# Power System Stability Improvement of FACTS Controller and PSS Design: A Time-Delay Approach

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

- This paper investigates the simultaneous tuning of the PSS and FACTS controller considering the potential time delays. Its goal is to improve power system stability in the presence of potential time delay.
- GOA is utilized to fine-tune control parameters for the proposed fuzzy lead-lag controller design. To illustrate the robustness of the proposed design methodology, simulation results for both single-machine infinite-bus and multi-machine power systems are presented under different disturbances and faults.
- The percentage decrease in J value with the GOA technique compared with the recently published WOA, well-established GA, and DE are 16.32%, 14.56%, and 13.72%, respectively, in the SMIB system. The percentage decrease in J value with the proposed GOA technique compared with the recently published WOA, well-established GA, and DE are 1.41%, 9.98%, and 13.31%, respectively, for a multi-machine system.

## 2. System Modeling

_{B}and V

_{T}, respectively; V

_{1}and V

_{2}are the bus voltages, the output voltage of the SSSC converter and the DC voltage source is represented by V

_{cnv}and V

_{DC}, respectively; the line current is I and the total flow of real power in the transmission lines and that of a single line are each represented by P

_{L}and P

_{L1}, respectively.

#### Model of SSSC

## 3. The Proposed Approach

#### 3.1. Proposed Fuzzy Structured FACTS Controller Structure with PSS

_{PS}, a signal washout block serving as a high-pass filter, and a phase compensation block to provide appropriate phase-lead characteristics between input and output signals and which are two-staged, as shown in the figure. The output of the PSS structure shown in Figure 4, Vs cumulate with the reference voltage of the excitation system, V

_{ref}. From the washout function’s perspective, the time constant value T

_{WS}= T

_{WP}may lie somewhere between 1–20 s and is not critical. In the present analysis, ${K}_{PS}$ and ${K}_{PP}$ are the controller gains, ${k}_{1s},{k}_{2s},{k}_{3s}$ and ${k}_{1p},{k}_{2p},{k}_{3p}$ are the scaling factors and time constants (T

_{1s}, T

_{2s}, T

_{3S,}and T

_{4S}) to be computed.

#### 3.2. Optimization Problem

_{WS}=T

_{WP}= 10 s is used in the present work and is pre-specified [20]. The objective is to determine the time constants along with gains associated with the controller. As $\Delta {V}_{q}$ is zero during steady-state conditions, V

_{qref}becomes constant. However, during dynamic conditions, the modulation of the injected series voltage V

_{q}is done by applying a certain algorithm in order to damp out the system oscillations. V

_{qref}can be assumed to be constant due to the slow operation of the power flow loop during the steady state. Thus, under dynamic conditions, the effective value of V

_{q}can be formulated as

## 4. GOA Method

#### Overview of GOA

## 5. Results and Discussion

#### 5.1. SMIB Power System

#### 5.1.1. Case A: Nominal Loading Condition

_{e}= 0.85 pu and ${\delta}_{0}$ = 52.3 deg, which are the nominal loading conditions in terms of the occurrence of a severe disturbance in the system. A 3-cycles, 3-phase fault is imposed at the mid-section of the transmission line linking bus-2 and bus-3 at time t = 1 s, and the system returns to its previous state after it is cleared. The system’s various responses are depicted in Figure 10, Figure 11, Figure 12 and Figure 13, including speed deviation in pu, tie-line power P

_{L}in MW, power angle in $\delta $ (degree), and SSSC injected voltage V

_{q}in pu. From the different responses, we reached the conclusion that the GOA-optimized suggested controller provides improved dynamic response when compared with the well-established GA, DE algorithm, and recently published WOA-optimized controller. It can also be shown that the recommended GOA-optimized controller has good low-frequency oscillation damping capabilities and can easily stabilize the device by adjusting the SSSC-injected voltage. In comparison with recently published WOA, DE, and GA-optimized controllers, the suggested technique offers improved dynamic response in terms of minimal overshoot, minimum undershoot, and settling time, as shown in Figure 10, Figure 11, Figure 12 and Figure 13. As a result, the suggested controller increases the restriction on power system stability and capacity. Figure 14 displays various transmission delays considering speed deviation. Here it is observed that transport delays have a significant inverse effect on the system responses.

#### 5.1.2. Case B: Light Loading Condition

#### 5.1.3. Case C: Heavy Loading Condition

#### 5.2. Extension to Multi-Machine Power System

#### 5.2.1. Scenario 1: Three-Phase Fault Disturbance

#### 5.2.2. Scenario 2: Small Disturbance

- Initially, a SMIB system with a fuzzy lead-lag structured controller is considered, and the dominance of GOA as related to WOA, DE, and GA is demonstrated.
- The percentage decrease in J value with the GOA technique compared with recently published WOA, well-established GA, and DE are 16.32%, 14.56%, and 13.72%, respectively, in the SMIB system. The percentage decrease in J value with the proposed GOA technique compared with recently published WOA, well-established GA, and DE are 1.41%, 9.98%, and 13.31%, respectively, for the multi-machine system.
- The effectiveness of the GOA is validated with various load conditions and results confirmed that GOA performed better compared with the recently published WOA, and well-established GA and DE optimization algorithms.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

