# Integrating Hydrokinetic Energy into Hybrid Renewable Energy System: Optimal Design and Comparative Analysis

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## Abstract

**:**

_{2}emissions. Solar and wind technologies have been mostly developed to meet the energy demand of off-grid remote areas or locations without grid connections. However, it is well-known that the power generation of these resources is affected by daily fluctuations and seasonal variability. One way to mitigate such an effect is to incorporate hydrokinetic resources into the energy system, which has not been well investigated yet. Therefore, this study examines the prospects of designing a hybrid system that integrates hydrokinetic energy to electrify an off-grid area. Hydrokinetic energy generation depends on water flow velocity (WFV). We estimate WFV by a model-based approach with geographical and weather data as inputs. Together with the models of the other components (wind turbine, PV panel, battery, and diesel generator) in the micro-grid, an optimization problem is formulated with the total net present cost and the cost of energy as performance criteria. A genetic algorithm (GA) is used to solve this problem for determining an optimal system configuration. Applying our approach to a small community in Nigeria, our findings show that the flow velocity of a nearby river ranges between 0.017 and 5.12 m/s, with a mean velocity of 0.71 m/s. The resulting optimal micro-grid consists of 320 kW of PV, 120 units of 6.91 kWh batteries, 2 (27 kW) hydrokinetic turbines, an 120 kW converter, zero wind turbines, and a 100 kW diesel generator. As a result, the total energy generated will be 471,743 kWh/year, of which 12% emanates from hydrokinetic energy. The total net present cost, the cost of energy, and the capital cost are USD 1,103,668, 0.2841 USD/kWh, and USD 573,320, respectively.

## 1. Introduction

^{3}/s, and the hydrokinetic potential in the northern part of the country is estimated at 66.18 MW, while that of the southern part is 42.97 MW. Chen et al. [28] observed that the discharge at the Yangtze River in China has an annual average of 3.0 × 10

^{4}m

^{3}/s. The authors in [29] proposed a flow velocity model for assessing the available hydrokinetic energy in Amazon in Brazil. The authors concluded that the highest and lowest average velocities in the Amazon River were 2.27 m/s and 0.735 m/s, respectively, and the energy potential ranges between 0.1 and 1488.6 kW. In comparison to meteorological data, which are readily available and used for solar and wind energy applications, there is a paucity of information for a worldwide database that evaluates the flow velocity and energy potential of each river network [30], hence, limiting the application of hydrokinetic power. Moreover, the predominance of hydropower, due to its predictability, high efficiency, and high energy output, has made hydrokinetic power less of a focus. However, rural and remote areas without a grid connection can benefit from clean, safe, and sustainable energy emanating from free-flowing water [31].

## 2. Evaluation of Flow Velocity

#### 2.1. Estimation of Cumulative Abstraction

#### 2.2. Estimation of the Evapotranspiration

^{2}/d), $M$ is the advection energy (MJ/m

^{2}/d), $l$ is the latent heat of vaporization (MJ/kg), $f\left({U}_{2}\right)$ is a linear approximated wind function relating to the wind speed (m/s) measured at 2 m height, ${e}_{s}$ is the saturated vapor pressure (kPa), and ${e}_{a}$ is the vapor pressure (kPa).

^{−3}(MJ/kg/°C), $l$ is the latent heat of vaporization, 2.45 (MJ/kg), and $p$ is the atmospheric pressure (kPa), which is a function of the elevation of the location, expressed as follows [73]:

^{2}/d), and $\propto $ is the albedo, the fraction of solar radiation reflected by the surface. Its value can range between 0.05 and 0.95. ${Q}_{a}$ is the extra-terrestrial solar radiation (MJ/m

^{2}/d), $n$ is the duration of sunshine for the day (hours), $N$ is the maximum possible duration of sunshine or daylight hours (hours), $\sigma $ is the Stefan–Boltzmann constant, 4.903 × 10

^{−9}(MJ/K

^{4}/m

^{2}/d), $T$ is the air temperature (°C), and ${e}_{a}$ is the actual vapor pressure (kPa).

