Frequency Stabilization Based on a TFOIDAccelerated Fractional Controller for Intelligent Electrical Vehicles Integration in LowInertia Microgrid Systems
Abstract
:1. Introduction
1.1. Microgrid Challenges
1.2. Literature Review
1.3. Problem Statement and Paper Contribution
 A new strategy for optimal fractionalorder LFC enhancing the resilience of multimicrogrid systems is developed. The method employs a centralized TFOIDAccelerated controller to manage power output from traditional power stations and electric vehicles. The controller’s accelerated derivative structure effectively counters highfrequency disturbances, while its tilt component and fractional integration address lowfrequency disturbances.
 The GO technique is used to optimize control parameters for proposed controllers across different interconnected multiMG systems. This optimizer determines the best settings to achieve optimal system response and stability, considering the constraints of various multiMG systems.
 The suggested approach leverages installed RESs and EV batteries by concurrently designing the proposed coordinated LFC and EV controllers.
 The evaluation of the proposed method’s robustness and effectiveness takes into account a range of anticipated scenarios, RESs, and uncertainties.
 A thorough comparison with controllers from the existing literature demonstrates the superior performance of the proposed controller.
References  Controllers  Algorithms  Category  Main Characteristics of Category 

[44,45]  I  ESO with BE, JBO  IOCbased  Easily implementable 
[21]  I, PI  PSO  singleloop  Low ability to mitigate disturbance 
[20,46]  PI  HHO, ARO  structure  Possess simple singleloop structure 
[47,48]  PID  ICA, ABC  Reduced robustness at parametric uncertainty  
[19]  Nonlinear PI  DO  
[49]  FuzzyPIDD2  GBO  
[50,51]  FOPID  SCA, MDWA  FOCbased  Increased number of tunable parameters 
[26]  TID  MRFO  singleloop  Higher flexibility than IOC methods 
[52]  FOPIDF  ICA  structure  Better mitigation of disturbance 
[31]  iFOI  GWO  Moderate disturbance rejection performance  
[30]  FOPIDA  GWO  
[27]  TFOID  AEO, SMA  
[53]  PDPI  ESMOA  Multiloop  Higher number of tunable parameters 
[54]  PIPDF  DTBO  based control  Mitigating both high and lowfrequency disturbance 
[57]  FOIDF  ICA  structures  Highest in design flexibility 
[55]  PITDF  SSA  Enhanced performance compared to IOC and FOC singleloop methods  
[56]  PDPID  BA  
[42]  FOPIIDDF  CSA  
[58]  2DOF PID  TLBO  
[59]  3DOF TID  SSA  
Proposed  Centralized TFOIDAccelerated  Growth Optimizer (GO)  Singleloop modified FOC  Including tilt component and fractional integration address lowfrequency disturbances 
Including accelerated derivative structure effectively counters highfrequency disturbances  
Centralized single controller for LFC and EV control  
Proving better possibility for rejecting disturbances  
Proposed  Centralized TFOIDAccelerated  Growth Optimizer (GO)  Singleloop modified FOC  Coordinated LFC and EV control in the design process of the optimum controller 
Applies recently developed powerful Growth Optimizer (GO) algorithm  
Simultaneous determination of optimized parameter set of controllers in both areas 
1.4. Paper Organization
2. Overall Structure and Model of Studied Power System
2.1. Overall Structure Description
2.2. EV Model Description
2.3. PV Plant Representation
2.4. Wind Plant Representation
2.5. Representations of Thermal and Hydraulic Generators and Grid
2.6. Complete System Representation
3. Development of Proposed TFOIDAccelerated Controller
3.1. LFC Based on FOC Method
3.2. FOCBased LFC Representation
3.3. Proposed FOCBased LFC Using TFOIDAccelerated Controller
4. Proposed Optimal Controller Design
4.1. Growth Optimizer Description and Algorithm
Algorithm 1 Pseudocode for proposed parameters tuning based on GO algorithm 

4.1.1. Learning Stage
4.1.2. Reflection Stage
4.2. Proposed GO AlgorithmBased TFOIDAccelerated Design
5. Results and Discussion
 Scenario 1: The impact of onestep load pattern (1SLP).
