# Tidal Supplementary Control Schemes-Based Load Frequency Regulation of a Fully Sustainable Marine Microgrid

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## Abstract

**:**

## 1. Introduction

- Simulation and control of a 100% renewable energy microgrid including tidal, wave and offshore wind hybrid generation system.
- The effect of different supplementary control schemes in terms of the integrator, fractional integrator, and non-linear fractional integrator on the dynamic performance of load frequency control (LFC) is examined.
- Design of hybrid system controllers and tidal supplementary controller by using a novel black widow optimization technique and comparing it with other state-of-art optimization techniques.

## 2. Microgrid Modelling

#### 2.1. Modeling of the Tidal Generating System

#### 2.2. Modeling of Wave Generating System

#### 2.3. Modeling of Wind Generating System

#### 2.4. Modeling of Microgrid

## 3. Controllers

#### 3.1. Blade Pitch Controllers

#### 3.2. Tidal Speed Controller

#### 3.3. Tidal Supplementary Control Schemes

- (i)
- Integrators (I scheme), which have the transfer function ${G}_{I}=\frac{{K}_{I}}{s}$
- (ii)
- Fractional integrators (FI scheme), which have the transfer function ${G}_{FI}$ = $\frac{{K}_{I}}{{s}^{\lambda}}$
- (iii)
- Non-linear fractional integrators (NFI), which have the output ${\mathrm{U}}_{NFI}\left(\mathrm{s}\right)=\left(\frac{{\mathrm{e}}^{\left(\mathrm{Gx}E\right)}+{\mathrm{e}}^{-\left(\mathrm{Gx}E\right)}}{2}\frac{{\mathrm{K}}_{\mathrm{I}}}{{\mathrm{s}}^{\mathsf{\lambda}}}\right)E\left(s\right)$

## 4. Control Design

#### 4.1. Optimization Problem Definition

- i.
- Black widow
- ii.
- Quasi oppositional harmony search
- iii.
- Teaching and learning-based optimization
- iv.
- Particle swarm optimization
- v.
- Genetic algorithm

- Objective Function ($\mathrm{O}$): Minimization of integral absolute error (IAE) (${O}_{1}$) and minimization of integral time absolute error (ITAE) (${O}_{2}$):$${O}_{1}=\mathrm{min}\underset{0}{\overset{\mathrm{T}}{{\displaystyle \int}}}\mathsf{\Delta}f\mathrm{dt}$$$${O}_{2}=\mathrm{min}\underset{0}{\overset{\mathrm{T}}{{\displaystyle \int}}}\mathrm{t}\ast \mathsf{\Delta}f\mathrm{dt}$$$$\mathrm{O}=0.5\ast {O}_{1}+0.5\ast {O}_{2}$$
- Variables: PID control parameters, tidal additional damping, and inertia, in addition to tidal supplementary control schemes parameters.
- Constraints: G and λ.

_{I}and λ) and the constraint considered in its design is 0 ≤ λ ≤ 1 only. In non-linear fractional integrators, there are three variables (K

_{I,}G, and λ) and the constraints considered are 0 ≤ λ ≤ 1 and 0 ≤ G ≤ 1 only.

#### 4.2. Black Widow Optimization

- Initial population: This is used in each optimization technique; it has other names, like chromosomes in the genetic algorithm and particle position in the particle swarm algorithm. In the black window, it has the name widow. To start the optimization, a candidate widow matrix with size N
_{pop}× N_{var}is generated, where N_{var}represents the solution of the problem array while N_{pop}represents the number of populations. - Procreate: In this step, an array called α is created such that the offspring is produced through (20) and (21):$${y}_{1}=\alpha \times {x}_{1}+\left(1-\alpha \right)\times {x}_{2}$$$${y}_{2}=\alpha \times {x}_{2}+\left(1-\alpha \right)\times {x}_{1}$$
- Cannibalism: There are three kinds of cannibalism: (a) sexual cannibalism, where the female black widow eats her husband; in the algorithm, we can identify male and female through their fitness function; (b) sibling cannibalism, where the strong spider siblings eat their weaker siblings; in the algorithm, the cannibalism rating is set according to the determined number of survivors; and (c) baby cannibalism, where baby spiders eat their mother; in the algorithm, strong and weak spider siblings are recognized through fitness value.
- Mutation: Random selection of Mutepop number of individuals. Mutepop is calculated according to the mutation rate.
- Convergence: The same concept of many algorithms comes in the proposed algorithm; three stop conditions may be used: (a) a predefined number of iterations; (b) the fitness value is almost constant for several iterations; and (c) the desired accuracy is reached.

