# Optimum Fractional Tilt Based Cascaded Frequency Stabilization with MLC Algorithm for Multi-Microgrid Assimilating Electric Vehicles

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## Abstract

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## 1. Introduction

- •
- A new improved fractional order methodology is proposed in the paper for controlling frequency in multi-area RES-EV-based microgrid systems. The modified controller presents two cascaded inner and outer control loops based on 1+TD and FOTIDF, respectively, forming the proposed 1+TD/FOTIDF controller. Also, the proposed 1+TD/FOTIDF coordinates and controls EV batteries’ participation in the frequency regulation process.
- •
- A new modified liver cancer optimization algorithm (MLCA) is proposed to overcome the limitations of the conventional strategy of Liver cancer optimization algorithm (LCA). The proposed MLCA can avoid the early concourse to local optima and the debility of its exploration process. The proposed MLCA is based on three improvement mechanisms, including chaotic mutation (CM), quasi-oppositional based learning (QOBL), and the fitness distance balance (FDB).
- •
- The proposed MLCA is applied to optimally determine the parameters of the proposed 1+TD/FOTIDF controller. The obtained results show a better response and mitigation of different step generation/loading changes compared to other optimization methods and/or conventional controllers.

## 2. MG Model and Description

#### 2.1. MGs’ Construction

#### 2.2. Modeling of Thermal and Hydraulic Generators

#### 2.3. Modeling EVs’ BESSs

#### 2.4. Wind Plant’s Model

#### 2.5. Modeling of PV Power Plants

#### 2.6. MG’s Complete Model

## 3. Overview of LFC and FO Operators

#### 3.1. LFC Schemes in Literature

#### 3.2. FO Operators Representation

#### 3.3. Proposed 1+TD/FOTIDF LFC

## 4. The Proposed Modified Liver Cancer Optimization Algorithm and Its Performance Verification

#### 4.1. Liver Cancer Optimization Algorithm

#### 4.1.1. Tumor Size Estimation

#### 4.1.2. Tumor Replication

#### 4.1.3. Tumor Spreading

#### 4.2. The Proposed Modified Liver Cancer Algorithm

#### 4.2.1. The FDB Method

#### 4.2.2. The QOBL Method

#### 4.2.3. The Chaotic Mutation

#### 4.3. MLCA Verification and Results Discussion

#### 4.3.1. Application 1: Evaluation of the MLAC in Benchmark Functions

#### 4.3.2. Statistical Analysis

#### 4.3.3. Convergence Analysis

#### 4.3.4. Boxplot Analysis

#### 4.3.5. Wilcoxon and Fredman Tests

#### 4.4. The Proposed MLCA-Based Control Parameters Optimization Process

## 5. Results and Discussions

#### 5.1. Scenario 1: 2% Step Load Change (SLC)

#### 5.2. Scenario 2: SLC with PV Irradiation Case A

#### 5.3. Scenario 3: SLC with PV Irradiation Case B

#### 5.4. Scenario 4: SLC with sever PV Irradiation Case C

#### 5.5. Scenario 5: High RESs of PV and Wind Generation

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

## References

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**Figure 2.**Modelling and representation of various components of interconnected MGs with RESs and EVs.

