# Mixing Renewable Energy with Pumped Hydropower Storage: Design Optimization under Uncertainty and Other Challenges

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Proposed Layout

^{2}and a permanent population of 2755 residents, as per the 2021 census conducted by the Hellenic Statistical Authority. Sifnos attracts an average of 100,000 tourists during the summer months. Its energy needs are mainly covered by a 9.0 MW oil power plant, while renewables have a small share in the island’s energy mix. Specifically, there is a 1.20 MW wind park and two photovoltaic parks of 0.20 MW cumulative installed power. According to an analysis of the island’s energy profile for 2020, performed by the Hellenic Electricity Distribution Network Operator, the total energy demand was 17.3 GWh, while the hourly peak demand was 5.4 MW, occurring during the summer months.

^{3}. This capacity ensured energy autonomy for up to consecutive 16 days, starting from a fully charged state and without storing any excess energy during that time span.

## 3. HRES Simulation and Optimization

#### 3.1. Configuration and Key Assumptions of the Simulation

_{0}is the freestream wind speed at the hub height level, a is an induction factor, k is a decay coefficient, L is the distance between the turbines, and D

_{L}is the large turbine’s blade diameter. The a and k values are set equal to 0.10 and 0.038, respectively, as suggested in [34]. In our case, we considered the use of four wind turbines, i.e., two large ones with 2.3 MW and two small ones with 0.9 MW of nominal power, respectively, distanced at 400 m. It is important to remark that the greater distance between the turbines might initially seem ideal, since the associated wind speed reduction is reduced; however, it does not necessarily result in optimal layouts [35].

_{min}is the minimum power produced during cut-in conditions, P

_{max}is the rated power, V

_{wind}is the actual wind speed, V

_{min}is the cut-in wind speed, V

_{max}is the cut-out wind speed, and a and b are the shape parameters. The two parameters were calibrated against the empirically derived power curve data provided by the manufacturer. For the wind turbine types used in our simulation, we obtained a = 2.25 and b = 20. The aforementioned formula can accurately describe the wind speed-to-power conversion process, as it considers turbine-specific characteristics, unlike the high polynomial order formulas that are commonly used to describe the wind power curve [37,38,39].

- The reservoir has a trapezoidal shape, and thus the storage and area curves are linear functions of elevation;
- The intake is set to an elevation of 1.2 m from the upper reservoir’s bottom to ensure sufficient capacity for deposit management;
- The pump’s power capacity is 6.0 MW and equal to the maximum potential surplus estimated as the difference between the total capacity of wind turbines (6.4 MW) and the minimum hourly demand (0.4 MW), occurring in winter during the night;
- The turbine’s power capacity is also 6.0 MW, which is slightly higher than the maximum hourly load (5.4 MW) in order to account for uncertainties, as discussed later;
- The total efficiency values of the turbines and pumps are considered constant and equal to 0.85 and 0.80, respectively;
- The penstock’s length and diameter are 910 and 1.0 m, respectively, as specified in our preliminary design analysis.

#### 3.2. Breakdown of the Simulation Model

_{Net}> 0), the PHS system was set to its charging phase, thus pumping water from the sea to the upper reservoir, provided that there was a sufficient storage capacity (S

_{total}< S

_{max}). Similarly, if there were energy deficits (P

_{Net}< 0), the discharge phase was begun and the water was released downstream through the turbine, thus generating electrical energy, provided that there was available water stored in the upper reservoir (S

_{total}> V

_{dead}). This process was repeated until the final step equaled the simulation length, which, in our case, was 20 years (which is the typical economic life of such projects).

#### 3.3. Setup of the Optimization Problem

- The civil engineering works (excavations, roadworks, etc.);
- The purchase, installation, and maintenance of the electromechanical equipment (wind turbines, PVs, pumps, and turbines) and the conveyance system (GRP pipes);
- Specific works associated with reservoir waterproofing.

#### 3.4. Results: Benchmark Scenario

^{3}and a PV power capacity of 1.09 MW. Furthermore, the key metrics of the optimized benchmark scenario are presented in Table 3. We observed that the proposed solution ensured a quite satisfactory reliability level of approximately 95%; thus, the existing oil station will only have a complementary role in the island’s energy mix by operating 5% of the time. We also underlined that the small capacity factor of the hydropower station (actual vs. potential energy production) did not indicate a reduced performance. In contrast, it revealed its pivotal supporting role in fulfilling the deficits by the other two renewables, especially during peak energy demand periods. As far as the other renewables’ capacity factors were concerned, they were in line with the climatic regime of the study area.

## 4. Issues of Uncertainty in Hybrid Renewable Energy Systems

#### 4.1. Wind Process Uncertainty

#### 4.2. Energy Demand Uncertainty

#### 4.3. Wind-to-Power Conversion Uncertainty

## 5. HRES Simulations and Optimizations under Uncertainty

#### 5.1. Incorporating Uncertainty in the Simulation

#### 5.2. Results of Monte Carlo Scenarios

#### 5.3. Insight into the Trade-Off between Reservoir Size and Overall System Profit

## 6. The Challenge of Seawater

#### 6.1. Conveyance System

#### 6.2. Electromechanical Equipment

- Crevice corrosion, which is the most ordinary form of corrosion, is initiated by changes in the local chemistry within a crevice. It is usually associated with a stagnant solution in the micro-environments that tends to occur in crevices. In seawater pumps, crevices can be found where seals and impellers are fastened to the shaft and flange faces are cast in for pipework connections;
- Erosion corrosion can occur from the seawater’s rapid flow rate;
- Cavitation occurs when a fluid’s operational pressure drops below its vapor pressure and causes gas pockets and bubbles to form and collapse. This common phenomenon occurs when a pump operates outside its normal design parameters. The formed bubbles erode the steel;
- Corrosion fatigue derives from the combination of alternating or cycling stresses in a corrosive environment, mainly affecting seawater pump shafts.