## 5. Simulation Results

_{sh}), overshoot (O

_{sh}), settling time (t

_{s}) in addition to peak time (t

_{p}), and the number of iterations performed using each optimization technique. The results show that the black widow algorithm has the best performance over other algorithms. Therefore, the tests applied on the system to compare between different supplementary controllers will be applied using the black widow algorithm only. The dynamic study of the microgrid in terms of load frequency control, under the action of black widow tuned control schemes installed in the studied system, was subjected to the following tests:

- Test 1: A step increase in the demand;
- Test 2: Real demand variation at a certain day;
- Test 3: Sinewave variation of the wave generation system;

#### 5.1. System Performance under Test 1

- Strategy a: System without supplementary control
- Strategy b: System with integrator supplementary control
- Strategy c: System with fractional integrator supplementary control
- Strategy d: System with non-linear fractional integrator supplementary control.

#### 5.2. System Performance under Test 2

#### 5.3. System Performance under Test 3

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

System | Parameters |
---|---|

Tidal | Capacity: 1 MW, rated rotor speed (ω_{r}) = 13 rpm, tidalspeed (V) = 2.4 m/s, TSR = 6.1, rotor radius (r) = 11.5 m, rotor blades = 3, blade length = 10.6 m, rotor position = upstream, M _{T} = 0.3878 s, T_{P} = 0.01 s, T_{T} = 0.08 s, T_{w} = 6 s, angle limits: minimum = 0° and maximum = 90°, d_{1} = 0.18, d_{2} = 85, d_{3} = 0.38, d_{4} = 10.2, d_{5} = 6.2, d_{6} = 0.025, d_{7} = −0.043 |

Wave | Capacity: 1 MW, K_{wave} = 1, T_{wave} = 0.3 s, T_{inv} = T_{conv} = 0.01 s |

Offshore wind | Capacity: 1 MW, K_{p1} = 1.250, K_{p2} = 1.000, K_{p3} = 1.400, K_{TP} = 0.0033, K_{IG} = 0.9969, K_{PC} = 0.0800, T_{p1} = 0.6000 s, T_{p2} = 0.0410, T_{p3} = 1.000, T_{W} = 4.000. |

Microgrid | H = 5, D = 0.8, f = 50 Hz |

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**Figure 2.**Tidal turbine modes of operation [24].

**Figure 3.**Tidal rotor speed vs. power output at different blade pitch angles [24].

**Figure 4.**Deloading philosophy of tidal turbine [24].

**Table 1.**Tidal turbine modes of operation [21].

Mode No. | Condition | Operation |
---|---|---|

I | V ≤ V_{min} | No power generation with pitch angle setting 90 degrees. |

II | V_{min} < V ≤ V_{rated} | Optimum power extraction from the turbine to reach optimum efficiency, Blade pitch angle is set at 4 degrees in this work |

III | V_{rated} < V ≤ V_{max} | Constant power operation turbine, blade pitch angle is varied from 4 degrees to 90 degrees to avoid overload. |

IV | V > V_{max} | No power output and blade pitch angle is set at 90 degrees. |

Method | ITAE | IAE | $\int}{\left(\mathsf{\Delta}f\right)}^{2}\ast {10}^{-6$ | Number of Iterations | $\mathbf{Transient}\mathbf{Response}\mathbf{of}\mathsf{\Delta}\mathit{f}$ | |||
---|---|---|---|---|---|---|---|---|

