# GA-Based Permutation Logic for Grid Integration of Offshore Multi-Source Renewable Parks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- (A)
- Energy loss reduction is achieved by implementing the proposed commutation logic, which entails reducing costs associated with grid integration.
- (B)
- An energy output smoothing method is proposed to control an offshore multi-source park by a unique closed loop, avoiding the need to implement separate smoothing techniques for each power park.
- (C)
- An islanded generation system consisting of offshore floating photovoltaic, wind, and wave power (OPWW) parks integrated into the mainland grid is considered.
- (D)
- The potential of offshore renewable sources as electricity flexibility service providers, whose coordinated scheme with the distributed system operator (DSO) at the PCC is non-storage-dependent, is unveiled.
- (E)
- A combined capacity factor is calculated for each performed permutation and later optimized to reduce seasonal variability.
- (F)
- A seasonal GA-based permutated control strategy is suggested, where the set-point imposed by the demand curve can be tracked at an individual pace for each source.

## 2. Methodology and Calculations

#### 2.1. Studied Area and Power Profiles

#### 2.1.1. Installation Site under Study

#### 2.1.2. Generation Profile

^{2}, 25 °C. The wave power matrix is 600 kW nominal (WaveStar), and the wind turbine is the Vestas 3 MW. The treatment of the whole dataset consists of normalizing the values concerning the installed capacity of each source and applying reverse engineering design criteria to obtain the desired power from the irradiance and wind speed. However, the data related to wave power is only scaled up to the desired rated value.

#### 2.1.3. Demand Profile

- (a)
- When the permutation logic is performed without optimization, the load at the PCC is assumed to have a Y-connected resistive impedance, whose rated value is 0.6 Ω [28], and varies according to the demand profile, with the current flowing throughout the whole power system. Hence, demand and generation curves are shifted.
- (b)
- For the optimization process, the normalized demand is multiplied by a factor equal to the average value of the total generation. Thus, both curves are no longer shifted.

#### 2.2. Main Components of the Studied Multi-Source Park

#### 2.2.1. OFPV Generation

^{2}, 25 Celsius. To obtain the desired profile, it is also necessary to calculate the appropriate amount of PV inverters for grid integration purposes.

- PV panels

- Power inverter

- (a)
- PV panels at each row are connected only in series.

- (b)
- Calculations are based on the rated DC input voltage instead of the absolute maximum DC voltage.
- (c)
- Vmp and Imp are the voltage and current values taken to calculate the total rated power summed by the panels connected to each inverter. Short-circuit (SC) current and open-circuit (OC) voltage are only used for compliance purposes.

- Connection to the power transformer

#### 2.2.2. Offshore Wind Turbine

^{3}), ${A}_{swept}$ is the area swept by the blades (38,000 m

^{2}), and ${v}_{out}$ is the wind speed registered after the swept area.

#### 2.2.3. Wave Energy Converters (WECs)

- (a)
- The data are taken from the Station 46327 wave measurement buoy—San Francisco Bay, California [26].
- (b)
- The total power of the wave power park is assumed to be 5 MW, with each wave energy converter rated at 30 kW.
- (c)

#### 2.2.4. Offshore Transmission System

- Power transformer

- (a)
- The charging factor assumed for the power transformer is 50% of the installed capacity of the three farms sums up to 18 MW; therefore, the combined sources are only needed to occupy up to 45% of the total capacity of the power transformer.
- (b)
- To avoid using more transformers, it is assumed that the downstream voltage is the same as the studied wind turbine (6.6-kV). However, the inverter used for the studies has a rated AC grid voltage (Vac,r) of 800-V, so it has to be assumed that the PV panels are connected to a dedicated 1000-KVA 6.6/0.69-kV distribution transformer sharing the power park with the main transformer.
- (c)
- In general, larger losses are registered for lower voltage levels due to a higher current value. However, results drastically change when the losses are studied on different components needed to connect wind turbines to the grid. For example, losses at the WT transformers and sea-to-land cables are directly proportional to voltage, whereas the collection grid losses are the opposite. On top of that, losses at substation transformers vary slightly, as well as the efficiency at nominal power [33]. In such a case, 66 kV offers a perfect balance between losses and efficiency without incurring higher costs due to transport system over-dimensioning.

