Optimal Design of a Hybrid Power System for a Remote Fishpond Based on Hydro-Turbine Performance Parameters

Abstract

This paper proposes an optimal solution for the design of a hybrid power system that will supply a remote fishpond in eastern Serbia. In terms of structure, this off-grid system should be a hydro-photovoltaic-diesel-converter-battery setup. The optimization objectives are to minimize total net present cost (NPC) and greenhouse gas (GHG) emissions and to maximize total annual electricity generation based on the modification of hydro-turbine performance. This study considers the following three cases of a hydro-turbine with fixed propeller blades: having fixed guide vanes, for the annual average flow rate-Case 1; having adjustable guide vanes, for smaller flow rates-Case 2 and having adjustable guide vanes, for higher flow rates-Case 3. The optimization is performed using HOMER Pro v. 3.16.2 software. The results show that the total NPC, levelized cost of energy (COE) and GHG emissions in Case 3 are 16.6%, 16.8% and 13.1% lower than in Case 1, and 8.1%, 8% and 11.7% lower than in Case 2, respectively. It is also found that the total annual electricity generation and power output from the entire system in Case 3 are 33.3% and 1.2% higher than in Case 1, and 11.9% higher and not different than in Case 2, respectively.

1. Introduction

Clear rivers in remote rural areas are often suitable for the construction of fishponds. However, due to the large distances from the electricity distribution system, it is necessary to construct hybrid power systems for their supply. One such fishpond is the trout pond of Jablanica, built next to the river of Radovanska Reka at the foot of the mountain of South Kučaj in eastern Serbia. In this area, hydropower and solar radiation are available sources of renewable energy [1,2,3] suitable for off-grid hybrid power systems. In recent years, there have been large variations in river flows in this area, so that the river flows were extremely large in winter and extremely small in summer. Accordingly, it is necessary to construct an off-grid hybrid power system for the supply of the trout pond of Jablanica, which will effectively exploit the existing water resource.

In a number of available research papers, hybrid power systems with micro-hydro power plants (MHPPs), photovoltaic (PV) generators and diesel generators, designed to power various remote consumers, were analyzed. Simulation and sizing of a hybrid hydro-PV-diesel power system for electrification of rural areas in equatorial Africa were performed in [4]. For the considered conditions, an optimal hybrid system of 8.12 kW was proposed for powering a remote village. The total net present cost (NPC) and the levelized cost of energy (COE) for this system were 70,042 $ and 0.278 $/kWh, respectively. An evaluation of the potential for a small hydro-PV hybrid power system in a remote area of Nigeria can be found in [5]. In this particular case, the available hydropower can satisfy the monthly electricity demand in the amount of 59–100%, depending on the month of the year [5]. A feasibility study on a hydro-PV hybrid power system operating at an existing dam for water supply in southern Brazil was conducted in [6]. This study suggested the use of existing pumps as turbines in combination with a PV generator installed on floating structures [6]. PV-hydro hybrid power systems together with some configurations, operation strategies, complementarity over time between energy sources in southern Brazil and preliminary estimates of costs were discussed in [7].

A techno-economic and environmental analysis of different hybrid power systems for the supply of a typical rural village in Iraq was presented in [8]. It was found that this hybrid system, consisting of a 14.7 kW MHPP, a 13 kW PV generator, a 5 kW diesel generator, 8 storage batteries and a 9 kW converter, has a total NPC of 113,201 $ and low greenhouse gas (GHG) emissions [8]. The potential application of hydro-PV-diesel hybrid power systems to off-grid electrification of a typical rural village in Nigeria was examined in [9]. According to this study, an optimal hybrid system with a total NPC of 963,431 $ and a levelized COE of 0.112 $/kWh is possible. In [10], for a small hydro-PV-diesel hybrid power system, it was found that increasing the price of diesel fuel from 0.55 $/l to 1.2 $/l can increase the associated levelized COE from 0.131 $/kWh to 0.206 $/kWh. The viability of hydro-PV-diesel power system options with the aim of finding the technically and economically best configuration for the electricity supply of a village in western Ethiopia was analyzed in [11]. This analysis showed that the total consumption of electricity can be covered by 79% of electricity obtained from hydropower, 20% from solar energy, and only 1% from diesel fuel. The hybrid power system proposed in [11] was also cost competitive with 0.133 $/kWh.

In addition to the above-mentioned hybrid power systems based on hydropower and solar energy, there are hybrid power systems in the literature that use energy from renewable energy sources such as wind, biomass, biogas, and the like. A study on optimizing the components of a biomass–biogas power system to meet the electrical needs of a remote agricultural farm in northern India was conducted in [12]. An off-grid hybrid power system with renewables for rural electrification in India using PVs and anaerobic digestion was modeled in [13]. A PV-wind hybrid power system supplying a farm in a semi-arid area of Algeria was optimized in [14]. An off-grid hybrid power system with a wind turbine, a PV generator and a gas generator to power a residential complex in Iran was modeled and studied in [15]. The concept of an alternative hybrid power system that combines PVs and digesters fueled by goat manure as the basis for sustainable development of rural areas in Brazil was introduced in [16]. An optimized design of a PV-wind-diesel hybrid power system for sustainable development of coastal areas in Bangladesh, considering the total NPC, levelized COE and GHG emissions, was provided in [17]. The performance parameters of a PV-wind-diesel hybrid power system to power a small community in Indonesia were simulated and optimized in [18]. A hybrid power system consisting of a photovoltaic generator, a wind generator, a diesel generator, a storage battery unit, a converter, an electrolyzer, and a hydrogen tank was considered in [19]. This system was created to provide uninterrupted power and meet the different load demands of some village communities in India [19]. In most of the publications reviewed here, the optimization was performed using HOMER Pro v. 3.16.2 software.

