# Improving the Frequency Response of Hybrid Microgrid under Renewable Sources’ Uncertainties Using a Robust LFC-Based African Vulture Optimization Algorithm

^{1}

^{2}

^{*}

## Abstract

**:**

^{−5}.

## 1. Introduction

- Design and simulation of a robust cascaded controller called (1+PD)-PID in order to regulate the system response in terms of frequency and tie-line power deviations;
- Using a novel AVOA optimization algorithm to find the optimal controller parameters to ensure an optimal behavior of the controller;
- Testing the effectiveness and validation of the (1+PD)-PID controller by subjecting the microgrid to various types of fluctuations and uncertainties such as distinct step load disturbances, variable load variations, and RES fluctuations;
- Verifying the superiority of the (1+PD)-PID controller by comparing its performance against that of other controllers such as the conventional PID controller, FOPID controller and TID controller.

## 2. Structure of The Two-Area Hybrid Power System

- Non-reheat Thermal System:

- Power System:

- PV System:

- Wind Turbine Generator (WTG):

## 3. Structure of the (1+PD)-PID Cascaded Controller

_{1}= B

_{2}= B is the frequency bias parameter, $\mathsf{\Delta}{F}_{i}$ is the deviation in frequency in the ith interconnected area and $\mathsf{\Delta}{P}_{tie}$ is the deviation in the tie-line power of nearby control areas. The transfer functions in the s-domain of the proposed controller can be expressed by:

_{1}, K

_{d}

_{1}, Kp

_{2}, K

_{i}and K

_{d}

_{2}, respectively. Finally, using AVOA’s effective search behavior, the optimum or nearly optimum combination of the presented controller parameters is obtained within the specified constraints for the minimal value of the objective function (${J}_{obj})$.

## 4. African Vulture Optimization Algorithm (AVOA)

#### 4.1. Exploration Phase

#### 4.2. Exploitation Phase

_{1}, P

_{2}, P

_{3}, L

_{1}and L

_{2}, respectively. Finally, the AVOA algorithm has been shown to be efficient in solving various types of optimization problems [29]. The AVOA major steps can be outlined as follows:

- Determine the iterations maximum number and the size of the population;
- Compute the vulture fitness value;
- Select $R\left(i\right)$ using Equation (12) for all vultures;
- Use Equation (11) to compute the position of the best vulture;
- Depending on the vulture satiation rate, use Equation (13) or Equation (16) to update the position of the vulture;
- Save the position of the optimal vulture then compute the value of the fitness function as long as the iteration maximum number is not reached.

## 5. Results and Discussions

#### 5.1. Scenario 1: System Performance under 10% SLP in Area-1

#### 5.1.1. Comparison of AVOA Performance with Other Optimization Algorithms

_{1}, ΔF

_{2}) and the change in the tie-line power (Δ${P}_{tie}$). Obviously, AVOA has the best performance among other optimization algorithms, and it has the lowest fitness function of 6.01 × 10

^{−5}against 12.64 × 10

^{−5}, 26.28 × 10

^{−5}, 27.61 × 10

^{−5}, and 35.65 × 10

^{−5}for GOA, HHO, ALO and GA, respectively.

#### 5.1.2. Applying the Proposed AVOA Algorithm to Different Controllers

_{1}, ΔF

_{2}) and the change in the tie-line power (Δ${P}_{tie}$). It can be obviously noted that the proposed controller has a better response than the other controllers.

^{−5}against 8.14 × 10

^{−4}, 15.72 × 10

^{−4}, and 19.42 × 10

^{−4}for the TID, FOPID and PID controllers, respectively. Table 3 introduces the system performance in terms of maximum over-shoot (MO), maximum under-shoot (MU) and settling time (TS) values of the deviation of frequency in each area and tie-line power deviation for 10% SLP in area 1. The obtained simulation results clearly show that the (1+PD)-PID controller defeats the other competing controllers in the system performance specifications, especially the settling time. Settling time refers to how quickly the system can regain its equilibrium and the time it takes for the system to dampen the turbulence. For example, the settling time of the frequency deviation in Area-1 is 0.122246 S for the proposed controller versus 0.4792 S, 0.5353 S and 0.8649 S for TID, FOPID and PID controllers, respectively. Additionally, the maximum under-shoot of the frequency deviation in Area-1 is 0.0026 for (1+PD)-PID controller against 0.0051, 0.0059 and 0.0076 for TID, FOPID and PID controllers, respectively. Consequently, the proposed (1+PD)-PID controller proves its validity and efficacy in improving system stability and its superiority over the other competing controllers.

#### 5.2. Scenario 2: The System Performance for Random Load Profile

_{1}, ΔF

_{2}and Δ${P}_{tie}$, due to the applied load profile, are shown in Figure 9.

#### 5.3. Scenario 3: The Effect of Installing Solar PV Unit in Area-1

_{1}, ΔF

_{2}and Δ${P}_{tie}$ using AVOA tuned (1+PD)-PID, TID, FOPID and PID controllers under the penetration of PV solar power generation. It is evident that the proposed controller offers the best performance and the least fluctuations in frequency and tie-line power in this case compared to the other controllers with which it is being compared.

#### 5.4. Scenario 4: The Effect of Installing a Wind Farm Unit in Area-2

#### 5.5. Scenario 5: The Effect of Inserting RES into the System

_{1}) and in Area-2 (ΔF

_{2}) and tie-line power (Δ${P}_{tie}$) are presented in Figure 12 for different controllers under the circumstances of RES variation. It is clearly shown that the suggested controller has the best performance and the least variation in system frequency and interconnected tie-line power of nearby areas compared to other comparable controllers. Hence, the effectiveness, validity, reliability, and robustness of the proposed controller ((1+PD)-PID) tuned by the selected optimization algorithm (AVOA) were strictly proven in controlling hybrid power systems in terms of frequency and tie-line power in case of multi-area systems under various types of uncertainties.