- Offshore 6.6-kV cable arrangement

- Offshore 66-kV cable arrangement

#### 2.3. Methodology Employed

- (a)
- The three sources are aggregated to the grid with a combination of sources based on a permutation logic, where each offshore power park is connected totally or partially to the power transformer from the aggregator side. This approach also implies total disconnection of one or several sources.
- (b)
- (c)
- A GA-based permutation logic is implemented.
- (d)
- The aggregation of the multi-source park with and without implementation of the optimization technique is compared for different seasons.
- (e)
- Permutated capacity factors are calculated.
- (f)
- Battery energy storage system (BESS) size is determined after performing the GA search.

#### 2.4. Methods

#### 2.4.1. Permutation Logic Analysis through the Aggregation of Multiple Offshore Renewable Energy Sources

#### 2.4.2. Capacity Factor Calculation Based on the Maximum Energy Output

_{2}-neutral energy technologies, independently of the economy market, surpass 40% of the electricity flexibility mix. Moreover, at least 10% of this flexibility mix is attained from other renewable sources different from hydropower [1], which enables us to envision the potential of variable renewable sources as flexibility service providers without depending on 100% of any storage system [23].

#### 2.4.3. Seasonal Permutation Logic with and without Employment of a GA-Based Optimization Technique

#### 2.4.4. BESS Sizing after Optimization

- (a)
- Calculate the energy supplied by the three sources combined based on the energy profiles depicted in Figure 2.
- (b)
- Start the GA optimization process.
- (c)
- Calculate the seasonal energy supply after performing the GA search (energy after curtailment).
- (d)
- Calculate the peak energy curtailed on each season and obtain the average value.
- (e)
- Calculate the current under the average peak energy obtained per season and the rated power of the main transformer.
- (f)
- Calculate the BESS size according to the current.
- (g)
- Calculate the number of batteries needed based on the ampere-hours of each battery.
- (h)
- Form strings to comply with the voltage and current requirements at the transformer side. If needed, place a dedicated distribution transformer for the final BESS.

- (a)
- The specifications of each battery are assumed to be 48 V/170 Ah/5 kW, in accordance to design criteria found for commercial Li-ion batteries, such as SIRIUS SuperCap 3550-48-B-1.7C-M-SD-A-G (KiloWatts Labs), VTLF48V-A267 (Vottery), and LPBA48170 (Felicity Solar).
- (b)
- The required duration or the time during the load that must be supplied is 10 h. Moreover, the BESS can be prepared for peak shaving [37].
- (c)
- The state of discharge (SoD) is assumed to be 20%.
- (d)
- No capacity rating or charge/discharge curve is considered.
- (e)
- The BESS sizing is not included in the GA search. It is calculated afterward.
- (f)
- No inverter is studied for the BESS. However, it is considered that an arrangement of this nature needs a dedicated distribution transformer if connected to the downstream side of the main transformer (6.6 kV). The rated power of the distribution transformer is estimated according to the peak energy after curtailment.
- (g)
- The charge/discharge current is set as 105 A (5 kW/48 V).
- (h)
- No costs are estimated, neither for the batteries nor the distribution power transformer.
- (i)
- The size of the BESS is calculated with the following:$$Siz{e}_{batt}{}_{Li-ion}=\frac{100\xb7I\xb7t}{100-Q}$$
- (j)
- After calculating the BESS size, the number of batteries for that is given by the ratio between the BESS size in A-h and the capacity of each battery (170 A-h).
- (k)
- The transmission and distribution cable arrangements connected to the main transformer are not upgraded.
- (l)
- Even though the BESS is sized with the help of calculations, there were no simulations undertaken with the arrangements that have been obtained.

## 3. Results

#### 3.1. Permutation Logic Analysis through Aggregation of Multiple Offshore Renewable Sources

- (A)
- For bipartite power parks, the best combination is OFPV and wave power parks (Decode pins #11–14). It diminishes the energy losses and gets a good balance between capacity factor and losses.
- (B)
- In tripartite power parks (OPWW), there is a direct relationship between energy losses and the power park capacity factor. Namely, the greater the power park capacity factor, the higher the losses at the PCC. However, this direct correlation is not manifested in bipartite power parks.
- (C)
- For tripartite power parks, the best balance between energy losses and capacity factor is offered by the combination where wind energy is the only one not curtailed (Decode pin #25). In contrast, curtailing the wind power entails a drastic reduction of both magnitudes (Decode pin #24).