Moreover, there are hybrid power systems that consist only of renewable energy sources and include technologies to evaluate the performance of PV generators. In this regard, a hybrid power system consisting of a PV generator, a power-to-hydrogen unit, a hydrogen storage and a fuel cell was proposed in [20] to satisfy the domestic load of a residential building. In that study, the performance parameters of alkaline electrolysis cells were evaluated considering the inclusion of a two-switch buck-boost converter [20]. Furthermore, considering grid disturbances and recovery scenarios, a novel techno-economic approach for an off-grid remote industrial microgrid to enhance the PV hosting capacity by integrating a storage battery unit was analyzed in [21].

Specifically, this paper aims to (i) design a hydro-PV-diesel-converter-battery hybrid power system for the off-grid supply of the trout pond of Jablanica located far from the Serbian distribution system; (ii) carry out optimization and techno-economic analysis of the proposed system for two different types of hydro-turbine and three different cases of operation and (iii) identify the configuration of the proposed system with better performance based on the obtained results. The proposed system consists of one MHPP, one PV generator, one diesel generator, one converter and one storage battery unit. The MHPP would be located next to the settling basin for fishpond water and would use water from the settling basin overflow. According to the literature, there are different hydro-turbines such as gravitational water vortex turbine [22], Francis turbine [23,24], Savonius hydrokinetic turbine [25], bulb turbine [26], propeller S-turbine [26], etc., as well as their numerous modifications.

This paper, in particular, deals with the following two types of propeller S-turbine: hydro-turbine with fixed propeller blades and fixed guide vanes-Case 1, and hydro-turbine with fixed propeller blades and adjustable guide vanes-Case 2 and Case 3. The annual average flow rate through the settling basin is assumed in Case 1, while smaller and higher flow rates through the settling basin are assumed in Case 2 and Case 3, respectively. In Case 1, it is taken into account that the fixed propeller blades and fixed guide vanes are optimized and customized for the annual average flow rate through the settling basin by a scaling procedure. In Case 2 and Case 3, it is taken into account that the fixed propeller blades are designed for flow rates through the settling basin different from the annual average flow rate. In Case 2, it is also assumed that the adjustable guide vanes are optimized and customized for smaller flow rates through the settling basin (i.e., low hydro-turbine efficiency in the summer months and in dry years), that is, for a flow rate that is 20% smaller than the annual average flow rate through the settling basin. In Case 3 it is assumed that the adjustable guide vanes are optimized and customized for higher flow rates through the settling basin (i.e., more efficient operation of the hydro-turbine in the winter months).

In this paper, the HOMER Pro v. 3.16.2 software is used for the simulation of the considered off-grid hybrid power system, as well as for verification of the associated techno-economic criteria. The objective function aims here to maximize the generation of electricity, reduce total NPC and minimize GHG emissions, based on the variable flow rate through the considered hydro-turbine.

2. Energy Resources of the Trout Pond of Jablanica

The altitude of the trout pond of Jablanica is 820 m, and the geographical coordinates are 43°53′47.47″ north latitude and 21°47′11.55″ east longitude. Figure 1 shows the exact location of the trout pond of Jablanica in Google Maps. A dam on the river of Radovanska Reka that directs the flow of water into the fishpond is located near the source of that river. In addition to the settling basin, the fishpond contains 15 feeding and 6 spawning basins for fish. The river of Radovanska Reka has excellent conditions for the life and growth of different species of trout. The microclimatic conditions around this fishpond are favorable, i.e., the water does not freeze in the winter, and the pond is surrounded by hills that protect it from a stronger wind effect.

In previous periods, the trout pond of Jablanica has been supplied with electricity from a diesel generator only. This study proposes a hybrid power system configuration that would utilize the available renewable energy sources (water and solar radiation) as well as the existing construction and infrastructure of the fishpond. As already mentioned, the proposed hybrid power system would consist of the MHPP, PV generator, diesel generator, converter and storage battery unit. The hydro-turbine in the MHPP is assumed to be a propeller S-turbine that will use water from the settling basin overflow with a net head of 2.9 m. Figure 2 shows a vertical cross-section of the MHPP at the outlet of water from the settling basin, where the numerals represent the height values. The water from the settling basin is directed to the propeller S-turbine by means of a pipe having a diameter of 500 mm and a length of 8 m.