 Scenario 2: The impact of twostep load pattern (2SLP).
 Scenario 3: The impact of multiload pattern (MLP).
 Scenario 4: The impact of the RESs fluctuations.
 Scenario 5: The impact of high penetration of RESs fluctuations.
 Scenario 6: The impact of parameters uncertainties.
5.1. Scenario 1
5.2. Scenario 2
5.3. Scenario 3
5.4. Scenario 4
5.5. Scenario 5
5.6. Scenario 6
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters  Symbols  Area a  Area b 

Nominal power system size  ${P}_{rx}$ (MW)  1200  1200 
Droop gain  ${R}_{x}$ (Hz/MW)  2.4  2.4 
Frequency bias  ${B}_{x}$ (MW/Hz)  0.4249  0.4249 
Valve gate limit (minimum)  ${V}_{gmin}$ (p.u.MW)  0.5  0.5 
Valve gate limit (maximum)  ${V}_{gmax}$ (p.u.MW)  0.5  0.5 
Thermal governor time constant  ${T}_{g}$ (s)  0.08   
Thermal turbine time constant  ${T}_{t}$ (s)  0.3   
Hydraulic governor time constant  ${T}_{s1}$ (s)    41.6 
Hydraulic transient droop time constant  ${T}_{s2}$ (s)    0.513 
Hydraulic governor reset times  ${T}_{s3}$ (s)    9.6 
Water starting time of hydraulic turbines  ${T}_{w}$ (s)    1 
Area’s inertia constant  ${H}_{x}$ (p.u.s)  0.0833  0.0833 
Area’s damping coefficient  ${D}_{x}$ (p.u./Hz)  0.00833  0.00833 
PV transfer function time constant  ${T}_{pv}$ (s)    1.3 
PV transfer function gain  ${K}_{pv}$    1 
Wind transfer function time constant  ${T}_{wT}$ (s)  1.5   
Wind transfer function gain  ${K}_{WT}$  1   
EV numbers in each area    150,000  150,000 
EV participation    5%  5% 
Battery state of charges  SOC  95%  95% 
Controller  Area  ${\mathit{K}}_{\mathit{p}}$  ${\mathit{K}}_{\mathit{i}}$  ${\mathit{K}}_{\mathit{d}}$  ${\mathit{K}}_{\mathit{t}}$  ${\mathit{K}}_{\mathit{a}}$  n  $\mathit{\lambda}$  ${\mathit{\mu}}_{1}$  ${\mathit{\mu}}_{2}$ 

PID  Areaa  4.9765  4.8871  4.3139  ―  ―  ―  ―  ―  ― 
Areab  4.3636  3.4465  1.2884  ―  ―  ―  ―  ―  ―  
PIDAccelerated  Areaa  3.0992  3.9542  1.0558  ―  2.0205  ―  ―  ―  1.556 
Areab  3.9701  2.9021  1.9667  ―  1.3563  ―  ―  ―  1.238  
TID  Areaa  ―  2.5674  3.9984  1.8184  ―  4.955  ―  ―  ― 
Areab  ―  1.1892  1.9497  2.9809  ―  4.961  ―  ―  ―  
TFOIDAccelerated  Areaa  ―  4.8906  4.7948  4.0327  2.3681  2.631  0.923  0.416  1.271 
Areab  ―  3.4132  3.2288  4.2643  2.1538  3.028  0.499  0.723  1.682 
$\mathbf{\Delta}\mathit{fa}$  $\mathbf{\Delta}\mathit{fb}$  $\mathbf{\Delta}{\mathit{P}}_{\mathit{tie}}$  

${\mathit{O}}_{\mathit{sh}}$  ${\mathit{U}}_{\mathit{sh}}$  $\mathit{ST}$  ${\mathit{O}}_{\mathit{sh}}$  ${\mathit{U}}_{\mathit{sh}}$  $\mathit{ST}$  ${\mathit{O}}_{\mathit{sh}}$  ${\mathit{U}}_{\mathit{sh}}$  $\mathit{ST}$  
CASE 1  PID  0.00086  0.0054  17.11  0.00051  0.0038  21.45  0.00005  0.0011  18.32 