#### 3.2. Seasonal Permutation Logic before Optimization

#### 3.3. Seasonal Permutation Logic with Employment of a GA-Based Optimization Technique

- (a)
- In some instances, not all sources may be present; hence, the available sources are used to fulfill the demand.
- (b)
- When one or more sources are unavailable, the GA combines what is available and sets the other(s) to zero.
- (c)
- When none of the sources are available, the energy supply is set to zero, and the algorithm continues to the next day (notice the white bars on the plots in Figure 12).

#### 3.4. BESS Sizing after Optimization

## 4. Discussion

#### Seasonal Permutation Logic without Optimization

- (A)
- For individual power parks, the higher the rated power, the higher the energy losses, which is expected considering that the studied PV emplacement has scales of 1:5 and 1:12 if compared to wave and wind power parks, respectively.
- (B)
- When the power parks are bipartite, it is evidenced that curtailing wind power is more beneficial when it is connected to either PV or wave emplacements, but when PV and wave emplacements share the cluster, curtailing wave energy is a better solution when no storage system is available. Further, combining OFPV and wave reports additional benefits at this particular emplacement: a more drastic reduction of energy losses. However, these do not overmuch deviate regardless of the season. Due to wind speed being inversely proportional to temperature, wave energy can play the role of a " storage system" when OFPV emplacement is no longer available because of a lack of irradiance.
- (C)
- Curtailing OFPV energy from combined OFPV and wind power parks does not significantly decrease losses. However, these are considerably lower during summer–fall (July or October) than during winter–spring (January or April). That proves that increasing the installed capacity of PV emplacements is the best way to go due to the capacity of wind turbines increasing, but the rated power ratio between PV and wind emplacements shall be high enough to reach a balance between energy losses and seasonal variability.
- (D)
- The power park capacity factor, although highly variable depending on the sources combined at the aggregator, is higher during the winter and lower during the summer, except in those cases where there is a bipartite OFPV and wave power park. In such a case, the capacity factor is reduced during the spring.
- (E)
- Between spring and fall, the capacity factor slightly deviates, seasonally speaking, independently of the combination, whereas, between winter and summer, the deviation is no longer slight. On top of that, curtailing OFPV over wind or wave energy on bipartite combinations substantially increases the capacity factor, especially in those seasons where irradiance impacting the PV panels is lower. It can open the gate for adjusting the rated power ratio instead of using large energy storage systems that would become economically unfeasible if placed on dedicated offshore floaters.
- (F)
- On tripartite power parks, the capacity factor can be higher whether either OFPV or wave energy is curtailed or not, whereas it is drastically reduced when wind energy is curtailed. Indeed, curtailing only OFPV energy barely affects the performance of the power park in terms of seasonal capacity factor and energy losses but can drastically deprecate the energy losses when measured for a wider time interval, as depicted in Figure 9 (Decode pins #21 and 26). The same applies when wave energy is curtailed over wind and/or OFPV energy (Decode pins #23 and 25).
- (G)
- If we look at Figure 10 and Figure 11 together, with special emphasis on Decode pins ranging from #19 to #26 (see Table 3), it is evidenced that the energy losses attributed to the combination of the three power sources become larger with less curtailment in renewable sources. Additionally, the capacity factor varies considerably among seasons, which is not a desirable behavior of the system.
- (H)
- Once the optimization process is performed, it is evidenced that the main goal of the proposed single-objective function is achieved, and the energy losses are strongly dependent on seasons. Further, it is not always possible to curtail all the generation sources to match the consumption pattern. Hence, it is strongly advisable to include storage systems that are properly sized and complement them with metal-clad cells on substations to deviate the energy curtailed to another population settlement in the same county, which can be completed in the mainland substation and is cheaper.
- (I)
- Despite the variability reduction in the combined capacity factor, it is evidenced that this variable has to be included as a variable in a multi-objective optimization process to obtain a higher magnitude.
- (J)
- Since offshore wind turbines are currently being designed for higher-rated power, it is advisable to increment in a reasonable proportion the installed capacity of OFPV, even though the combined capacity factor can be lowered. This is particularly important for those sites where the peak demand is almost coincident with the peak generation, such as the site studied for this research.
- (K)
- Lastly, when the demand curve is directly used as the set-point for generation, it is evidenced that each power source accommodates itself in such a way that it can track individually the consumption pattern, which unveils the potential of renewable energies as flexibility service providers even in the absence of storage systems [1].
- (L)
- If the BESS is placed onshore, it will require a considerable number of battery units, but they might not need to include a distribution power transformer offshore, which avoids the necessity of building floaters or foundations, as well as upgrading the main transformer and cables, which, consequently, reduces the costs.
- (M)
- It is recommended to perform BESS sizing during the GA search and compare it to the battery sizing performed afterward. Thus, the optimization process should include this sizing as another variable subjected mainly to space, location, and cost constraints.