^{2}/d), and ${R}_{n}$ is the net radiation. The parameter $B$ denotes the effective long-wave radiation that will occur if the surface temperature equals the air temperature, which can be estimated as follows [70]:

#### 2.3. Estimation of the Base Flow

^{3}/s), and ${A}_{ch}$ is the cross-sectional area of the channel (m

^{2}). The cross-sectional area of the channel is expressed as follows:

## 3. System Modeling of the Proposed HRES

#### 3.1. PV Model

^{2}), ${G}_{STC}$ is the solar irradiance level at the standard test condition (STC) with a value of 1 kW/m

^{2}, ${\mathsf{\lambda}}_{p}$ is the temperature coefficient (%/°C), ${T}_{c}$ is the cell operating temperature (°C), and ${T}_{c,STC}$ is the cell temperature measured at STC with 25 °C. Moreover, the cell temperature ${T}_{c}$ is expressed as follows [88]:

^{2}, ${n}_{pv}$ is the PV conversion efficiency (%), and $\tau \alpha $ is the effective solar transmittance–absorptance of the PV with an assumed value of 0.9.

#### 3.2. Wind Power Model

^{2}), ${V}^{in}$ is the cut-in speed, (m/s), ${V}^{out}$ is the cut-out speed (m/s), ${C}_{p}$ is the power coefficient of performance,${P}^{rate}$ is the rated power of the wind turbine (kW) at a rated speed of ${V}^{rate}$ (m/s), while $\mathsf{\rho}$ is the air density (kg/m

^{3}). The total power generated by multiple wind turbines will be as follows:

#### 3.3. Hydrokinetic Model

^{2}), ${\mathsf{\rho}}_{w}$ is the density of water (kg/m

^{3}), ${\mathsf{\eta}}_{HKT}$ is the combined HKT-generator efficiency,${C}_{p,H}$ is the HKT power coefficient, ${{v}_{w}}^{in}$ is the cut-in water velocity, ${{v}_{w}}^{out}$ is the cut-out water velocity, ${{v}_{w}}^{rate}$ is the rated water velocity, and ${{P}_{HKT}}^{rate}$ is the rated power of HKT.

#### 3.4. Battery Storage Model

#### 3.5. Diesel Generator Model

#### 3.6. Power Converter Model

## 4. Problem Formulation and Solution Approach

## 5. A Case Study

#### 5.1. Data Acquisition for Estimating the Flow Velocity

^{2}. Using the DEM, soil data is obtained from the digital soil map of the world [105]. Further descriptions of the datasets used with their corresponding sources are tabulated in Table 4. The composition of the soil data, as seen from the soil map in Figure 4 and Table 5, shows that the study area comprises clayey soil, loamy soil, and water bodies.

#### 5.2. Meteorological Data for HRES

^{2}/d in February, with an annual average of 4.70 kWh/m

^{2}/d. As expected, there is a daily variation of solar radiation for different days and seasons of the year. Radiation values for a typical day in January are usually higher than in July due to the seasonal variations.

#### 5.3. Load Demand

#### 5.4. Component Specification of the HRES

## 6. Results and Discussions

#### 6.1. Results of Flow Velocity

^{3}/s, respectively. A breakdown of the monthly discharge, as depicted in Table 9, indicates that the maximum discharge occurs in September, while the minimum is in December. Moreover, the months of May to October have the highest discharge values (greater than 85 m

^{3}/s). This is not surprising because these months fall under the wet months in Nigeria (the dry season starts around November and runs till April, while the wet season starts around May and runs till October).

^{3}/s is the primary source of discharge to the river channel. In Figure 7b, the discharge to the river comes from both direct and base flows, due to the wet months (1st September to 31st October) with significant rainfall. The precipitation ranges between 0.39 and 73 mm within this period.

^{3}/s, resulting in a flow velocity of 0.024 m/s. Similarly, in region D (13th–18th March), the base flow has a constant value of 2.95 m

^{3}/s, resulting in a flow velocity of 0.12 m/s.

#### 6.2. Results of the Off-Grid HRES

#### 6.2.1. Economic Evaluation

#### 6.2.2. Technical Evaluation

^{2}, and the power output from the PV is increased to 42.56 kW. The total renewable power produced is 42.86 kW, greater than the load demand of 29.51 kW. Thus, the excess energy is charged to the battery bank, then increasing the battery energy to 691.87 kW. There is a load deficit at 76:00 h and 77:00 h because the system fails to satisfy the demand of 25.5 kW and 22 kW, respectively. This is because there is no generation from PV, a minimal generation from HKT, and the battery reaches its minimum energy level (331.68 kWh). Since the load demand in this period is not within the bounds of the DG, there will be no dispatched power from the DG. However, at 78:00 h, the DG will be active and, together with the HKT, will supply the load demand of 31.35 kW.