The histogram of the monthly average stream flow for the river of Radovanska Reka is presented in Figure 3. The stream flow (i.e., river flow) decreases during spring and summer, from May to October (the month when the stream flow should be at a minimum of 90 l/s), and increases during the autumn and winter, from November to April (months during which significant rainfalls and snowfalls should occur). The highest monthly average stream flow occurs in April and amounts to 845 l/s. The annual average stream flow and annual average residual stream flow for the river of Radovanska Reka are 328.04 l/s and 32.80 l/s, respectively.

The performance characteristic curves for the two considered types of propeller S-turbine are taken from [26] and represented in Figure 4.

By comparing the curves from Figure 4a,b a significant improvement in the performance parameters of the optimized hydro-turbine design corresponding to Cases 2 and 3 can be observed. In particular, the optimal power output of the turbine increases from 6.4 kW to 8.5 kW, and the optimal flow rate of the turbine increases from 265 l/s to 350 l/s. In addition, it can be seen that the optimal hydro-turbine design can operate with a flow rate of Q = 350 l/s and a net head of H = 2.9 m, achieving an optimal efficiency of η ≈ 0.86. By reducing the flow rate below that corresponding to optimal operation, the efficiency of the hydro-turbine decreases sharply because the propeller blades and guide vanes are fixed. Accordingly, it is assumed in Cases 2 and 3 that the guide vanes can be adjusted so that the hydro-turbine can operate (with lower efficiency) in the summer months and in dry years when the flow rates are significantly reduced (up to 30% of the optimal flow rate). In this particular case, HOMER Pro v. 3.16.2 software is used to estimate the power output and efficiency of the hydro-turbine.

3. Techno-Economic Analysis

A techno-economic analysis of the two configurations of the proposed hybrid power system (each with a different hydro-turbine) is performed using HOMER Pro v. 3.16.2 software [27]. Figure 5 provides the schematic representation of the proposed off-grid hybrid power system. The initial data required to conduct this analysis are the daily load profile of the system and data on system components (MHPP, PV generator, diesel generator, converter and storage battery unit).

Models used in HOMER Pro v. 3.16.2 software for the components of the proposed off-grid hybrid power system are taken from [27,28] and represented in

Table 1. Models used for the components of the proposed off-grid hybrid power system.

MHPP	Storage Battery Unit
$P_{hyd}=\frac{{\eta }_{hyd}·{\rho }_{water}·g·h_{net}·Q_{turbine}}{1000}$ where Phyd is the power output of the MHPP (kW), ηhyd is the efficiency of the MHPP (%), ρwater is the water density (1000 kg/m3), g is the acceleration due to gravity (9.81 m/s2), hnet is the net head (m), and Qturbine is the flow rate through the MHPP (m3/s).	$c_{bw}=\frac{C_{rep,batt}}{N_{batt}·Q_{lifetime}·\sqrt{{\eta }_{rt}}}$ where cbw is the battery wear cost depending on the cost of cycling energy through the battery unit ($), $C_{rep,batt}$ is the cost of replacing the battery unit ($), $N_{batt}$ is the number of batteries in the battery unit, $Q_{lifetime}$ is lifetime throughput of a single battery (kWh), and ${\eta }_{rt}$ is the battery round-trip efficiency (fractional).
PV generator
$P_{PV}=Y_{PV}·f_{PV}·\left(\frac{{\overline{G}}_T}{{\overline{G}}_{T,STC}}\right)\left[1+{\alpha }_p·\left(T_c-T_{c,STC}\right)\right]$ where $P_{PV}$ is the power output of the PV generator (kW), $Y_{PV}$ is the rated capacity of the PV generator, meaning its power output at the standard test conditions (STC) (kW), $f_{PV}$ is the PV derating factor (%), ${\overline{G}}_T$ is the solar irradiance in the current time step (kW/m2), ${\overline{G}}_{T,STC}$ is the solar irradiance at the STC (1 kW/m2), ${\alpha }_P$ is the temperature coefficient of power (%/°C), $T_c$ is the PV cell temperature in the current time step (°C), and $T_{c,STC}$ is the PV cell temperature at the STC (25 °C).	$Q_{lifetime,i}=\frac{f_i·d_i·Q_{max}·V_{nom}}{1000}$ where $f_i$ is the number of cycles to failure, $d_i$ is the depth of discharge (%), $Q_{max}$ is the maximum capacity of the battery (Ah), and $V_{nom}$ is the nominal voltage of the battery (V).
	Economic modeling
	$C_{NPC,tot}=\frac{C_{ann,tot}}{CRF·\left(i,R_{proj}\right)}$ where $C_{NPC,tot}$ is the total NPC ($), $C_{ann,tot}$ is the total annualized cost ($/year), $CRF$ is a function returning the capital recovery factor, $i$ is annual real interest rate (discount rate) (%), and $R_{proj}$ is the projected lifetime (year).
Diesel generator
$F=F_0·Y_{gen}+F_1·P_{gen}$ where $F$ is the fuel consumption rate (l/h), $F_0$ is the fuel curve intercept coefficient (l/h/kW), $F_1$ is the fuel curve slope (l/h/kW), $Y_{gen}$ is the rated capacity of the generator (kW), and $P_{gen}$ is the output of the generator in the current time step (kW).	$CRF\left(i,N\right)=\frac{\left[i·{\left(1+i\right)}^N\right]}{\left[{\left(1+i\right)}^N-1\right]}$ where $i$ is annual real interest rate (%), and $N$ is the number of years.
	$COE=\frac{C_{ann,tot}}{E_{prim,AC}+E_{def}+E_{grid,sales}}$ where $COE$ is the levelized COE ($/kWh), $C_{ann,tot}$ is the total annualized cost of the system ($/year), $E_{prim}$ is the AC primary load that is supplied with electricity (kWh/year), $E_{def}$ is the deferrable load that is supplied with electricity (kWh/year), and $E_{grid,sales}$ is the electricity sold to the grid (kWh/year).
$c_{gen,fixed}=c_{om,gen}+\frac{c_{rep,gen}}{R_{gen}}+F_0·Y_{gen}·c_{fuel,eff}$ where $c_{gen,fixed}$ is the generator fixed COE ($), $c_{om,gen}$ is the operating and maintenance (O&M) cost ($/h), $c_{rep,gen}$ is the cost of replacing ($), $R_{gen}$ is the generator lifetime (h), $F_0$ is the fuel curve intercept coefficient (l/h/kW), $Y_{gen}$ is the rated capacity of the generator (kW), and $c_{fuel,eff}$ is the effective price of diesel fuel ($/l).

