# Optimal Coordination of Wind Power and Pumped Hydro Energy Storage

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## Abstract

**:**

_{CO2}) and conventional grid energy purchases are reduced by 24.69% and 24.68%, respectively. Moreover, it is shown that the benefits of adding hydro storage, combined with increasing the number of wind turbine units, reduces the cost of energy of renewables (COE

_{Renewables}). Therefore, combining hydro storage with wind power is economically, environmentally, and technically a more efficient alternative to the conventional power generation.

## 1. Introduction

_{PS}) was optimally minimized. The economically feasible solution was considered to find detailed solutions. This work aims to help decision-makers find the best technical solutions before actual implementation of the proposed energy configuration.

## 2. Description of the Proposed System

_{PS}). Then, based on the best fitness, many indicating corresponding functions were computed, such as the wind and hydro fraction (WH

_{f}), grid purchases, the footprint of the renewables, and carbon dioxide emissions (E

_{CO2}). This procedure aimed to help design engineers replicate the same criteria to find optimal solutions for other system configurations to be adopted based on these technical studies and negotiations between electric utilities and investors. Economic, technical, and environmental feasibility impacts were also studied.

#### 2.1. PHS Station Data

#### 2.2. Wind Speed and Probability Distribution Function

_{R}(v)) is given by Equation (1) [20,21].

_{a}is the average wind speed in a specific area in (m/s). The wind speed logarithmic law shown in Equation (2) was used to model the variation of wind speed due to the difference in height between the anemometers of the metrological station and the hub of the proposed wind turbine. In addition, it considered the terrain roughness between two altitudes [12,22].

_{0}is the wind speed corresponding to the height (H

_{0}) and Z

_{0}is the roughness coefficient. A case study was conducted in Aqaba, which is the free Trade Area in Jordan. The wind speed was measured in a specific location using anemometer installed at 45 m above ground level, in which the output data was taken on a monthly average basis. Then, Rayleigh distribution was used to obtain hourly data, as shown in Figure 2. The roughness factor of the logarithm used for this case was 0.03 to adjust for the wind speed of open terrain areas [22]. Also, the hub height of the proposed wind turbine was 80 m (Table 2) which was also considered in the logarithm. The wind speed-based Rayleigh distribution function in Aqaba for twelve months is shown in Figure 2.

_{WF}) was computed using Equation (3). L and W are the dimensions of the wind farm, which was considered to have a rectangular shape. For the row spacing (RS) and column spacing (CS) values shown in Table 3, Equations (4) and (5) were used to calculate L and W.

_{r}, N

_{row}, and N

_{col}are the rotor diameter, number of rows, and number of columns, respectively. These helped to compute the maximum and minimum wind areas, i.e., the A

_{max}and A

_{min}. A footprint cap limit of 20,000 Dunam was considered for the on-grid wind hydro energy system.

#### 2.3. Load Demand Hourly Data

## 3. Mathematical System Formulation

#### 3.1. Modeling of the Hydro Station

_{rated}, in kW was optimized, the energy in kWh, W

_{rated}, was estimated based on the assumption made in Section 2.1. Then, the potential energy (in J/m

^{3}), W

_{J}, and (in kWh/m

^{3}), W

_{kWh}, of water in the upper reservoir were computed using Equation (6) and Equation (7), respectively.

_{water}is the density of water (1000 kg/m

^{3}), g is the gravitational acceleration (9.81 m/s

^{2}), and H is the actual head of the PHS station [12].

^{3}), V

_{water}, was computed using Equation (8). At this point, the area required for the PHS station, A

_{PHS}, was computed using Equation (9) for a given mean depth, D [12]. Furthermore, Equation (10) was used to compute the water flow (F

_{water}) in the pipeline in (m

^{3}/s) [23].

#### 3.2. Modeling of the Wind Turbine Power Curve

_{R}), while Region 2 exists between V

_{R}and the cut-out wind speed [6], as shown in Figure 4. This shows the ideal model representation of a wind turbine and the corresponding main regions.

_{R}is the rated power generated by a wind turbine. Further, the corresponding A, B and C parameters are given in Equations (12)–(14) [9,24,25]. This model is different from the ones described in [12]. The output power in Region 1 runs smoothly between V

_{I}and V

_{R}with no protrusions at the cut-in value, as shown in the models described in [12], see Figure 5. This will result in an accurate computation of the output power extracted from the wind farm. This leads to precise computations in the output wind power and energy and thus in the number of units sizing, geographical footprint, economic and environmental indicators.

#### 3.3. Objective Function

_{PS}) to reflect the price of the energy supplied by the on-grid hybrid wind hydropower system, as designed and sized to cover the load demand shown in Figure 3. It was computed by dividing the system’s cost by the system’s absorbed energy, as shown in Equation (15) [26].

#### 3.4. Indicators of the Objective Function

_{PS}. These included the wind and hydro fraction (WH

_{f}), as shown in Equation (16), and carbon dioxide emissions (E

_{CO2}).