## 5. Conclusions

- (a)
- The proposed permutated aggregator fulfills its primary function, allowing the power parks to contribute partially and individually to diminish the energy losses at the PCC, which eliminates the need to disconnect any source.
- (b)
- Genetic programming and GA are a good match when it comes to performing permutated control on multi-source parks, which can help to improve the performance of the transformers’ on-load tap changers (OLTC). However, more research on this topic is needed.
- (c)
- The capacity factor of the multi-source park is improved in terms of seasonal variability (standard deviation), although its value is considerably reduced when the demand is utilized as a set-point to be individually tracked.
- (d)
- Without any storage system involved, the multi-source park has demonstrated to be capable of providing flexibility services towards mainland grids, which is aligned with the new energy policies stated in WEO 2021.
- (e)
- A reasonable proportion between OFPV/wind/wave power parks is advisable due to the considerably higher capacity of the wind turbines. Thus, the proposed GA-based permutation logic would not rely too much on the partial braking of wind turbines, which can be detrimental to their performance.
- (f)
- Even though the studied energy technologies are capable of providing individual flexibility services, it is not always possible to curtail generation to track the demand at the same pace. Hence, optimized storage sizing is recommendable.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

AC | Alternate Current |

BESS | Battery energy storage system |

DC | Direct current |

DER | Distributed Energy Resources |

DSM | Demand-Side Management |

GA | Genetic Algorithm |

KPIs | Key Performance Indicators |

MPPT | Maximum Power Point Tracking |

OC | Open-circuit |

OFPV | Offshore floating Photovoltaic Power |

OPWW | Offshore Photovoltaics, Wind, and Wave Power |

PCC | Point of Common Coupling |

RES | Renewable Energy Sources |

SC | Short-circuit |

STEPS | Stated Policies Scenario |

WEC | Wave energy converter |

WEO | World Energy Outlook |

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**Figure 5.**3-8 multiplexer model with its truth table. Reproduced with permissions from [35].