U_{sh} | O_{sh} | t_{s} | t_{p} | |||||

Black widow | 0.0059 | 0.0011 | 0.39 | 15 | −0.01 | 0.0025 | 1.75 | 1.5 |

Quasi-oppositional | 0.0064 | 0.0016 | 0.42 | 21 | −0.02 | 0.003 | 3.5 | 2 |

TLBO | 0.0071 | 0.0019 | 0.48 | 18 | −0.022 | 0.006 | 4.5 | 2.8 |

PSO | 0.0085 | 0.0026 | 0.61 | 25 | −0.025 | 0.007 | 15 | 4 |

GA | 0.0089 | 0.0027 | 0.64 | 23 | −0.025 | 0.009 | 15 | 4 |

Control Scheme | $\mathit{M}$ | ${\mathit{D}}_{1}$ | Supplementary Control | Tidal Blade Pitch Controller | Tidal Speed Regulator | Wind Blade Pitch Controller | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{K}}_{\mathit{I}}$ | $\mathit{\lambda}$ | $\mathit{G}$ | ${\mathit{K}}_{\mathit{P}}$ | ${\mathit{K}}_{\mathit{I}}$ | ${\mathit{K}}_{\mathit{D}}$ | ${\mathit{K}}_{\mathit{\omega}\mathit{T}\mathit{P}}$ | ${\mathit{K}}_{\mathit{\omega}\mathit{T}\mathit{I}}$ | ${\mathit{K}}_{\mathit{\omega}\mathit{T}\mathit{D}}$ | ${\mathit{K}}_{\mathit{P}}$ | ${\mathit{K}}_{\mathit{I}}$ | ${\mathit{K}}_{\mathit{D}}$ | |||

No scheme | 150 | 147 | none | none | none | 10 | 3 | 0.4 | 50 | 17 | 12 | 16 | 5 | 0.3 |

I scheme | 122 | 85 | 10 | none | none | 17 | 14 | 11 | 14 | 5 | 4 | 17 | 1 | 0.2 |

FI scheme | 146 | 75 | 7 | 0.43 | none | 11 | 9 | 0.16 | 6 | 4 | 1.4 | 8 | 5 | 2 |

NFI scheme | 98 | 56 | 13 | 0.64 | 0.72 | 14 | 7 | 1.14 | 8 | 3 | 0.57 | 21 | 17 | 8 |

Control Scheme | $\mathit{D}$ = 0.8 | $\mathit{D}$ = 1 | $\mathit{D}$ = 1.2 | $\mathit{D}$ = 1.4 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

ITAE | IAE | t_{s} | ITAE | IAE | t_{s} | ITAE | IAE | t_{s} | ITAE | IAE | t_{s} | |

No scheme | 0.087 | 0.061 | 17 | 0.079 | 0.050 | 15 | 0.071 | 0.038 | 12 | 0.059 | 0.032 | 11 |

I scheme | 0.064 | 0.052 | 5 | 0.058 | 0.043 | 4.3 | 0.049 | 0.035 | 3.7 | 0.041 | 0.026 | 3.4 |

FI scheme | 0.053 | 0.039 | 4.2 | 0.041 | 0.031 | 3.9 | 0.036 | 0.024 | 3.1 | 0.023 | 0.017 | 2.8 |

NFI scheme | 0.031 | 0.022 | 1.8 | 0.029 | 0.018 | 1.7 | 0.024 | 0.014 | 1.6 | 0.018 | 0.009 | 1.5 |

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**MDPI and ACS Style**

Fayek, H.H.; Mohammadi-Ivatloo, B.
Tidal Supplementary Control Schemes-Based Load Frequency Regulation of a Fully Sustainable Marine Microgrid. *Inventions* **2020**, *5*, 53.
https://doi.org/10.3390/inventions5040053

**AMA Style**

Fayek HH, Mohammadi-Ivatloo B.
Tidal Supplementary Control Schemes-Based Load Frequency Regulation of a Fully Sustainable Marine Microgrid. *Inventions*. 2020; 5(4):53.
https://doi.org/10.3390/inventions5040053

**Chicago/Turabian Style**

Fayek, Hady H., and Behnam Mohammadi-Ivatloo.
2020. "Tidal Supplementary Control Schemes-Based Load Frequency Regulation of a Fully Sustainable Marine Microgrid" *Inventions* 5, no. 4: 53.
https://doi.org/10.3390/inventions5040053