**Figure 5.**P-V curves as a function of ambient conditions. (

**a**) With irradiance level variations; (

**b**) With temperature variations.

**Figure 6.**Literature examples of IO LFC (tunable LFC gains are colored): (

**a**) PI; (

**b**) PID; (

**c**) PIDD; (

**d**) PIDF.

**Figure 7.**Literature examples of FO LFC (tunable LFC gains are colored): (

**a**) FOPI; (

**b**) FOPID; (

**c**) TID; (

**d**) FOTIDF.

**Figure 14.**Performance results at Scenario 1 with GRC. (

**a**) $\Delta {f}_{a}$ (P.U); (

**b**) $\Delta {f}_{b}$ (P.U); (

**c**) $\Delta {P}_{tie}$ (P.U).

**Figure 15.**Performance results at Scenario 1 without GRC. (

**a**) $\Delta {f}_{a}$ (P.U); (

**b**) $\Delta {f}_{b}$ (P.U); (

**c**) $\Delta {P}_{tie}$ (P.U).

**Figure 16.**Frequency response $\Delta {f}_{a}$ (P.U) with and without GRC of the proposed controller.

**Figure 18.**Performance results at Scenario 2. (

**a**) $\Delta {f}_{a}$ (P.U); (

**b**) $\Delta {f}_{b}$ (P.U); (

**c**) $\Delta {P}_{tie}$ (P.U).

**Figure 20.**Performance results at Scenario 3. (

**a**) $\Delta {f}_{a}$ (P.U); (

**b**) $\Delta {f}_{b}$ (P.U); (

**c**) $\Delta {P}_{tie}$ (P.U).

**Figure 23.**Performance results at Scenario 4. (

**a**) $\Delta {f}_{a}$ (P.U); (

**b**) $\Delta {f}_{b}$ (P.U); (

**c**) $\Delta {P}_{tie}$ (P.U).

**Figure 26.**Performance results at Scenario 5. (

**a**) $\Delta {f}_{a}$ (P.U); (

**b**) $\Delta {f}_{b}$ (P.U); (

**c**) $\Delta {P}_{tie}$ (P.U).

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

Maximum Power value (${P}_{max}$) | 115 W |

Voltage at Maximum Power value (${V}_{mp}$) | 17.1 V |

Current at Maximum Power value (${I}_{mp}$) | 6.7 A |

Voltage value at Open-Circuit (${V}_{oc}$) | 21.8 V |

Current value at Short -Circuit (${I}_{sc}$) | 7.5 A |

Parameters | Symbols | Value | |
---|---|---|---|

Area $\mathit{a}$ | Area $\mathit{b}$ | ||

Rated MGs’ capacity | ${P}_{rx}$ (MW) | 1200 | 1200 |

Droops constant | ${R}_{x}$ (Hz/MW) | 2.4 | 2.4 |

Frequency bias values | ${B}_{x}$ (MW/Hz) | 0.4249 | 0.4249 |

Valve gate limiting value (minimum) | ${V}_{vlx}$ (p.u.MW) | −0.5 | −0.5 |

Valve gate limiting value (maximum) | ${V}_{vux}$ (p.u.MW) | 0.5 | 0.5 |

Time constant for thermal governor | ${T}_{g}$ (s) | 0.08 | - |

Thermal turbines’ (time constant) | ${T}_{t}$ (s) | 0.3 | - |

Governor of hydraulic generator (time constant) | ${T}_{1}$ (s) | - | 41.6 |

Transient droops time constant for hydraulic governor | ${T}_{2}$ (s) | - | 0.513 |

Governor of hydraulic generator resetting time | ${T}_{R}$ (s) | - | 5 |

Hydraulic turbines’ water starting time | ${T}_{w}$ (s) | - | 1 |

Inertia’s constants | ${H}_{x}$ (p.u.s) | 0.0833 | 0.0833 |

Damping coefficient | ${D}_{x}$ (p.u./Hz) | 0.00833 | 0.00833 |

PV generations time constant | ${T}_{PV}$ (s) | - | 1.3 |

PV generations’ gains | ${K}_{PV}$ (s) | - | 1 |

Wind generations’ time constants | ${T}_{WT}$ (s) | 1.5 | - |

Wind generations’ gains | ${K}_{WT}$ (s) | 1 | - |

EV BESSs’ models | |||

Penetration level | - | 10% | 10% |

BESS voltages (nominal) | ${V}_{nom}$ (V) | 364.8 | 364.8 |

BESS capacity | ${C}_{nom}$ (Ah) | 66.2 | 66.2 |

Series resistances | ${R}_{s}$ (ohms) | 0.074 | 0.074 |

Transient resistance | ${R}_{t}$ (ohms) | 0.047 | 0.047 |

Transient capacitances | ${C}_{t}$ (farad) | 703.6 | 703.6 |

Constants value | $RT/F$ | 0.02612 | 0.02612 |

BESS’s SOC (maximum) | % | 95 | 95 |

BESS’s energy capacity | ${C}_{batt}$ (kWh) | 24.15 | 24.15 |

Function | Type | Fmin | Boundaries | Description |
---|---|---|---|---|

F1 | Unimodal function | 300 | [−100, 100] | Shifted and full rotated Zakharov function |

F2 | Basic functions | 400 | [−100, 100] | Shifted and full rotated Rosenbrock’s function |

F3 | 600 | [−100, 100] | Shifted and full rotated expanded Schaffer’s F6 function | |

F4 | 800 | [−100, 100] | Shifted and full rotated non-continuous Rastrigin’s function | |