**Figure 8.**Results obtained after performing the permutation logic detailed in Table 3.

**Figure 10.**Accumulated energy and losses in 2016 (MWh)—seasonal comparison. (

**a**) Accumulated energy for 4 months representing the seasons of 2016; (

**b**) Energy losses for 4 months representing the seasons of 2016.

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

Rated power (Wp) | 375 |

Vmp (V) | 34.10 |

Imp (A) | 11.01 |

VOC (V) | 41.89 |

ISC (A) | 11.43 |

Module Efficiency (%) | 20.59 |

Maximum DC voltage (V) | 1500 |

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

Absolute maximum DC input voltage (V) | 1500 |

Rated DC input voltage (V) | 1080 |

Number of independent MPPT | 12 |

Maximum DC input current for each MPPT (A) | 45 |

Maximum input short circuit current for each MPPT (A) | 60 |

Number of DC input pairs for each MPPT | 2 |

Decode Pin | Permutation Logic (Equation-Based) |
---|---|

0 | $Output=0$ |

1 | $Output=perc\xb7{P}_{{\mathrm{PV}}_{AC-side}}$ |

2 | $Output={P}_{{\mathrm{PV}}_{AC-side}}$ |

3 | $Output=perc\xb7{P}_{wind}$ |

4 | $Output={P}_{wind}$ |

5 | $Output=perc\xb7{P}_{wave}$ |

6 | $Output={P}_{wave}$ |

7 | $Output=perc\xb7\left({P}_{{\mathrm{PV}}_{AC-side}}+{P}_{wind}\right)$ |

8 | $Output=perc\xb7\left({P}_{{\mathrm{PV}}_{AC-side}}\right)+{P}_{wind}$ |

9 | $Output={P}_{{\mathrm{PV}}_{AC-side}}+perc\xb7({P}_{wind})$ |

10 | $Output={P}_{{\mathrm{PV}}_{AC-side}}+{P}_{wind}$ |

11 | $Output=perc\xb7\left({P}_{{\mathrm{PV}}_{AC-side}}+{P}_{wave}\right)$ |

12 | $Output=perc\xb7\left({P}_{{\mathrm{PV}}_{AC-side}}\right)+{P}_{wave}$ |

13 | $Output={P}_{{\mathrm{PV}}_{AC-side}}+perc\xb7\left({P}_{wave}\right)$ |

14 | $Output={P}_{{\mathrm{PV}}_{AC-side}}+{P}_{wave}$ |

15 | $Output=perc\xb7\left({P}_{wind}+{P}_{wave}\right)$ |

16 | $Output=perc\xb7({P}_{wind})+{P}_{wave}$ |

17 | $Output={P}_{wind}+perc\xb7\left({P}_{wave}\right)$ |

18 | $Output={P}_{wind\left(kW\right)}+{P}_{wave}$ |

19 | $Output=perc\xb7\left({P}_{{\mathrm{PV}}_{AC-side}}+{P}_{wind}+{P}_{wave}\right)$ |

20 | $Output=perc\xb7\left({P}_{{\mathrm{PV}}_{AC-side}}+{P}_{wind}\right)+{P}_{wave}$ |

21 | $Output=perc\xb7\left({P}_{{\mathrm{PV}}_{AC-side}}\right)+{P}_{wind}+{P}_{wave}$ |

22 | $Output={P}_{{\mathrm{PV}}_{AC-side}}+perc\xb7({P}_{wind}+{P}_{wave})$ |

23 | $Output={P}_{\mathrm{PV}{\left(kW\right)}_{AC-side}}+{P}_{wind\left(kW\right)}+perc\xb7({P}_{wave\left(kW\right)})$ |

24 | $Output={P}_{\mathrm{PV}{\left(kW\right)}_{AC-side}}+perc\xb7\left({P}_{wind\left(kW\right)}\right)+{P}_{wave\left(kW\right)}$ |

25 | $Output=perc\xb7({P}_{\mathrm{PV}{\left(kW\right)}_{AC-side}})+{P}_{wind\left(kW\right)}+perc\xb7({P}_{wave\left(kW\right)})$ |

26 | $Output={P}_{\mathrm{PV}{\left(kW\right)}_{AC-side}}+{P}_{wind\left(kW\right)}+{P}_{wave\left(kW\right)}$ |

$\mathbf{C}{\mathbf{f}}_{\mathbf{O}\mathbf{P}\mathbf{W}\mathbf{W}}\text{}(\%)$ | 16 January | 16 April | 16 July | 16 October | Standard Deviation |
---|---|---|---|---|---|

Before optimization | 20.69 | 14.34 | 12.99 | 15.44 | 3.37 |

After optimization | 9.69 | 7.84 | 7.27 | 7.74 | 1.07 |

Case 1 | Case 2 | Case 3 | |
---|---|---|---|

Battery rating (single unit) | 5 kW, 48 V | ||

Main transformer rating | 40 MW, 6.6/66 kV | ||

Dedicated BESS transformer rating | 10 MW, 0.69/6.6 kV | 10 MW, 0.69/6.6 kV | N/A |

Connection side | 0.69 kV | 6.6 kV | 66 kV |

Location | offshore | offshore | onshore |

Number of batteries in series | 18 | 14 | 1375 |

Number of rows | 64 | 85 | 4 |

Total number of batteries | 1152 | 1190 | 5500 |

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**MDPI and ACS Style**

Rojas-Delgado, B.; Ekweoba, C.; Lavidas, G.; Temiz, I.
GA-Based Permutation Logic for Grid Integration of Offshore Multi-Source Renewable Parks. *Machines* **2022**, *10*, 1208.
https://doi.org/10.3390/machines10121208

**AMA Style**

Rojas-Delgado B, Ekweoba C, Lavidas G, Temiz I.
GA-Based Permutation Logic for Grid Integration of Offshore Multi-Source Renewable Parks. *Machines*. 2022; 10(12):1208.
https://doi.org/10.3390/machines10121208

**Chicago/Turabian Style**

Rojas-Delgado, Brenda, Chisom Ekweoba, George Lavidas, and Irina Temiz.
2022. "GA-Based Permutation Logic for Grid Integration of Offshore Multi-Source Renewable Parks" *Machines* 10, no. 12: 1208.
https://doi.org/10.3390/machines10121208