.

The input parameters and costs related to the various components used in HOMER Pro v. 3.16.2 software are presented in this section. Components of different sizes are considered in order to find the optimal solution for the electrification of the given location. Two dispatch strategies are implemented to investigate the techno-economic performance of the proposed off-grid system, namely: cycle charging and load following. In the case of the cycle charging strategy, the diesel generator runs at its maximum supplying rated power to the primary load. The surplus of electricity generated goes towards lower-priority objectives. In decreasing order of priority, these objectives are: supplying electricity to the deferrable load and charging the storage battery unit. In the case of the load following strategy, the diesel generator operates just to supply the primary load with the required (sufficient) electricity. In that case, the supply of electricity to the deferrable load, or the charging of the storage battery unit (lower priority objectives) is made from renewable energy sources. The diesel generator can further increase the generation of electricity and sell that electricity to the grid if it is possible and if it is economically advantageous. The projected lifetime of the proposed hybrid power system should be 25 years at a real discount rate of 5.88%.

3.1. Daily Load Profile

The electricity generated by the proposed off-grid system is used to supply two buildings (equipped with devices), fishpond lighting, an oxygenator, and an ice maker. The typical daily load profile used in this analysis was obtained based on the average daily power requirements of these devices. The typical daily load profiles for the trout pond of Jablanica for days in January are shown in Figure 6.

In addition to the economic models presented in Table 1, HOMER Pro v. 3.16.2 software also uses a model for the other O&M costs. The other O&M costs include the system fixed O&M cost, financial penalty for capacity shortage, and financial penalty for emissions of pollutants. The other O&M costs are calculated using the following equation [27]:

$$C_{om,other}=C_{om,fixed}+c_{cs}·E_{cs}+C_{emissions}$$

(1)

where $C_{om,fixed}$ is the system fixed O&M cost on annual basis ($/year), $c_{cs}$ is the penalty for capacity shortage applicable to the system for any capacity shortage that occurs during the year ($/year), $E_{cs}$ is the annual capacity shortage (kWh/year), and $C_{emissions}$ is the penalty for emissions of pollutants on an annual basis ($/year).

HOMER Pro v. 3.16.2 software calculates the penalty for emissions of pollutants on an annual basis using the following equation [27]:

$$C_{emissions}=\frac{c_{C{O}_2}{M}_{C{O}_2}+c_{CO}{M}_{CO}+c_{UHC}{M}_{UHC}+c_{PM}{M}_{PM}+c_{S{O}_2}{M}_{S{O}_2}+c_{N{O}_x}{M}_{N{O}_x}}{1000}$$

(2)

where $c_{C{O}_2}$, $c_{CO}$, $c_{UHC}$, $c_{PM}$, $c_{S{O}_2}$ and $c_{N{O}_x}$ are the penalties for emissions of $C{O}_2$, $CO$, unburned hydrocarbons (UHC), particulate matter (PM), $S{O}_2$ and $N{O}_x$ in $/t, respectively; while $M_{C{O}_2}, M_{CO}$, $M_{UHC}$, $M_{PM}$, $M_{S{O}_2}$ and $M_{N{O}_x}$ are the annual emissions of $C{O}_2$, $CO$, UHC, PM, $S{O}_2$ and $N{O}_x$ in kg/year, respectively.