_{CO2}was computed by summing up the hourly multiplied grid energy purchases with a grid emission factor of 583.866667 gCO

_{2}/Wh.

## 4. Optimization Toolbox of Matlab

- Create initial population (usually a randomly generated string);
- Evaluate all the individuals (apply some function or formula to the individuals);
- Select a new population from the old population based on the fitness of the individuals and the required objective function;
- Apply some genetic operators (mutation, crossover, and inversion) to the population members to create new individuals;
- Evaluate the newly created individuals based on the required objective function.

## 5. Results and Discussion

_{PS}) and the rest of the corresponding indicators. Table 4 shows the results obtained using the GA, SA, and PS solvers. Also, many data corresponding to the optimal value of the COE

_{PS}are included in Table 4. The three aforementioned solvers of the Matlab optimization toolbox were selected to solve the problem described in this paper. The SA and PS solvers provided solutions that were 1.27634% and 1.98903% higher than the GA solution, respectively. Therefore, the GA solution was found to be feasible compared with the other solutions.

_{PS}values. The optimal value of the COE

_{PS}, which was found using the GA, is shown in Figure 6. This value was 28.7% less than the energy bought from the conventional electric network, which is an excellent indication for the economic feasibility of this suggested configuration.

_{CO2}in the suggested location was 634.645 kt/year [12], therefore, the emissions were mitigated by 68.66%, assuming that the renewable configuration in Figure 1 was adopted. Also, the geographical area of renewable plants (A

_{Renewables}) was increased. However, only 48.91% of the geographical area limit was used to install the designed hydro-wind energy system. Thus, the rest of the area (51.09%) could be used in the future as load demand and the system size grow.

_{discounted}) were calculated. The CF in Table 5 included the total cost found before in Table 4 using GA, and the energy savings of the renewable energy system. These energy savings were computed by multiplying the yearly renewable generation (436.438 GWh) by the energy purchased price of electric utilities in Jordan. Afterward, the CCF values were computed by cumulatively adding the discounted cost values. Then, the time to get back the total cost value was calculated using Equation (17). Note that Table 5 shows only 15 years of the 50-year project life-time, because the aim was to obtain a positive cost value from the CCF, which was held at the 11th year. This was just before the time when the total cost was retrieved. Table 5 shows that the DPP was computed to be around 10.271 years (10 years, 3 months, and 7 days).

_{l}is the year number at the last negative cost value of the CCF.

_{PS}and the grid purchases were reduced by 16.93% and 24.68%, respectively, showing the importance of the storage system for wind power that fluctuates naturally. These cost and emissions reductions are significant, especially for non-oil producing countries, such as Jordan, which imports around 96% of its energy needs as oil and natural gas. The carbon emissions reduction was improved compared with the wind-only system. Furthermore, renewable penetration increased by 56.64% as a result of adding the PHS system, resulting in a more environmentally friendly power system.

## 6. Conclusions

_{PS}). A wind–hydro grid connected power system was proposed as an adjunct to an existing power grid. This was mathematically modeled and then coded in Matlab. The GA of the Matlab optimization toolbox was used to find the optimal feasible value of the COE

_{PS}, which was 0.0955388 $/kWh. This was 28.7% less than the conventional energy from the power grid. The discounted payback period was 10 years, 3 months, and 7 days. Furthermore, carbon emissions were reduced by 68.66% compared with experimentally estimated data. As a result, the grid energy purchases were also reduced. Specifically, comparing the system described in this study with the formerly studied on-grid wind-only system showed that the COE

_{PS}, E

_{CO2}, COE

_{Renewables}, and grid energy purchases were reduced by 12.26%, 24.69%, 1.52%, and 24.68%, respectively. These are very promising results, especially for oil-importing countries, such as Jordan, where imported energy is a significant financial burden to the economy. The proposed wind power system with hydro storage is recommendable for its clean and economical features, compared with the conventional fossil-fueled grid or wind-only on-grid renewable configurations.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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

Lifetime | Years | 50 [16] |

Usable state of charge [1] | % | 85 |

Roundtrip efficiency (ζ) | % | 85 [17] |

Capital cost | $/kW | 1651.04 |

Operation and maintenance cost (OMC) | (%/Year of capital cost (CC)) | 1.5 |

Gross head | m | 50 |

Mean water depth | m | 15 |

Turbine | |

Manufacturer | USA |

Power | |

Rated power | 2.5 MW |

Cut-in wind speed | 4.0 m/s |

Rated wind speed | 12.5 m/s |

Cut-out wind speed | 25.0 m/s |

Survival wind speed | 70.0 m/s |

Rotor | |

Diameter | 96.0 m |

Swept area | 7238 m^{2} |

Number of blades | 3 |

Maximum rotor speed | 15.5 U/min |

Tip speed | 78 m/s |

Type | 46.7 |

Material | Fiberglass |

Power density | 345.4 W/m^{2} |

Gearbox | |

Type | Spur |

Stages | 2.0 |

Tower | |

Hub height | 80.0 m |

Type | Steel tube |

Shape | conical |

Corrosion protection | painted |

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

Life-time per unit | Years | 20 |

Row spacing of the farm (RS) | m | 384 |

Column spacing of the farm (CS) | m | 672 |

**Table 4.**Detailed results of the optimized system using genetic algorithm (GA), simulated annealing (SA), and pattern search (PS) algorithms.