#### 6.2.3. Comparison with the DG-Only System

## 7. Conclusions

- A detailed model of estimating the flow velocity of a river using the water transportation process has been presented in this study. The discharge results show that the maximum, minimum, and mean annual discharge are 122.90, 0.395, and 14.52 m
^{3}/s, respectively. Moreover, our result further indicates that the maximum velocity obtained is 5.12 m/s, while the minimum and mean velocities are 0.017 m/s and 0.71 m/s, respectively. This model-based method will benefit off-grid areas that do not have the requisite manpower to obtain measured or observed data. - The studied community has the potential to harness both solar and hydrokinetic energy. Moreover, wind technology is not an economically viable option compared to others due to the estimated low wind speed obtained in the area and the high cost of the wind generation component.
- The optimization result using GA shows that the optimal system architecture consists of 320 kW of PV panels, 120 units of 6.91 kWh batteries, two (27 kW) hydrokinetic turbines, 120 kW converters, zero wind turbines, and a 100 kW diesel generator. The total net present cost, cost of energy, and capital cost of the system are USD 1,103,668, 0.2841 USD/kWh and USD 573,320, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Transportation process of the water cycle [63].

AMC Level | Total 5-Day Antecedent Rainfall ($\mathit{P}$) (mm) | |
---|---|---|

Dry season | Wet season | |

I | $P<13$ | $P<36$ |

II | $13\le P\le 28$ | $36\le P\le 53$ |

III | $P>28$ | $P>53$ |

Parameter | ${\mathit{S}}_{\mathit{P}\mathit{V}}$ (kW) | ${\mathit{N}}_{\mathit{w}}$ (Unit) | ${\mathit{N}}_{\mathit{H}\mathit{K}\mathit{T}}$ (Unit) | ${\mathit{N}}_{\mathit{B}\mathit{a}\mathit{t}}$ (Unit) | ${\mathit{S}}_{\mathit{D}\mathit{G}}\left(\mathbf{k}\mathbf{W}\right)$ | $\mathit{L}\mathit{S}\mathit{P}\mathit{S}\left(\mathit{\%}\right)$ |
---|---|---|---|---|---|---|

Lower bound | 0 | 0 | 0 | 0 | 80 | 0 |

Upper bound | 500 | 10 | 5 | 300 | 300 | 2 |

Parameter | Value |
---|---|

Population size | 50 |

Maximum number of iterations | 500 |

Crossover fraction | 0.8 |

Function tolerance | 1e-6 |

Constraint tolerance | 1e-3 |

Selection function | Stochastic uniform |

Data Type | Description | Resolution | Remark | Source |
---|---|---|---|---|

Topography map | Digital elevation model (DEM) | 30 m × 30 m | Shuttle Radar Topography Mission | SRTM [104] |

Land use map | Land use | 30 m | Landsat Mission | Landsat 7 [106] |

Soil map | Soil type and texture | 10 km | Digital Soil Map of the World | DSMW [105] |

Weather data | Solar radiation, wind speed, precipitation, etc. | Prediction of Worldwide Energy Resources | NASA [103] |

S/N | Description | Area (km^{2}) | % of the Area |
---|---|---|---|

1 | Clayey loam | 45.32 | 24.52 |

2 | Loam | 89.76 | 48.57 |

3 | Water bodies | 49.72 | 26.91 |

S/N | Description | Area (km^{2}) | % of the Area |
---|---|---|---|

1 | Barren land | 10.26 | 5.58 |

2 | Residential | 2.28 | 1.24 |

3 | Forest, woods, and swamps | 56.08 | 30.48 |

4 | Pasture | 30.69 | 16.68 |

5 | Agricultural | 41.62 | 22.62 |

6 | Bare soil | 27.85 | 15.14 |

7 | Water | 15.19 | 8.26 |

Month | Jan. | Feb. | March | April | May | June | July | Aug. | Sept. | Oct. | Nov. | Dec. |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Solar radiation (kWh/m^{2}/d) | 5.79 | 5.91 | 5.49 | 5.29 | 4.60 | 3.67 | 3.64 | 4.33 | 4.30 | 4.76 | 5.40 | 5.60 |

Wind speed (m/s) | 3.35 | 3.65 | 3.94 | 3.92 | 2.83 | 4.56 | 5.27 | 5.38 | 4.89 | 4.11 | 2.97 | 3.00 |

Temperature (°C) | 26.17 | 27.07 | 27.32 | 27.16 | 26.78 | 25.88 | 25.10 | 24.85 | 25.09 | 25.59 | 26.23 | 26.30 |

PV Module | Model: CS6X-325P. Manufacturer: Canadian Solar. Rated capacity: 325 W. Module type: polycrystalline. Efficiency: 16.94%. Temperature power coefficient: −0.41(%/°C). Operating temperature: −40 °C to +85 °C. Lifetime: 25 years [108]. Derating factor: 80%. Capital cost: 664 USD/kW. Replacement cost: 580 USD/kW [109]. Operation and maintenance cost (USD/year): 2% of capital cost. |