#### 6.3. Groundwater Degradation Due to Seawater Effects

## 7. Conclusions

^{3}), with a minor loss of reliability.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

EAS | Evolutionary Annealing Simplex |

EIA | Environmental Impact Assessment |

FPV | Floating Photovoltaic |

GRP | Glass-Reinforced Polyester |

HDPE | High-Density Polyethylene |

HRESs | Hybrid Renewable Energy Systems |

OECD | Organization for Economic Cooperation and Development |

PHS | Pumped Hydropower Storage |

PREN | Pitting Resistance Equivalent Number |

PV | Photovoltaic |

SCADA | Supervisory Control and Data Acquisition |

WTG | Wind Turbine Generator |

WTPC | Wind Turbine Power Curve |

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**Figure 1.**(

**a**) The island of Sifnos and the HRES proposed siting (red circle) and (

**b**) the proposed HRES layout (source: Google Earth, after processing).

**Figure 5.**Example of randomly generated power curves for (

**a**) the large turbine (E-44) and (

**b**) small turbine (E70 E-4).

**Figure 6.**Fitting of the normal (

**left**) and log-normal distributions (

**right**) to the mean annual profit and reservoir active depth, respectively, where (

**a**) displays the theoretical density functions and (

**b**) displays the cumulative density functions.

Wind Turbines | ||
---|---|---|

Model | Enercon E-44 | Enercon E-70 E4 |

Rated power (kW) | 900.0 | 2300.0 |

Minimum power (kW) | 4.0 | 2.0 |

Cut-in wind speed (m/s) | 3.0 | 2.5 |

Rated wind speed (m/s) | 16.5 | 15.0 |

Cut-out wind speed (m/s) | 34.0 | 34.0 |

Tower height (m) | 55.0 | 113.0 |

Rotor diameter (m) | 44.0 | 71.0 |

Solar panels | ||

Surface area (m^{2}) | 1.94 | |

Nominal power (W) | 340.0 | |

Efficiency (%) | 17.5 |

Unit Cost (EUR) | Unit of Measurement | |
---|---|---|

Excavations | 6.00 | m^{3} |

Waterproofing membranes | 1.50 | m^{2} |

Conveyance system | 25.0 | m |

Installed wind power | 1,200,000 | MW |

Installed solar power | 1,100,000 | MW |

Energy profit | 300 | MWh |

Energy penalty | 350 | MWh |

Mean annual production from wind turbines and solar panels (GWh) | 24.98 |

Mean annual production from PHS system (GWh) | 4.69 |

Reliability (%) | 94.76 |

Mean annual profit (EUR) | 789,131 |

Investment cost (EUR) | 15,526,518 |

Ordinary annuity (EUR) | 1,814,222 |

Payback period (years) | 5.90 |

Capacity factors | |

Photovoltaics | 0.207 |

Small wind turbines | 0.304 |

Large wind turbines | 0.424 |

Hydropower station | 0.108 |

Mean | Standard Deviation | 10% Quantile | 50% Quantile | 90% Quantile | |
---|---|---|---|---|---|

Reservoir active depth (m) | 3.07 | 0.76 | 3.96 | 2.98 | 2.36 |

Reservoir storage capacity (m^{3}) | 329,882 | 53,370 | 400,282 | 323,278 | 274,583 |

Solar power capacity (MW) | 1.69 | 0.03 | 1.70 | 1.69 | 1.67 |

Mean annual energy production from wind turbines and solar panels (GWh) | 24.24 | 1.90 | 26.78 | 24.43 | 21.86 |

Mean annual energy production from PHS system (GWh) | 4.93 | 0.19 | 5.16 | 4.95 | 4.69 |

Reliability (%) | 94.89 | 1.50 | 96.75 | 95.11 | 92.98 |

Mean annual net profit (EUR) | 640,234 | 255,062 | 959,029 | 669,924 | 315,269 |

Investment cost (EUR) | 15,615,067 | 339,558 | 16,039,471 | 15,575,241 | 15,274,195 |

Ordinary annuity (EUR) | 1,820,737 | 24,986 | 1,851,966 | 1,817,807 | 1,795,283 |

Payback period (years) | 6.35 | 0.51 | 5.71 | 6.26 | 7.24 |

Capacity factors | |||||

Small wind turbines | 0.29 | 0.03 | 0.34 | 0.30 | 0.25 |

Large wind turbines | 0.41 | 0.03 | 0.46 | 0.41 | 0.37 |

Hydropower station | 0.09 | 0.01 | 0.10 | 0.09 | 0.08 |

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## Share and Cite

**MDPI and ACS Style**

Zisos, A.; Sakki, G.-K.; Efstratiadis, A.
Mixing Renewable Energy with Pumped Hydropower Storage: Design Optimization under Uncertainty and Other Challenges. *Sustainability* **2023**, *15*, 13313.
https://doi.org/10.3390/su151813313

**AMA Style**

Zisos A, Sakki G-K, Efstratiadis A.
Mixing Renewable Energy with Pumped Hydropower Storage: Design Optimization under Uncertainty and Other Challenges. *Sustainability*. 2023; 15(18):13313.
https://doi.org/10.3390/su151813313

**Chicago/Turabian Style**

Zisos, Athanasios, Georgia-Konstantina Sakki, and Andreas Efstratiadis.
2023. "Mixing Renewable Energy with Pumped Hydropower Storage: Design Optimization under Uncertainty and Other Challenges" *Sustainability* 15, no. 18: 13313.
https://doi.org/10.3390/su151813313