In any time step, HOMER Pro v. 3.16.2 software also calculates the storage energy cost as the average cost of the electricity that the system has injected into the storage battery unit up until that time step. Accordingly, the storage energy cost $c_{be,n}$ in time step n is [27]:

$$c_{be,n}=\frac{{\sum }_{i=1}^{n-1}{c}_{cc,i}}{{\sum }_{i=1}^{n-1}{E}_{cc,i}}$$

(3)

where $c_{be,n}$ is in $/kWh, $c_{cc,i}$ is the cost of cycle charging the storage battery unit in time step i in $, $E_{cc,i}$ is the amount of electricity injected into the storage battery unit in time step i in kWh.

The storage energy cost represents the average cost incurred by the system to deliberately charge the storage battery unit. The cost for one cycle of charging, appearing in the numerator of Equation (3), is the extra cost incurred by the system specifically for charging the storage battery unit. Excess electricity that charges the storage battery unit in a time step does not represent such a cost [27]. However, if the diesel generator provides more electricity than is required to power the load, and this is performed with the aim of charging the storage battery unit, then the operation of charging the storage battery unit does cause the system to incur extra costs. Such situations occur routinely when executing the cycle charging strategy. In each time step in which the diesel generator charges the storage battery unit, HOMER Pro v. 3.16.2 software calculates the associated cycle charge cost. The cycle charge cost is calculated as the difference between the actual cost of operating the system in the given time step and the cost that would have occurred in that time step if the system had not charged the storage battery unit [27]. In addition, when HOMER Pro v. 3.16.2 software implements the load following dispatch strategy, the energy storage cost will always be zero. This occurs because under the load following dispatch strategy the system never pays to charge the storage battery unit, it uses just excess electricity to charge them.

The load profile changes from day to day. By combining day-to-day and time-step-to-time-step variability, realistic-looking load data are generated. Figure 7 shows the monthly average daily loads of the trout pond of Jablanica generated for 15% day-to-day variability and 20% time-step-to-time-step variability.

According to Figure 6 and Figure 7, the average daily consumption of electricity during the year is 24.79 kWh, the peak power is 4.73 kW, and the load factor is 0.22.

3.2. Solar Radiation and PV Generator

The monthly average values of solar radiation and clearness index for the area of Boljevac are shown in Figure 8. Solar radiation data are obtained from NASA Surface Meteorology and Solar Energy [29] based on latitude and longitude for the municipality of Boljevac, where the trout pond of Jablanica is located.

The remaining data on the PV generator used in the simulations are the lifetime of PV panels of 25 years, the loss factor of 88%, the efficiency at the STC of 13%, the temperature coefficient of power of −0.485%/°C, the nominal operating cell temperature (NOCT) of 47.50 °C, the angle of inclination of 40°, and the azimuth of 0°. SHARP 250 W polycrystalline PV panels are considered [30]. The investment cost and replacement cost of these PV panels are 544 $/kV and 544 $/kV (1 $ was equal to 0.9159 € on 16 August 2023 [31]), respectively; while the annual O&M cost is 5 $/year. For the simulations, the following powers of PV panels: 0, 0.250, 0.5, 0.750, 1, 1.250,…, 15 kW are also used.

3.3. Hydropower and MHPP

Figure 3 shows the histogram of the monthly average stream flow for the river of Radovanska Reka. The penstock carrying water to the propeller S-turbine has a diameter of 500 mm and a length of 8 m. The flow rate of the turbine ranges from 220 l/s to 265 l/s for the hydro-turbine type corresponding with Case 1 and from 90 l/s to 350 l/s for the hydro-turbine type corresponding with Case 2 and Case 3. The net head of the turbine is 2.9 m. The lifetime of the MHPP is 25 years, while the predicted values of the investment and replacement costs are 1000 $/kW and 1000 $/kW [32], respectively. The annual O&M cost for the MHPP is 2.5% of the corresponding investment cost.

3.4. Diesel Generator

A three-phase Yamaha diesel generator of 12 kW is used [33]. In Serbia, the price of diesel fuel on 16 August 2023 was 1.705 $/l [34,35]. This price is used in the simulations. The corresponding investment, replacement and O&M costs are $3710, $1500 and 0.025 $/h, respectively. The fuel consumption and efficiency curves of the considered diesel generator are presented in Figure 9a,b, respectively. According to Figure 9a, the fuel curve intercept coefficient is 0.0208 l/h/kW (rated), and the fuel curve slope is 0.2767 l/h/kW (output). The lifetime of the considered diesel generator is 15,000 h.

The remaining properties of diesel fuel are a lower calorific value of 43.2 MJ/kg, a density of 820 kg/m3, a carbon content of 88%, and a sulfur content of 0.33%.

3.5. Converter

The selected converter is of the Occren NB type and has a rated power of 1 kW [36]. This converter converts DC voltage of 24 V or AC voltage of 220 V ± 36% and 50 Hz ± 10 Hz into AC voltage of 220 V ± 6% and 50 Hz ± 0.5 Hz [36]. The lifetime and efficiency of this converter are 15 years and 95%, respectively. The costs of investment and replacement are the same and amount to 235 $/kW. The annual O&M cost is 5 $/year. The converter powers used in the simulations are as follows: 0, 1, 2,…, 6 kW.