## References

- Ustun, T.S.; Hashimoto, J.; Otani, K. Impact of Smart Inverters on Feeder Hosting Capacity of Distribution Networks. IEEE Access
**2019**, 7, 163526–163536. [Google Scholar] [CrossRef] - Latif, A.; Hussain, S.M.S.; Das, D.C.; Ustun, T.S. Double stage controller optimization for load frequency stabilization in hybrid wind-ocean wave energy based maritime microgrid system. Appl. Energy
**2021**, 282, 116–171. [Google Scholar] [CrossRef] - Latif, A.; Paul, M.; Das, D.C.; Hussain, S.M.S.; Ustun, T.S. Price Based Demand Response for Optimal Frequency Stabilization in ORC Solar Thermal Based Isolated Hybrid Microgrid under Salp Swarm Technique. Electronics
**2020**, 9, 2209. [Google Scholar] [CrossRef] - Hussain, I.; Das, D.C.; Sinha, N.; Latif, A.; Hussain, S.M.S.; Ustun, T.S. Performance Assessment of an Islanded Hybrid Power System with Different Storage Combinations Using an FPA-Tuned Two-Degree-of-Freedom (2DOF) Controller. Energies
**2020**, 13, 5610. [Google Scholar] [CrossRef] - Latif, A.; Hussain, S.M.S.; Das, D.C.; Ustun, T.S. Optimization of Two-Stage IPD-(1+I) Controllers for Frequency Regulation of Sustainable Energy Based Hybrid Microgrid Network. Electronics
**2021**, 10, 919. [Google Scholar] [CrossRef] - Chauhan, A.; Upadhyay, S.; Khan, M.T.; Hussain, S.M.S.; Ustun, T.S. Performance Investigation of a Solar Photovoltaic/Diesel Generator Based Hybrid System with Cycle Charging Strategy Using BBO Algorithm. Sustainability
**2021**, 13, 8048. [Google Scholar] [CrossRef] - Das, A.; Dawn, S.; Gope, S.; Ustun, T.S. A Strategy for System Risk Mitigation Using FACTS Devices in a Wind Incorporated Competitive Power System. Sustainability
**2022**, 14, 8069. [Google Scholar] [CrossRef] - Ranjan, S.; Das, D.C.; Sinha, N.; Latif, A.; Hussain, S.M.S.; Ustun, T.S. Voltage stability assessment of isolated hybrid dish-stirling solar-thermal-diesel microgrid with STATCOM using mine blast algorithm. Electr. Power Syst. Res.
**2021**, 196, 107239. [Google Scholar] [CrossRef] - Singh, N.K.; Koley, C.; Gope, S.; Dawn, S.; Ustun, T.S. An Economic Risk Analysis in Wind and Pumped Hydro Energy Storage Integrated Power System Using Meta-Heuristic Algorithm. Sustainability
**2021**, 13, 13542. [Google Scholar] [CrossRef] - Das, A.; Dawn, S.; Gope, S.; Ustun, T.S. A Risk Curtailment Strategy for Solar PV-Battery Integrated Competitive Power System. Electronics
**2022**, 11, 1251. [Google Scholar] [CrossRef] - Latif, A.; Hussain, S.M.S.; Das, D.C.; Ustun, T.S. Optimum Synthesis of a BOA Optimized Novel Dual-Stage PI − (1 + ID) Controller for Frequency Response of a Microgrid. Energies
**2020**, 13, 3446. [Google Scholar] [CrossRef] - Dey, P.P.; Das, D.C.; Latif, A.; Hussain, S.M.S.; Ustun, T.S. Active Power Management of Virtual Power Plant under Penetration of Central Receiver Solar Thermal-Wind Using Butterfly Optimization Technique. Sustainability
**2020**, 12, 6979. [Google Scholar] [CrossRef] - Abdolrasol, M.G.M.; Hannan, M.A.; Hussain, S.M.S.; Ustun, T.S.; Sarker, M.R.; Ker, P.J. Energy Management Scheduling for Microgrids in the Virtual Power Plant System Using Artificial Neural Networks. Energies
**2021**, 14, 6507. [Google Scholar] [CrossRef] - Latif, A.; Hussain, S.M.S.; Das, D.C.; Ustun, T.S. Design and Implementation of Maiden Dual-Level Controller for Ameliorating Frequency Control in a Hybrid Microgrid. Energies
**2021**, 14, 2418. [Google Scholar] [CrossRef] - Dawn, S.; Gope, S.; Das, S.S.; Ustun, T.S. Social Welfare Maximization of Competitive Congested Power Market Considering Wind Farm and Pumped Hydroelectric Storage System. Electronics
**2021**, 10, 2611. [Google Scholar] [CrossRef] - Kumar, K.K.P.; Soren, N.; Latif, A.; Das, D.C.; Hussain, S.M.S.; Al-Durra, A.; Ustun, T.S. Day-Ahead DSM-Integrated Hybrid-Power-Management-Incorporated CEED of Solar Thermal/Wind/Wave/BESS System Using HFPSO. Sustainability
**2022**, 14, 1169. [Google Scholar] [CrossRef] - Farooq, Z.; Rahman, A.; Hussain, S.M.S.; Ustun, T.S. Power Generation Control of Renewable Energy Based Hybrid Deregulated Power System. Energies
**2022**, 15, 517. [Google Scholar] [CrossRef] - Gholipour, E.; Isazadeh, G.H. Design of a new adaptive optimal wide area IPFC damping controller in Iran transmission network. Int. J. Electr. Power Energy Syst.