Wind Turbine | Model: EO25III. Manufacturer: Eocycle. Rated capacity: 25 kW. Cut-in wind speed: 2.75 m/s. Cut-out wind speed: 20 m/s. Rotor diameter: 15.8 m. Lifetime: 20 years [110]. Capital cost: USD 175,000 [111]. Replacement cost: USD 120,000. Operation and maintenance (USD/year): 5% of capital cost. |

Hydrokinetic Turbine | Model: TIGRIS-27 H. Rated capacity: 27 [email protected] m/s. Cut-in water velocity: 0.5 m/s. Lifetime: 20 years. Number of blades: 3 Rotor diameter: 3 m. Power coefficient: 0.43 [112]. Capital cost: 1150 USD/kW [113]. Replacement: 1000 USD/kW. Operation and maintenance cost (USD/year): 5% of capital cost. |

Storage Battery | Model: Surrette 6CS25P. Manufacturer: Rolls. Type: Lead–acid. Nominal voltage: 6V. Nominal capacity: 6.91 kWh. Round trip efficiency: 80%. [114]. Lifetime: 5 years. Capital cost: 271 USD/kWh [115]. Replacement cost: 200 USD/kWh. Operation and maintenance cost (USD/year): 0.5% of the capital cost. |

Power converter | Model: S219cph. Manufacturer: Leonics. Rated capacity: 5 kW. DC input voltage: 48 Vdc. Efficiency: 96% [116]. Lifetime: 10 years. Capital cost: 245 USD/kW. Replacement cost: 245 USD/kW [117]. Operation and maintenance cost (USD/year): 4% of capital cost. |

Diesel generator | Model: DE150E0. Manufacturer: CAT. Engine speed: 1500 RPM. Lifetime: 60,000 h. Voltage: 400/230 Vac. Frequency: 50 Hz [118]. Fuel price: 0.7 USD/L. Capital cost: 447 USD/kW [119]. Replacement cost: 400 USD/kW. Operation and maintenance cost (USD/h): 0.4. |

Month | Jan. | Feb. | March | April | May | June | July | Aug. | Sept. | Oct. | Nov. | Dec. |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean discharge (m^{3}/s) | 1.48 | 1.07 | 6.98 | 2.75 | 13.82 | 31.33 | 17.39 | 29.15 | 33.15 | 26.62 | 9.05 | 0.75 |

Max discharge (m^{3}/s) | 9.82 | 10.91 | 32.18 | 19.51 | 96.57 | 103.4 | 109.6 | 85.10 | 122.9 | 86.92 | 30.04 | 5.33 |

Min discharge (m^{3}/s) | 0.58 | 0.59 | 2.96 | 1.25 | 4.83 | 10.49 | 5.95 | 10.79 | 11.66 | 9.44 | 3.31 | 0.39 |

Capital Cost (USD) | Replacement Cost (USD) | OM Cost (USD) | Fuel Cost (USD) |
---|---|---|---|

44,700 | 47,541 | 29,897 | 1,467,800 |

System | TNPC (USD) | COE (USD/kWh) | Capital Cost (USD) | Fuel Cost (USD) | DG Operation (h/year) | Fuel Consumed (L/year) | Total Load Served (kWh/year) |
---|---|---|---|---|---|---|---|

DG-only | 1,589,918 | 0.5182 | 44,700 | 1,467,763 | 5925 | 166,220 | 233,320 |

Optimal HRES | 1,103,668 | 0.2841 | 573,320 | 34,822 | 141 | 3943.5 | 307,940 |

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**MDPI and ACS Style**

Ileberi, G.R.; Li, P.
Integrating Hydrokinetic Energy into Hybrid Renewable Energy System: Optimal Design and Comparative Analysis. *Energies* **2023**, *16*, 3403.
https://doi.org/10.3390/en16083403

**AMA Style**

Ileberi GR, Li P.
Integrating Hydrokinetic Energy into Hybrid Renewable Energy System: Optimal Design and Comparative Analysis. *Energies*. 2023; 16(8):3403.
https://doi.org/10.3390/en16083403

**Chicago/Turabian Style**

Ileberi, Gbalimene Richard, and Pu Li.
2023. "Integrating Hydrokinetic Energy into Hybrid Renewable Energy System: Optimal Design and Comparative Analysis" *Energies* 16, no. 8: 3403.
https://doi.org/10.3390/en16083403