3.6. Batteries

The storage battery unit is assumed to consist of batteries of the Trojan type [37]. These batteries are designed for cyclic operation with a rated voltage of 12 V, a capacity of 115 Ah (1.39 kWh), and a lifetime throughput of 1212 kWh. For Trojan batteries, the costs of investment and replacement are the same and amount to 235 $ per piece, while the annual O&M cost is 5 $/year. The number of batteries used in the simulations is as follows: 0, 1, 2, 3, 4,…, 40.

4. Results and Discussion

Simulations were performed for both considered configurations consisting of MHPP, PV generator, diesel generator, converter and batteries with the option of excluding only PV generator or MHPP from the configurations (i.e., systems under consideration), as well as for each considered case of operation separately (Cases 1, 2 and 3). After 70,028 simulations and 13 min and 55 s of running HOMER Pro v. 3.16.2 software individually for each of the three cases, this software showed the categorized system solutions, i.e., categorized system configurations by profitability from the most profitable to the least profitable. From the three cases considered, the load-following strategy was chosen.

The results of the considered system configurations are given in

Table 2. Power, total NPC and total annual electricity generation for the individual components of the considered system configurations in Cases 1–3.

Component or Entire System	Power (kW)			Total NPC ($)			Total Annual Electricity Generation (kWh/Year)
	Case 1	Case 2	Case 3	Case 1	Case 2	Case 3	Case 1	Case 2	Case 3
MHHP	6.4	8.5	8.5	8468	10,132	10,132	23,444 (62.4%)	32,979 (73.7%)	38,399 (76.7%)
PV generator	10	8.25	8.25	8026	6621	6621	13,184 (35.1%)	10,877 (24.3%)	10,877 (21.7%)
Diesel generator	12	12	12	10,731	10,617	9766	936 (2.5%)	922 (2%)	814 (1.6%)
Storage battery unit	25	24	18	11,255	7750	5641	/	/	/
Converter	5	4	4	1903	1522	1522	/	/	/
Entire system	28.4	28.75	28.75	40,383	36,643	33,683	37,564 (100%)	44,777 (100%)	50,090 (100%)

and Figure 10 and Figure 11. Table 2 outlines the power, total NPC and electricity generation for the individual components of the considered system configurations in Cases 1–3. This table also contains the appropriate data on the entire system configurations. Figure 10 presents a summary of costs for the individual components of the considered system configurations over the projected lifetime in Cases 1–3. Figure 11 shows the monthly average power of the MHPP, PV generator and diesel generator for Cases 1–3.

From Table 2 it is obvious that the performance parameters of the hydro-turbine affect the design of the considered hybrid power system. Compared to Case 1, the power output and the total annual generation of electricity for the MHPP are higher in Case 2 or Case 3. In the case of the PV generator, compared to Case 1, the same parameters are lower in Cases 2 and 3. In addition, the total NPC for the entire system in Cases 2 and 3 is 9.3% and 16.6% lower than in Case 1, respectively. Also, the power output and total annual electricity generation from the entire system in Case 3 are 1.2% and 33.3% higher than in Case 1, and not different and 11.9% higher than in Case 2, respectively. The increase in the power output of the entire system from 28.4 kW to 28.75 kW can be explained as follows. By optimizing the propeller S-turbine, the power output of the MHPP increases from 6.4 kW (Case 1) to 8.5 kW (Case 2 or 3). This means that more electricity is obtained from the MHPP and less from the PV generator due to a significantly higher total NPC in the case of MHPP. Consequently, the power output of the PV generator reduces by 1.75 kW, the number of batteries used for electricity storage decreases from 25 in Case 1 to 24 in Case 2 or 18 in Case 3, and the power of the converter decreases from 5 kW in Case 1 to 4 kW in Cases 2 and 3. At the same time, the power output of the diesel generator remains unchanged, but different amounts of fuel are used, namely: 324 l in Case 1, 319 l in Case 2 and 282 l in Case 3.

Based on the models from Table 1 and the results from Table 2, the values of the levelized COE are 0.346 $/kWh for Case 1, 0.313 $/kWh for Case 2, and 0.288 $/kWh for Case 3. Table 2 also shows that the total NPC for the entire system amounts to $40,383 in Case 1, $36,643 in Case 2, and $33,683 in Case 3. Thus, the total NPC of the entire system in Case 3 is lower than in Case 1 or Case 2. However, the total annual electricity generation for the entire system in Case 3 (50,090 kWh/year) is significantly higher than in Case 1 (37,564 kWh/year) or in Case 2 (44,777 kWh/year). The value of the levelized COE obtained here is close to the values of the levelized COE obtained for hybrid hydro-PV-diesel systems considered in [4,10]. As mentioned above, it was found in [8,10] that many factors affect the total NPC and levelized COE. In this regard, the price of diesel fuel is one of those factors. The price of diesel fuel in this study is high (1705 $/l), which in this study, compared to the corresponding values from other studies, led to the increased values of the levelized COE.