F5 | 900 | [−100, 100] | Shifted and rotated Levy function | |

F6 | Hybrid functions | 1800 | [−100, 100] | Hybrid function 1 (N = 3) |

F7 | 2000 | [−100, 100] | Hybrid function 2 (N = 6) | |

F8 | 2200 | [−100, 100] | Hybrid function 3 (N = 5) | |

F9 | Composition functions | 2300 | [−100, 100] | Composite function 1 (N = 5) |

F10 | 2400 | [−100, 100] | Composite function 2 (N = 4 | |

F11 | 2600 | [−100, 100] | Composite function 3 (N = 5) | |

F12 | 2700 | [−100, 100] | Composite function 3 (N = 5) |

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

PSO | ${t}_{max}$, $Np$, $C1$, $C2$, $W1$ | 300, 30, 2,2, 0.7 |

SCSC | ${t}_{m}ax$, $Np$, Sensitivity range ($rg$), Phases control range (R) | 300, 30, [2 - 0], [−2rg, 2rg] |

SCA | ${t}_{max}$, $Np$, b | 300, 30, [2 - 0] |

ZOA | ${t}_{max}$, $Np$, R | 300, 30, 0.01 |

LCA | ${t}_{max}$, $Np$ | 300, 30 |

MLCA | ${t}_{max}$, $Np$, $\delta $ | 300, 30, 4 |

Function No. | Optimizer | Average | Best | Worst | SD |
---|---|---|---|---|---|