## 6. Results and Discussions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**(

**a**) The deviation of frequency in Area-1 (ΔF

_{1}); (

**b**) the deviation of frequency in Area-2 (ΔF

_{2}); (

**c**) the deviation of tie-line power (Δ${P}_{tie}$) for 10% load change in Area-1 under the influence of (1+PD)-PID controller and different optimization algorithms.

**Figure 7.**(

**a**) The deviation of frequency in Area-1 (ΔF

_{1}); (

**b**) the deviation of frequency in Area-2 (ΔF

_{2}); (

**c**) the deviation of tie-line power(Δ${P}_{tie}$) for 10% load change in Area-1.

**Figure 9.**(

**a**) The deviation of frequency in Area-1 (ΔF

_{1}); (

**b**) the deviation of frequency in Area-2 (ΔF

_{2}); (

**c**) the deviation of tie-line power (Δ${P}_{tie}$) for random load profile in Area-1.

**Figure 10.**System responses under solar PV fluctuations at Area-1: (

**a**) ΔF

_{1}, (

**b**) ΔF

_{2}and (

**c**) ΔP

_{tie}.

**Figure 11.**System responses under wind power generation at Area-2: (

**a**) ΔF

_{1}, (

**b**) ΔF

_{2}and (

**c**) ΔP

_{tie}.

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

${K}_{T}$ | 1 | ${T}_{T}$ | 0.3 s |

${K}_{g}$ | 1 | ${T}_{g}$ | 0.03 s |

${K}_{PS}$ | 120 Hz/pu.MW | ${T}_{PS}$ | 20 s |

${K}_{PV}$ | 1 | ${T}_{PV}$ | 1.3 s |

${K}_{WT}$ | 1 | ${T}_{WT}$ | 1.5 s |

${B}_{1}$, ${B}_{2}$ | 0.425 pu.MW/Hz | ${R}_{1}$, ${R}_{2}$ | 2.4 Hz/pu.MW |

${a}_{12}$ | −1 | ${T}_{12}$ | 0.545 pu.MW/Hz |

(1+PD)PID | TID | FOPID | PID | |||||
---|---|---|---|---|---|---|---|---|

Area 1 | Kp11 Kd11 N1 Kp1 Ki1 Kd1 N2 | 127.0878 1.3142 600 85.536 149.906 0.88764 600 | Kt1 N1 Ki1 Kd1 App1 | 375 7.805 375 53.75 9.5 | Kp1 Ki1 λ1 Kd1 μ1 | 180 180 1 17 1.23 | Kp1 Ki1 Kd1 | 148.58 150 25.67 |

Area 2 | Kp22 Kd22 N3 Kp2 Ki2 Kd2 N4 | 5.2932 0.3625 600 1.9495 2.7302 0.1812 600 | Kt2 N2 Ki2 Kd2 App2 | 282.177 17.6448 14.027 209.509 16.574 | Kp2 Ki2 λ2 Kd2 μ2 | 60.37 44.26 1.25 16.15 1.22 | Kp2 Ki2 Kd2 | 139.08 147.71 59.76 |

Fitness Function | 6.01 × 10^{−5} | 8.14 × 10^{−4} | 15.72 × 10^{−4} | 19.42 × 10^{−4} |

Controller | ΔF_{1} | ΔF_{2} | ΔP_{tie} | ||||||
---|---|---|---|---|---|---|---|---|---|

MO | MU | TS | MO | MU | TS | MO | MU | TS | |

(1+PD)PID | 0.00066 | 0.0026 | 0.1246 | 1.95 × 10^{−5} | 1.65 × 10^{−5} | 0.9827 | 1.16 × 10^{−7} | 1.2 × 10^{−5} | 1.08 |

TID | 0.0019 | 0.0051 | 0.4792 | 0 | 2.36 × 10^{−4} | 4.92 | 0 | 9.97 × 10^{−5} | 4.93 |

FOPID | 4.8 × 10^{−7} | 0.0059 | 0.5353 | 4.46 × 10^{−7} | 5.4 × 10^{−4} | 3.90 | 1.9 × 10^{−7} | 2.28 × 10^{−4} | 3.91 |

PID | 0.0013 | 0.0076 | 0.8649 | 0 | 5.4 × 10^{−4} | 3.94 | 0 | 2.29 × 10^{−4} | 3.94 |

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**MDPI and ACS Style**

Hossam-Eldin, A.; Mostafa, H.; Kotb, H.; AboRas, K.M.; Selim, A.; Kamel, S.
Improving the Frequency Response of Hybrid Microgrid under Renewable Sources’ Uncertainties Using a Robust LFC-Based African Vulture Optimization Algorithm. *Processes* **2022**, *10*, 2320.
https://doi.org/10.3390/pr10112320

**AMA Style**

Hossam-Eldin A, Mostafa H, Kotb H, AboRas KM, Selim A, Kamel S.
Improving the Frequency Response of Hybrid Microgrid under Renewable Sources’ Uncertainties Using a Robust LFC-Based African Vulture Optimization Algorithm. *Processes*. 2022; 10(11):2320.
https://doi.org/10.3390/pr10112320

**Chicago/Turabian Style**

Hossam-Eldin, Ahmed, Hamada Mostafa, Hossam Kotb, Kareem M. AboRas, Ali Selim, and Salah Kamel.
2022. "Improving the Frequency Response of Hybrid Microgrid under Renewable Sources’ Uncertainties Using a Robust LFC-Based African Vulture Optimization Algorithm" *Processes* 10, no. 11: 2320.
https://doi.org/10.3390/pr10112320