The bar charts in Figure 10 show that the renewables (MHPP and PV generator) have relatively higher capital and operating costs than the diesel generator, but that the diesel generator has high fuel costs. For Case 1 from Figure 10a, the total costs referred to the storage battery unit are the highest, at $11,256. For Case 2 from Figure 10b, the total costs referred to the diesel generator are the highest, at $10,617.72. Whilst, for Case 3 from Figure 10c, the total costs of MHPP are the highest, amounting to $10,132. In all three cases the operating costs of the diesel generator are very low, amounting to $84.03 for Case 1, $82.74 for Case 2, and $73.04 for Case 3.

Figure 11 shows the monthly average power of the MHPP, PVs and diesel generator for all three considered cases. The optimized propeller S-turbine from Case 2 or Case 3 enables the operation of the MHPP at lower stream flows in July, August, September and December. Thus, the total annual electricity generation from the MHPP in Case 3 is 14,955 kWh/year higher than in Case 1, and 5420 kWh/year higher than in Case 2. The total annual electricity generation from the PV generator in Case 2 or Case 3 is 2307 kWh/year lower than in Case 1. The total annual electricity generation from the diesel generator in Case 3 is 122 kWh/year and 108 kWh/year lower than in Case 1 and Case 2, respectively. These observations are made using the data from Table 2.

Figure 12 shows hourly plots of the power output of the MHPP, PV generator and diesel generator, and hourly plots of power input of the storage battery unit for Case 1, Case 2 and Case 3. From Figure 12, it can be seen that the main electricity sources are the MHPP and PV generator and that the auxiliary electricity sources are the diesel generator and storage battery unit. Figure 12a shows that MHPP participated in electricity generation from January 1 up to June 30 with a total of 4344 h of operation during the year and a maximum power output of 5.44 kW. The PV generator provides electricity throughout the year with a total of 4383 h of operation and a maximum power output of 10.2 kW. From 1 July up to 31 December, the diesel generator participates in electricity generation with a total of 260 h of operation per year and a maximum power output of 3.6 kW. In the same period, the storage battery unit operates simultaneously with a maximum power input of 6.83 kW.

In addition, compared to Case 1 from Figure 12a, it is evident from Figure 12b that, in Case 2, the participation of MHPP in the total annual electricity generation increases from 1 July up to 30 September. In this case, the MHPP participates in electricity generation with a total of 6552 h of operation per year and a maximum power output of 7.23 kW. At the level of year in Case 2, the PV generator operates with a total of 4383 h (per year) and a maximum power output of 8.41 kW, while the diesel generator operates with a total of 256 h (per year) and a maximum power output of 6.56 kW. Compared to Case 1, the operating time of the diesel generator in Case 2 is shortened, and thus the GHG emissions.

In Case 3 from Figure 12c, there is a participation of MHPP in the generation of electricity even in December, so the operating time of MHPP is additionally increased and amounts to a total of 7296 h per year. In Case 3, the maximum power outputs of the MHPP and PV generator remain the same as in Case 2, while the maximum power input of the storage battery unit is now 4.92 kW.

For all considered cases, the operation regimes in which one of the renewable energy sources (PV generator or MHPP) fails are also simulated. Again, the objective is to optimize, that is, maximize the performance of system components. The results of these simulations are given in

Table 3. Maximum power outputs from the system components obtained for Cases 1–3 when the PV generator or MHPP is off.

Case	Power Output of MHPP (kW)	Power Output of PV Generator (kW)	Power Output of Diesel Generator (kW)	Input Power of Storage Battery Unit (kW)	Power Output of Converter (kW)
					Inverter	Rectifier
1 *	5.44	/	3.6	3	2.71	3
1 **	/	12.2	3.6	9.02	4.42	3.2
2 *	7.23	/	3.6	2.73	2.7	2.73
2 **	/	12.2	3.6	9.02	4.42	3.2
3 *	7.23	/	3.6	2.73	2.66	2.73
3 **	/	12.2	3.6	9.02	4.42	3.2

* PV generator is off. ** MHPP is off.

.

Since the diesel generator appears in all considered cases, it means that there also are GHG emissions. Concentrations of various pollutants such as CO₂, CO, SO₂, etc., are outlined in

Table 4. GHG emissions.

Pollutant	Emissions (kg/Year)
	Case 1	Case 2	Case 3
Carbon dioxide	848	835	737
Carbon monoxide	5.29	5.21	4.6
Unburned hydrocarbons	0.233	0.23	0.203
Particulate matter	0.0317	0.0313	0.0276
Sulphur dioxide	1.71	1.69	1.49
Nitrogen oxides	4.98	4.9	4.33
Total	860.25	847.06	747.65

. In particular, Table 4 shows that the total GHG emissions in Case 3 are 112.6 kg/year lower than in Case 1, and 99.41 kg/year lower than in Case 2. This is because the diesel generator participates in the total annual electricity generation with only 1.6% in Case 3, with 2% in Case 2, and with 2.5% in Case 1.

Table 5. Comparative presentation of the obtained results and the results of other studies on similar hydro-PV-diesel hybrid power systems.