TID  0.00043  0.0049  16.12  0.00055  0.0034  18.22    0.0010  16.89  
FOTID  0.00059  0.0036  14.12  0.00054  0.0032  15.14    0.00084  14.75  
TFOIDAccelerated    0.0014  10.42  0.00012  0.00092  13.02    0.00035  12.81  
CASE 2 40 s  PID  0.0012  0.022  57.99  0.0066  0.036  56.43  0.0093  0.00048  >100 s 
TID  0.00056  0.016  50.13  0.00086  0.022  52.78  0.0061  0.00027  >100 s  
FOTID    0.014  38.65  0.0019  0.021  38.76  0.0.0056    >100 s  
TFOIDAccelerated  0.00038  0.0091  37.98  0.0018  0.011  37.96  0.0038  0.00019  49.01  
CASE 3 30 s  PID  0.0045  0.027  51.76  0.0026  0.016  51.52  0.00028  0.0055  50.22 
TID  0.0025  0.021  49.53  0.0024  0.014  49.53  0.00012  0.0041  48.40  
FOTID  0.0023  0.013  45.78  0.0022  0.013  45.76  0.00009  0.0026  43.19  
TFOIDAccelerated  0.00023  0.0041  38.54  0.00041  0.0029  41.11  0.00002  0.0011  39.21  
CASE 4 30 s  PID  0.022  0.0014  Osc.  0.036  0.0071  Osc.  0.00044  0.0095  Osc. 
TID  0.015  0.00079  Osc.  0.021  0.00086  Osc.  0.00028  0.0059  Osc.  
FOTID  0.0092  0.00019  Osc.  0.013  0.0016  Osc.  0.00017  0.0039  Osc.  
TFOIDAccelerated  0.0042  0.00024  Osc.  0.0053  0.00083  Osc.  0.00002  0.0019  Osc.  
CASE 5  PID  0.03525  0.00445  Osc.  0.04935  0.00617  Osc.  0.00116  0.00532  Osc. 
TID  0.01913    Osc.  0.02931  0.00201  Osc.  0.00081  0.00469  Osc.  
FOTID  0.01464    Osc.  0.0218  0.00145  Osc.  0.00058  0.00221  Osc.  
TFOIDAccelerated  0.00521    Osc.  0.00788  0.00106  Osc.  0.00055  0.00158  Osc. 
Parameter  Change  Controller  ${\mathbf{\Delta}}_{{\mathit{f}}_{\mathit{a}}}$  ${\mathbf{\Delta}}_{{\mathit{f}}_{\mathit{b}}}$  $\mathbf{\Delta}{\mathit{P}}_{\mathit{tie}}$  

MO  MU  ST  MO  MU  ST  MO  MU  ST  
${T}_{t}$  +50%  PID  0.00096  0.00622  20.19  0.00074  0.00409  19.17  0.00004  0.00131  23.85 
TID  0.00068  0.00565  18.46  0.00066  0.00371  16.52  0.00001  0.00125  22.31  
FOTID  0.00051  0.00422  14.32  0.00078  0.0034  14.97  −  0.00095  18.53  
FOTIDA  0.00010  0.00179  12.12  0.00016  0.00097  14.48  −  0.00039  18.41  
−50%  PID  0.00063  0.00429  19.22  0.00039  0.00363  16.43  0.00003  0.00103  17.21  
TID  0.00020  0.00392  17.33  0.00016  0.00341  15.33  −  0.00096  15.66  
FOTID  0.00026  0.00276  15.23  0.00013  0.00322  13.79  −  0.00075  14.98  
FOTIDA  0.00003  0.00118  14.44  0.00005  0.00091  13.47  −  0.00032  14.53  
${T}_{g}$  +50%  PID  0.00078  0.0055  16.21  0.00048  0.00368  19.55  0.00003  0.00113  22.14 
TID  0.00036  0.0053  15.72  0.00048  0.00346  18.11  −  0.00114  20.22  
FOTID  0.00048  0.0040  13.99  0.00049  0.00322  15.90  −  0.00087  18.19  
FOTIDA  0.00007  0.0016  13.54  0.00011  0.00092  15.11  −  0.00036  17.11  
−50%  PID  0.00122  0.00547  16.42  0.00069  0.00422  19.66  0.00018  0.00121  23.09  
