrm{d}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{l}={\displaystyle \frac{1}{2}\left(D-\sqrt{D^2-W^2}\right)}$(18) where, D = cutter diameter W = width of the workpiece $\mathrm{I}\mathrm{f}D\ge W,\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{a}\mathrm{c}\mathrm{h}={\displaystyle \frac{D}{2}}$for milling cutters, feed per revolution equals feed per tooth times the number of teeth on the cutter (Adithan 2007). A cutter with 2 teeth number is suggested for face milling and a cutter with 3 teeth number is suggested for slotting when the surface roughness is considered (Kaining Shi et al. 2019).

In Equation (19), N is the angular velocity of the workpiece in rpm. It is defined as follows. (19) $N={\displaystyle \frac{1000\times S}{\pi D}}$(19) where, S is the cutting speed of the tool in metres per minute, average cutting speeds and feeds per tooth for various materials are given in Table 7 and Table 8.

Table 7. Feed per tooth of cutters.

Types of cutters	Slab mill (Helix angle up to 30^0)	Slab mill (Helix angle 30^0 60^0)	Face mill	End mill	Slot mill	Form relieved cutter
Feed per tooth (mm)	0.10–0.25	0.07–0.20	0.12–0.50	0.02–0.25	0.07–0.12	0.07–0.20

Table 8. Cutting speed of different materials.

Material being cut	brass	C.I	Bronze	Mild steel	Hard C steel	Hard alloy steel	Aluminum
S, mpm	45–60	21–30	24–45	21–30	15–18	9–18	15–30

In Equation (16), time allowances include personal allowances (5% for males and 7% for females, fatigue allowances 5%, and contingency allowances less than 5% of basic machining time). The average hourly labour wage in Ethiopia is 1.5 USD (Ethiopia 2020). In all cases, the labour cost should be multiplied by six, because the impeller has six blades.

Surface grinding is a machining method used to round the blade tip and adjust blade inlet angles, estmation of time (T) in seconds for grinding is calculated by the general equation in Equation (16) (Adithan 2007). Specifically, for surface grinding, the machining time can be calculated as: (20) $\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}={\displaystyle \frac{L\times b}{S\times 1000f}\times \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{a}\mathrm{s}\mathrm{s}\left(n\right)}$(20)

$L$ is the length of the workpiece + allowance/over travel (mm),

$b$is the width of the workpiece (mm),

$S$ is the speed of the table in m/min (Equation (19)).

Most surface grinding operations use wheel speeds of 1,800–2,100 m/min (Girma 2015),

$f$is feed mm/stock.

The number of passes (n) can be defined by Equation (21). (21) $n={\displaystyle \frac{d}{t}}$(21) where, d is the depth of stock to be removed (the length of the material to be removed) and t depth per cut (for finishing the depth of cut is from 0.15–0.025 mm) (James et al. 2013).

The cost of machinery includes the estimated power cost and maintenance charges for the tools, jigs, fixtures, and dies required in the production. The depreciation amount per year (D) of the machine can be calculated using Equation (22). (22) $D={\displaystyle \frac{C-S}{n}}$(22) where C is the initial cost of the machine, S is the scrap (or salvage) value, and n is the estimated life of the machine in years.

The estimated total cost is the sum of the labour costs and machinery costs since the cost of materials in this case is zero. Table 9 lists the costs of the pump running as a turbine with and without impeller modification. The cost of a purpose-made turbine i.e. cross-flow turbine (mostly used in micro-hydropower systems in developing countries (Ali et al. 2023; Kan, Binama et al. 2022; Kan, Chen. et al. 2021; Kan, Xu et al. 2022; Kan, Yang, et al. 2021; Kan, Zang, et al. 2022; Ram Adhikari 2018; Simão et al. 2019) is also presented in the same table. The cost of energy for both PAT and cross-flow turbine can be calculated using Equation (23) (Motwani et al. 2013). (23) $\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{\mathrm{A}\mathrm{L}\mathrm{C}\mathrm{C}}{{\mathrm{A}}_{\mathrm{e}}}}$(23)

Table 9. Costs and payback period of PAT and cross-flow turbine.

	$\mathrm{I}\mathrm{I}\mathrm{C}\left(\mathrm{\$}\right)$	${\mathrm{A}}_{\mathrm{R}}$  = ($/year)	PBP (year)	Cost of energy ($/kWh)
Initial	2241.12	654.70	3.42	0.0642
Decreasing blade thickness	2285.86	668.35	3.42	0.0642
Blade tip rounding	2266.06	676.53	3.35	0.0623
Blade inlet angle	2266.06	685.06	3.31	0.0611
Blade grooving	2294.29	690.94	3.32	0.0615
Cross-flow turbine	2610.12	432.16	6.04	0.1000

where ALCC is the annual life cycle cost and A_e is the annual energy generation.

Blade tip rounding, blade inlet angle, and blade grooving have lower payback periods when compared with decreasing blade thickness and PAT without modification. Generally, the difference between the payback periods for the applied modification techniques is not significant as shown in Figure 5. The payback period of a cross-flow turbine is 6.04 years, it much higher than the PATs payback period i.e. 3.42 years.

Figure 5. Payback periods for different modification techniques and cross-flow turbine.

The cost of energy in the case of a cross-flow turbine is 0.100 $/kWh while the average cost of energy for the pump running as a turbine is 0.062 $/kWh. Therefore, the cost of energy of the MHP coupled with PAT is decreased by 38%. From Table 9 and Figure 6, the payback period and the cost of energy for the PAT without impeller modification is 3.42 years and 0.0642 $/kWh respectively.

Figure 6. Payback period and cost of energy for impeller modification.

These values dramatically decreased to 3.27 years and 0.0601 $/kWh for impeller modification with zero cost. Practically, impeller modification with zero cost is not possible, therefore increasing the cost of modification from zero up to the maximum viable cost. Figure 6 shows if the modification cost is greater than 30% of PAT’s cost the project needs more payback period than PAT without modification. For the cost of energy, the modification cost should be less than 50% of the cost of PAT. Generally, the modification cost needs to be less than or equal to 25% of the initial cost of the PAT to use the less cost advantage of PAT.

3. Conclusion

This study presents the economic analysis of a PAT as a power generating application, considering the site located in south-west Ethiopia. The economic benefits of impeller modification are also analysed. The economic analysis indicators, implemented in this research show that the application of PAT for MHP projects plays an important role in decreasing the payback period and the cost of energy. This research study aims to figure out the cost of impeller modification, which makes the project more profitable. From the results achieved, the following can be concluded:

1. Based on the projected system lifetime, the energy generation cost and payback period of the MHP plant coupled with PAT are approximately 40% less than the cross-flow turbine. Furthermore, readily available maintenance knowledge in the local areas further reduces the operational cost.

2. Up to 15% of the initial investment cost can be saved when substituting PAT instead of using a purpose-made turbine.

3. To take advantage of PAT's lower cost advantage, impeller blade alteration should be implemented as cheaply as possible.

Overall, the results confirm that the MHP coupled with PAT has a positive impact to increase the viability of utilising MHP resources. Impeller modification has no remarkable advantage from an economic point of view. Future studies will be extended to identify other potential hydro-power resources like irrigation networks, to increase the total energy production. The application of more than one pump can also be considered in future works to expand the economic and environmental advantage to other villages.

Availability of data

The datasets generated during and/or analysed during the current study are not publicly available but are available from the corresponding author on reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors recognized that, the financial support by Addis Ababa Science and Technology University (AASTU) under internal research grants [grant number EM-229/19-1/21].