Study or Reference	Total NPC ($)	Levelized COE ($/kWh)	Total Annual Electricity Generation (kWh/Year)	Main Source of Electricity Generation (kWh/Year)
This study, Case 3	33,683	0.288 $/kWh	50,090	MHPP 38,399
[4]	70,042	0.278 $/kWh	25,515	MHPP 15,493
[8]	113,201	0.054 $/kWh	227,504	MHPP 189,262
[9]	963,431	0.112 $/kWh	1,518,895	MHPP 1,178,600
[10]	/	0.131–0.206 $/kWh	/	/
[11]	997,334	0.133 $/kWh	/	MHPP 497,075
[38]	316,827	0.566 $/kWh	55,344	MHPP 45,144
[39]	6,804,257	/	101,572	MHPP 55,885
[40]	2,650,126	0.5611 $/kWh	620,002	MHPP 508,874

compares the obtained results with the results of other studies dealing with similar hydro-PV-diesel hybrid power systems. It follows from Table 5 that the lowest value for the total NPC is obtained in this study. The values of the levelized COE and total annual electricity generation vary depending on the cost of individual system components, system size, and other factors listed in Table 1. In each of the studies outlined in Table 5, the associated MHPP has the largest contribution to the total annual electricity generation, which was one of the reasons for performing the optimization of the considered off-grid system based on the performance of the propeller S-turbine.

5. Conclusions

Based on the obtained results, it can be concluded that the remote trout pond of Jablanica, located in eastern Serbia, could be independently and efficiently powered by the considered hydro-PV-diesel-converter-battery hybrid system using hydropower from the settling basin overflow. In that case, the characteristics of the settling basin overflow can be used to optimize the design of the hydro-turbine, and thus the entire off-grid hybrid power system. The optimization and techno-economic analysis of the considered hydro-PV-diesel-converter-battery hybrid power system were successfully performed using HOMER Pro v. 3.16.2 software for two different types of hydro-turbine and three different cases of operation.

The first type of hydro-turbine (having fixed propeller blades and fixed guide vanes) was designed for a flow rate of 265 l/s through the settling basin (Case 1). Whilst, the second type of hydro-turbine (having fixed propeller blades and adjustable guide vanes) was designed for a flow rate of 350 l/s through the same settling basin (Case 2 and Case 3). In Case 2, it was taken into account that the hydro-turbine can operate with low efficiency in the summer months and in dry years, namely: with a flow rate that is 20% smaller than the annual average flow rate through the settling basin. In Case 3, it was taken into account that the operation of the hydro-turbine can be more efficient in the winter months. In Case 2 and Case 3, it was also assumed that the guide vanes are adjustable so that the hydro-turbine can operate all year round, regardless of the flow rate through the settling basin.

Specifically, this study compares three optimal solutions obtained for two different configurations of the considered hydro-PV-diesel-converter-battery hybrid power system, each of which was selected automatically from a set of 70,028 simulation results using HOMER Pro v. 3.16.2 software. The simulation results showed that the optimal configuration of the off-grid hybrid power system in Case 3 should consist of 8.5 kW MHPP, 8.25 kW PV generator, 12 kW diesel generator, 4 kW converter and 18 storage batteries. In this regard, it was also shown that the considered modification of hydro-turbine performance can affect (i.e., improve) the performance of the entire off-grid hybrid power system. In particular, this modification can increase the power output of the MHPP from 6.4 kW to 8.5 kW, as well as the total annual electricity generation of the entire system from 37,564 kWh/year in Case 1 to 44,777 kWh/year in Case 2 or 50,090 kWh/year in Case 3, which is an increase of 19.2% (Case 2) or 33.3% (Case 3) compared to Case 1.

In addition, the modification can reduce the total NPC of the entire system from 40,383 $ in Case 1 to 36,643 $ in Case 2 or 33,683 $ in Case 3, which is a decrease of 9.3% (Case 2) or 16.6% (Case 3) compared to Case 1. This can also reduce the levelized COE from 0.346 $/kWh in Case 1 to 0.313 $/kWh in Case 2 or 0.288 $/kWh in Case 3, which is a decrease of 9.5% (Case 2) or 16.8% (Case 3) compared to Case 1. Moreover, the same modification can reduce GHG emissions of the entire system from 860.25 kg/year in Case 1 to 847.06 kg/year in Case 2 or 747.65 kg/year in Case 3, which is a decrease of 1.5% (Case 2) or 13.1% (Case 3) compared to Case 1. Similarly, compared to Case 1, the reductions in the number and power of PV panels, converters and batteries obtained in Case 2 and Case 3 were the results of the same modification of hydro-turbine performance.

The analysis of the obtained results and the results collected from other relevant studies resulted in the conclusion that the associated MHPP usually had the largest contribution to the total annual electricity generation from the given hydro-PV-diesel-converter-battery hybrid system. This study proposed a generally applicable approach to further increase the contribution of any MHPP in the total annual generation of electricity from the proposed hybrid power system. Finally, fishponds and farms of different kinds, which will be constructed along clear mountain rivers, will always be good places to apply the proposed approach.