F1 | SCSO | 3093.775 | 349.1486 | 8691.832 | 2493.022 |

SCA | 3458.404 | 1164.057 | 6460.631 | 1667.455 | |

PSO | 300.0105 | 300.0001 | 300.1228 | 0.024964 | |

ZOA | 2406.967 | 323.1252 | 7635.127 | 2195.524 | |

LCA | 1447.707 | 700.4051 | 3349.518 | 711.4054 | |

MLCA | 300 | 300 | 300.001 | 0.000205 | |

F2 | SCSO | 455.7817 | 401.0632 | 720.0985 | 68.29365 |

SCA | 494.0413 | 432.2709 | 542.0408 | 25.87232 | |

PSO | 424.9348 | 400 | 471.3437 | 30.60353 | |

ZOA | 476.7607 | 404.1804 | 910.9457 | 99.36141 | |

LCA | 420.9453 | 401.0094 | 442.2129 | 12.7182 | |

MLCA | 409.3691 | 400 | 470.8066 | 19.38046 | |

F3 | SCSO | 619.4869 | 603.0549 | 640.0254 | 10.06907 |

SCA | 625.8878 | 618.392 | 649.0927 | 6.258529 | |

PSO | 620.3777 | 603.8081 | 639.1443 | 10.40486 | |

ZOA | 621.8001 | 610.0043 | 633.3335 | 5.858331 | |

LCA | 605.1606 | 601.5796 | 610.2001 | 2.407723 | |

MLCA | 603.0268 | 600.2005 | 611.2571 | 3.185232 | |

F4 | SCSO | 829.3113 | 806.1021 | 844.7062 | 8.741245 |

SCA | 848.0268 | 837.5241 | 860.1306 | 6.503605 | |

PSO | 821.6901 | 809.9496 | 842.7831 | 7.669336 | |

ZOA | 816.5859 | 809.1074 | 830.5366 | 5.63061 | |

LCA | 834.6409 | 814.102 | 854.8532 | 10.1297 | |

MLCA | 825.3515 | 804.9748 | 832.8336 | 6.299992 | |

F5 | SCSO | 1141.826 | 915.4967 | 1469.342 | 171.9704 |

SCA | 1083.895 | 992.3169 | 1283.928 | 80.46401 | |

PSO | 1054.136 | 900 | 1362.665 | 153.0541 | |

ZOA | 1061.449 | 940.9945 | 1283.71 | 96.35584 | |

LCA | 923.2255 | 901.7043 | 963.4934 | 16.85943 | |

MLCA | 909.5508 | 900.6334 | 957.7695 | 12.00111 | |

F6 | SCSO | 4481.64 | 2187.17 | 8161.352 | 1751.289 |

SCA | 7439635 | 963067.3 | 26425791 | 7135852 | |

PSO | 3052.999 | 1860.679 | 8084.839 | 1582.306 | |

ZOA | 3100.627 | 1881.875 | 7298.885 | 1587.5 | |

LCA | 21954.04 | 2048.434 | 136689.1 | 32740.4 | |

MLCA | 1923.427 | 1828.147 | 2521.161 | 141.062 | |

F7 | SCSO | 2048.494 | 2021.093 | 2089.621 | 18.7493 |

SCA | 2066.766 | 2041.341 | 2085.259 | 10.09232 | |

PSO | 2044.901 | 2012.969 | 2094.026 | 21.58967 | |

ZOA | 2053.452 | 2010.803 | 2114.428 | 22.98909 | |

LCA | 2046.143 | 2026.291 | 2066.935 | 11.5397 | |

MLCA | 2025.324 | 2008.956 | 2046.95 | 8.875774 | |

F8 | SCSO | 2227.988 | 2214.531 | 2239.62 | 6.081599 |

SCA | 2239.191 | 2231.123 | 2251.613 | 5.328733 | |

PSO | 2235.924 | 2200.537 | 2341.024 | 39.94917 | |

ZOA | 2231.259 | 2222.731 | 2352.093 | 25.27378 | |

LCA | 2229.289 | 2222.178 | 2231.57 | 2.287831 | |

MLCA | 2219.969 | 2203.455 | 2224.124 | 4.350484 | |

F9 | SCSO | 2594.81 | 2529.458 | 2678.021 | 35.10836 |

SCA | 2598.177 | 2557.816 | 2656.696 | 27.8627 | |

PSO | 2541.842 | 2529.284 | 2676.216 | 40.64008 | |

ZOA | 2614.066 | 2530.239 | 2718.711 | 45.68827 | |

LCA | 2539.873 | 2531.308 | 2556.745 | 6.301353 | |

MLCA | 2529.411 | 2529.284 | 2531.277 | 0.397224 | |

F10 | SCSO | 2530.18 | 2500.426 | 2635.02 | 53.1725 |

SCA | 2528.239 | 2501.45 | 2673.45 | 58.37221 | |

PSO | 2596.806 | 2500.387 | 2759.12 | 68.34379 | |

ZOA | 2578.921 | 2500.553 | 2681.633 | 71.62236 | |

LCA | 2500.802 | 2500.463 | 2501.487 | 0.222178 | |

MLCA | 2500.435 | 2500.276 | 2500.703 | 0.1111 | |

F11 | SCSO | 2831.009 | 2609.066 | 3309.952 | 170.1567 |

SCA | 3004.421 | 2793.088 | 3783.863 | 297.7186 | |

PSO | 2953.419 | 2600.001 | 5230.808 | 485.1794 | |