Parameter | Value (GA) | Value (SA) | Value (PS) |
---|---|---|---|

COE_{PS} ($/kWh) | 0.0955388 | 0.0967582 | 0.0974391 |

E_{CO2} (kt/year) | 198.9044 | 204.5988 | 207.5809 |

COE_{Renewables} ($/kWh) | 0.0631 | 0.0637 | 0.0641 |

Number of WTs | 47 | 45 | 44 |

A_{max} (m^{2}) | 9,676,800 | 7,142,400 | 8,506,368 |

A_{max} (Dunam) | 9676.800 | 7142.400 | 8506.368 |

A_{min} (m^{2}) | 6,856,704 | 6,561,792 | 6,266,880 |

A_{min} (Dunam) | 6856.704 | 6561.762 | 6266.880 |

Total cost (M$) | 441.3 | 426.37 | 419.44 |

WH_{f} (%) | 56.1427 | 54.3791 | 53.4641 |

Grid purchases cost (M$) | 45.649 | 46.956 | 47.641 |

Grid energy purchases (GWh) | 340.67 | 350.42 | 355.53 |

P_{rated} (PHS) (kW) | 18,118.5 | 19,226.37 | 20,039.45 |

E_{rated} (PHS) (kWh) | 181,185 | 192,263.7 | 200,394.5 |

W_{J} (J/m^{3}) | 4.905 × 10^{5} | ||

W_{kWh} (kWh/m^{3}) | 0.136359 | ||

V_{water} (m^{3}) | 1.56322 × 10^{6} | 1.65880 × 10^{6} | 1.72895 × 10^{6} |

A_{PHS} (in m^{2}) | 104,214.902 | 110,586.803 | 115,263.501 |

A_{PHS} (in Dunam) | 104.2149 | 110.5868 | 115.2635 |

F_{water} (m^{3}/s) | 43.457 | 46.115 | 48.065 |

Year (N) | PVF | CF (M$) | CF_{discounted} (M$) | CCF (M$) |
---|---|---|---|---|

0 | 1.000 | −441.300 | −441.300 | −441.300 |

1 | 0.944 | 58.483 | 55.234 | −386.066 |

2 | 0.892 | 58.483 | 52.165 | −333.901 |

3 | 0.842 | 58.483 | 49.267 | −284.633 |

4 | 0.796 | 58.483 | 46.530 | −238.103 |

5 | 0.751 | 58.483 | 43.945 | −194.158 |

6 | 0.710 | 58.483 | 41.504 | −152.654 |

7 | 0.670 | 58.483 | 39.198 | −113.456 |

8 | 0.633 | 58.483 | 37.020 | −76.436 |

9 | 0.598 | 58.483 | 34.964 | −41.472 |

10 | 0.565 | 58.483 | 33.021 | −8.451 |

11 | 0.533 | 58.483 | 31.187 | 22.736 |

12 | 0.504 | 58.483 | 29.454 | 52.190 |

13 | 0.476 | 58.483 | 27.818 | 80.008 |

14 | 0.449 | 58.483 | 26.272 | 106.280 |

15 | 0.424 | 58.483 | 24.813 | 131.093 |

DPP (Years) | 10.27096862 |

Parameter | Percentage Increase (+) or Decrease (−) in % |
---|---|

COE_{PS} | −12.26 |

E_{CO2} | −24.69 |

COE_{Renewables} | −1.52 |

Number of WTs | +104.35 |

A_{Renewables} (max) | +71.14 |

A_{Renewables} (min) | +21.79 |

Total cost | +110.83 |

WH_{f} | +56.64 |

Grid purchases cost | −24.69 |

Grid energy purchases | −24.68 |

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## Share and Cite

**MDPI and ACS Style**

Al-Masri, H.M.K.; Al-Quraan, A.; AbuElrub, A.; Ehsani, M.
Optimal Coordination of Wind Power and Pumped Hydro Energy Storage. *Energies* **2019**, *12*, 4387.
https://doi.org/10.3390/en12224387

**AMA Style**

Al-Masri HMK, Al-Quraan A, AbuElrub A, Ehsani M.
Optimal Coordination of Wind Power and Pumped Hydro Energy Storage. *Energies*. 2019; 12(22):4387.
https://doi.org/10.3390/en12224387

**Chicago/Turabian Style**

Al-Masri, Hussein M. K., Ayman Al-Quraan, Ahmad AbuElrub, and Mehrdad Ehsani.
2019. "Optimal Coordination of Wind Power and Pumped Hydro Energy Storage" *Energies* 12, no. 22: 4387.
https://doi.org/10.3390/en12224387