TID  0.00076  0.00458  15.29  0.00101  0.00369  18.64  −  0.00107  22.21  
FOTID  0.00073  0.00331  13.11  0.00073  0.00337  17.77  −  0.00084  17.55  
FOTIDA  0.00011  0.00142  13.01  0.00014  0.00096  16.99  −  0.00035  17.40  
R  +50%  PID  0.00091  0.00546  20.22  0.00053  0.00386  18.29  0.00005  0.00117  19.89 
TID  0.00049  0.00503  18.20  0.00064  0.00361  16.52  0.00001  0.00114  18.91  
FOTID  0.00067  0.00368  17.72  0.00065  0.00338  14.78  0.000007  0.00088  17.83  
FOTIDA  −  0.00150  15.41  0.00012  0.00094  14.01  0.000001  0.00036  15.49  
−50%  PID  0.00074  0.00544  19.53  0.00027  0.00372  20.17  0.00005  0.00111  19.89  
TID  0.00028  0.00475  18.72  0.00041  0.00312  19.11  −  0.00098  19.23  
FOTID  0.00043  0.00356  15.11  0.00051  0.00304  16.77  −  0.00077  18.10  
FOTIDA  −  0.00148  14.33  0.00012  0.00089  15.06  −  0.00034  15.65  
B  +50%  PID  0.00086  0.00598  21.01  0.00047  0.00293  21.03  0.00006  0.00131  18.25 
TID  0.00027  0.00374  19.10  0.00041  0.00228  20.89  −  0.00095  18.26  
FOTID  0.00042  0.00270  18.33  0.00040  0.00218  19.32  −  0.00075  17.29  
FOTIDA  0.00004  0.00108  17.43  0.00008  0.00059  19.09  −  0.00032  16.05  
−50%  PID  0.00151  0.00847  20.81  0.00112  0.00763  20.04  0.00006  0.00137  19.48  
TID  0.00059  0.00736  20.33  0.00057  0.00625  18.90  0.00003  0.00135  19.93  
FOTID  0.00086  0.00562  19.05  0.00080  0.00586  18.44  −  0.00105  17.80  
FOTIDA  0.00017  0.00249  18.90  0.00019  0.00177  18.49  −  0.00041  15.12 
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Abdelkader, M.; Ahmed, E.M.; Mohamed, E.A.; Aly, M.; Alshahir, A.; Alrahili, Y.S.; Kamel, S.; Jurado, F.; Nasrat, L. Frequency Stabilization Based on a TFOIDAccelerated Fractional Controller for Intelligent Electrical Vehicles Integration in LowInertia Microgrid Systems. World Electr. Veh. J. 2024, 15, 346. https://doi.org/10.3390/wevj15080346
Abdelkader M, Ahmed EM, Mohamed EA, Aly M, Alshahir A, Alrahili YS, Kamel S, Jurado F, Nasrat L. Frequency Stabilization Based on a TFOIDAccelerated Fractional Controller for Intelligent Electrical Vehicles Integration in LowInertia Microgrid Systems. World Electric Vehicle Journal. 2024; 15(8):346. https://doi.org/10.3390/wevj15080346
Chicago/Turabian StyleAbdelkader, Mohamed, Emad M. Ahmed, Emad A. Mohamed, Mokhtar Aly, Ahmed Alshahir, Yousef S. Alrahili, Salah Kamel, Francisco Jurado, and Loai Nasrat. 2024. "Frequency Stabilization Based on a TFOIDAccelerated Fractional Controller for Intelligent Electrical Vehicles Integration in LowInertia Microgrid Systems" World Electric Vehicle Journal 15, no. 8: 346. https://doi.org/10.3390/wevj15080346