ZOA | 3053.657 | 2745.179 | 3430.171 | 182.3106 | |

LCA | 2731.127 | 2636.21 | 2764.63 | 34.56173 | |

MLCA | 2624.072 | 2600 | 2750.473 | 56.29244 | |

F12 | SCSO | 2874.063 | 2861.454 | 2918.708 | 16.46731 |

SCA | 2873.296 | 2867.157 | 2891.819 | 4.697798 | |

PSO | 2951.277 | 2872.847 | 3121.534 | 69.80949 | |

ZOA | 2943.05 | 2895.543 | 3012.8 | 31.04917 | |

LCA | 2869.805 | 2865.583 | 2875.687 | 2.388877 | |

MLCA | 2871.416 | 2864.046 | 2898.943 | 7.599243 |

MLCA vs. | SCSO | SCA | PSO | FOX | LCA |
---|---|---|---|---|---|

F1 | 1.4157 × 10^{−9} | 1.4157 × 10^{−9} | 5.2120 × 10^{−9} | 1.4157 × 10^{−9} | 1.4157 × 10^{−9} |

F2 | 9.6957 × 10^{−6} | 3.6690 × 10^{−9} | 1.1159 × 10^{−1} | 3.3440 × 10^{−7} | 8.1897 × 10^{−5} |

F3 | 9.2880 × 10^{−9} | 1.4157 × 10^{−9} | 1.3079 × 10^{−8} | 1.5967 × 10^{−9} | 1.6708 × 10^{−3} |

F4 | 8.7677 × 10^{−2} | 1.4055 × 10^{−9} | 1.8376 × 10^{−2} | 2.1373 × 10^{−5} | 9.6989 × 10^{−4} |

F5 | 2.2857 × 10^{−9} | 1.4157 × 10^{−9} | 2.9771 × 10^{−2} | 1.8002 × 10^{−9} | 3.3128 × 10^{−4} |

F6 | 2.5742 × 10^{−9} | 1.4157 × 10^{−9} | 3.2928 × 10^{−5} | 2.6597 × 10^{−6} | 2.0288 × 10^{−9} |

F7 | 1.6471 × 10^{−6} | 1.5967 × 10^{−9} | 1.1285 × 10^{−4} | 6.7951 × 10^{−7} | 1.0585 × 10^{−7} |

F8 | 3.7045 × 10^{−7} | 1.4157 × 10^{−9} | 8.0086 × 10^{−1} | 1.8002 × 10^{−9} | 2.0288 × 10^{−9} |

F9 | 1.8002 × 10^{−9} | 1.4157 × 10^{−9} | 1.5288 × 10^{−6} | 1.5967 × 10^{−9} | 1.4157 × 10^{−9} |

F10 | 2.5677 × 10^{−8} | 1.4157 × 10^{−9} | 2.4184 × 10^{−6} | 2.0288 × 10^{−9} | 1.6401 × 10^{−8} |

F11 | 1.3090 × 10^{−7} | 1.4157 × 10^{−9} | 8.2805 × 10^{−9} | 2.2857 × 10^{−9} | 3.0175 × 10^{−7} |

F12 | 1.8064 × 10^{−1} | 3.3915 × 10^{−3} | 1.0414 × 10^{−8} | 1.5967 × 10^{−9} | 5.7365 × 10^{−1} |

Controller | Area | Parameters | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{K}}_{\mathit{t}\mathbf{1}}$ | ${\mathit{K}}_{\mathit{i}\mathbf{1}}$ | ${\mathit{K}}_{\mathit{d}\mathbf{1}}$ | ${\mathit{n}}_{\mathbf{1}}$ | ${\mathit{K}}_{\mathit{t}\mathbf{2}}$ | ${\mathit{K}}_{\mathit{i}\mathbf{2}}$ | ${\mathit{K}}_{\mathit{d}\mathbf{2}}$ | ${\mathit{n}}_{\mathbf{2}}$ | ${\mathit{\lambda}}_{\mathbf{1}}$ | ${\mathit{\mu}}_{\mathbf{1}}$ | ${\mathit{N}}_{\mathit{f}\mathbf{1}}$ | ||

FOTID | a | 2.245 | 1.987 | 1.713 | 2.234 | ― | ― | ― | ― | 0.622 | 0.574 | ― |

b | 2.956 | 2.016 | 0.895 | 2.923 | ― | ― | ― | ― | 0.714 | 0.882 | ― | |

TI/FOTID | a | 3.155 | 2.019 | ― | 2.862 | 2.868 | 3.036 | 1.156 | 3.634 | 0.882 | 0.857 | ― |

b | 2.738 | 1.583 | ― | 3.235 | 2.365 | 2.678 | 1.344 | 3.69 | 0.566 | 0.843 | ― | |

TD/FOTID | a | 3.928 | ― | 1.037 | 3.555 | 4.018 | 3.346 | 2.147 | 3.944 | 0.788 | 0.948 | ― |

b | 3.748 | ― | 1.164 | 4.022 | 3.571 | 3.176 | 2.291 | 3.891 | 0.758 | 0.788 | ― | |

1+TD/FOTIDF | a | 4.525 | ― | 3.851 | 4.576 | 4.864 | 3.865 | 3.998 | 4.977 | 0.948 | 0.877 | 151.36 |

b | 4.118 | ― | 4.073 | 4.281 | 3.954 | 4.279 | 3.092 | 4.583 | 0.882 | 0.915 | 189.5 |

Scenario | Controller | $\mathbf{\Delta}{\mathit{f}}_{1}$ (P.U) | $\mathbf{\Delta}{\mathit{f}}_{2}$ (P.U) | $\mathbf{\Delta}{\mathit{P}}_{\mathit{tie}}$ (P.U) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

PO | PU | ST (s) | PO | PU | ST (s) | PO | PU | ST (s) | ||

No.1 at 75 s | FOTID | 0.0019 | 0.0115 | 17 | 0.0021 | 0.0082 | 16 | 0.0005 | 0.0028 | 22 |

TI/FOTID | 0.0002 | 0.0079 | 9 | 0.0016 | 0.0058 | 20 | 0.0001 | 0.0024 | 18 | |

TD/FOTID | 0.0017 | 0.0058 | 15 | 0.0001 | 0.0023 | 10 | 0.0002 | 0.0016 | 10 | |

1+TD/FOTIDF | - | 0.0001 | 4 | - | 0.0005 | 5 | - | 8.4 × 10^{−5} | 6 | |

No.2 at 8:00 AM. | FOTID | 0.0016 | 0.0012 | FU | 0.0017 | 0.0011 | FU | 0.0004 | 0.0005 | FU |

TI/FOTID | 0.0017 | 0.0018 | FU | 0.0019 | 0.0015 | FU | 0.0006 | 0.0007 | FU | |

TD/FOTID | 0.0008 | 0.0009 | FU | 0.0005 | 0.0007 | FU | 0.0007 | 0.0009 | FU | |

1+TD/FOTIDF | 1 × 10^{−6} | 1 × 10^{−5} | FU | 1.1 × 10^{−6} | 1.01 × 10^{−5} | FU | 1 × 10^{−6} | 1.1 × 10^{−6} | FU | |

No.3 at 13:00 PM. | FOTID | 0.0012 | 0.0042 | FU | 0.0025 | 0.0073 | FU | 0.0016 | 0.0004 | FU |

TI/FOTID | 0.0011 | 0.0023 | FU | 0.0019 | 0.0041 | FU | 0.0011 | 0.0003 | FU | |

TD/FOTID | 0.0001 | 0.0021 | FU | 0.0014 | 0.0037 | FU | 0.0009 | 0.0001 | FU | |

1+TD/FOTIDF | 1 × 10^{−5} | 1 × 10^{−5} | FU | 0.9 × 10^{−5} | 1 × 10^{−6} | FU | 1 × 10^{−4} | 1 × 10^{−6} | FU | |

No.4 at 10:00 AM. | FOTID | 0.0057 | 0.0099 | FU | 0.0072 | 0.0133 | FU | 0.0039 | 0.0021 | FU |

TI/FOTID | 0.0028 | 0.0058 | FU | 0.0041 | 0.0033 | FU | 0.0022 | 0.0013 | FU | |

TD/FOTID | 0.002 | 0.004 | FU | 0.0036 | 0.0031 | FU | 0.0021 | 0.0011 | FU | |

1+TD/FOTIDF | 0.0001 | 0.0004 | FU | 0.0001 | 0.0001 | FU | 1 × 10^{−4} | 1 × 10^{−5} | FU | |

No.5 at 16:00 PM. | FOTID | 0.141 | 0.022 | FU | 0.123 | 0.0392 | FU | 0.033 | 0.0067 | FU |

TI/FOTID | 0.0826 | 0.0018 | FU | 0.0524 | 0.0141 | FU | 0.0192 | 0.0031 | FU | |

TD/FOTID | 0.0522 | 0.0151 | FU | 0.0198 | 0.011 | FU | 0.022 | 0.0023 | FU | |

1+TD/FOTIDF | 0.004 | - | 120 | 0.001 | - | 110 | 0.0013 | - | 180 |

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## Share and Cite

**MDPI and ACS Style**

Noman, A.M.; Aly, M.; Alqahtani, M.H.; Almutairi, S.Z.; Aljumah, A.S.; Ebeed, M.; Mohamed, E.A.
Optimum Fractional Tilt Based Cascaded Frequency Stabilization with MLC Algorithm for Multi-Microgrid Assimilating Electric Vehicles. *Fractal Fract.* **2024**, *8*, 132.
https://doi.org/10.3390/fractalfract8030132

**AMA Style**

Noman AM, Aly M, Alqahtani MH, Almutairi SZ, Aljumah AS, Ebeed M, Mohamed EA.
Optimum Fractional Tilt Based Cascaded Frequency Stabilization with MLC Algorithm for Multi-Microgrid Assimilating Electric Vehicles. *Fractal and Fractional*. 2024; 8(3):132.
https://doi.org/10.3390/fractalfract8030132

**Chicago/Turabian Style**

Noman, Abdullah M., Mokhtar Aly, Mohammed H. Alqahtani, Sulaiman Z. Almutairi, Ali S. Aljumah, Mohamed Ebeed, and Emad A. Mohamed.
2024. "Optimum Fractional Tilt Based Cascaded Frequency Stabilization with MLC Algorithm for Multi-Microgrid Assimilating Electric Vehicles" *Fractal and Fractional* 8, no. 3: 132.
https://doi.org/10.3390/fractalfract8030132