**2013**, 53, 529–539. [Google Scholar] [CrossRef] - Kundur, P.; Balu, N.J.; Lauby, M.G. Power System Stability and Control; McGraw-Hill: New York, NY, USA, 1994; Volume 7. [Google Scholar]
- Ali, E.S.; Abd-Elazim, S.M. Coordinated design of PSSs and TCSC via bacterial swarm optimization algorithm in a multimachine power system. Int. J. Electr. Power Energy Syst.
**2012**, 36, 84–92. [Google Scholar] [CrossRef] - Cai, L.J.; Erlich, I. Simultaneous coordinated tuning of PSS and FACTS damping controllers in large power systems. IEEE Trans. Power Syst.
**2005**, 20, 294–300. [Google Scholar] [CrossRef] - Padiyar, K.R.; Prabhu, N. Design and performance evaluation of sub-synchronous damping controller with STATCOM. IEEE Trans. Power Deliv.
**2006**, 21, 1398–1405. [Google Scholar] [CrossRef] - Abd-Elazim, S.M.; Ali, E.S. Coordinated design of PSSs and SVC via bacterial foraging optimization algorithm in a multi-machine power system. Int. J. Electr. Power Energy Syst.
**2012**, 41, 44–53. [Google Scholar] [CrossRef] - Ray, S.; Venayagamoorthy, G.K.; Watanabe, E.H. A computational approach to optimal damping controller design for a GCSC. IEEE Trans. Power Deliv.
**2008**, 23, 1673–1681. [Google Scholar] [CrossRef] - Panda, S.; Yegireddy, N.K.; Mohapatra, S.K. Hybrid BFOA–PSO approach for coordinated design of PSS and SSSC-based controller considering time delays. Int. J. Electr. Power Energy Syst.
**2013**, 49, 221–233. [Google Scholar] [CrossRef] - Bastos-Filho, C.J.; Chaves, D.A.; Silva, F.S.; Pereira, H.A.; Martins-Filho, J.F. Wavelength assignment for physical-layer-impaired optical networks using evolutionary computation. J. Opt. Commun. Netw.
**2011**, 3, 178–188. [Google Scholar] [CrossRef] - Jolfaei, M.G.; Sharaf, A.M.; Shariatmadar, S.M.; Poudeh, M.B. A hybrid PSS–SSSC GA-stabilization scheme for damping power system small signal oscillations. Electr. Power Energy Syst.
**2016**, 75, 337–344. [Google Scholar] [CrossRef] - Farah, A.; Belazi, A.; Alqunun, K.; Almalaq, A.; Alshammari, B.M.; Hamida, M.B.B.; Abbassi, R. A new design method for optimal parameters setting of PSSs and SVC damping controllers to alleviate power system stability problem. Energies
**2021**, 14, 7312. [Google Scholar] [CrossRef] - Ain, Q.; Jamil, E.; Hameed, S.; Naqvi, K.H. Effects of SSSC and TCSC for enhancement of power system stability under different fault disturbances. Aust. J. Electr. Electron. Eng.
**2020**, 17, 56–64. [Google Scholar] [CrossRef] - Khadanga, R.K.; Satapathy, J.K. Time delay approach for PSS and SSSC based coordinated controller design using hybrid PSO–GSA algorithm. Electr. Power Energy Syst.
**2015**, 71, 262–273. [Google Scholar] [CrossRef] - Kamarposhti, M.A.; Colak, I.; Iwendi, C.; Band, S.S.; Ibeke, E. Optimal coordination of PSS and SSSC controllers in power system using ant colony optimization algorithm. J. Circuits Syst. Comput.
**2022**, 31, 2250060. [Google Scholar] [CrossRef] - Khampariya, P.; Panda, S.; Alharbi, H.; Abdelaziz, A.Y.; Ghoneim, S.S. Coordinated Design of Type-2 Fuzzy Lead–Lag-Structured SSSCs and PSSs for Power System Stability Improvement. Sustainability
**2022**, 14, 6656. [Google Scholar] [CrossRef] - Kar, M.K.; Kumar, S.; Singh, A.K.; Panigrahi, S. A modified sine cosine algorithm with ensemble search agent updating schemes for small signal stability analysis. Int. Trans. Electr. Energy Syst.
**2021**, 31, e13058. [Google Scholar] [CrossRef] - Rout, B.; Pati, B.B.; Panda, S. Modified SCA algorithm for SSSC damping Controller design in Power System. ECTI Trans. Electr. Eng. Electron. Commun.
**2018**, 16, 46–63. [Google Scholar] [CrossRef] [Green Version] - Bindumol, E.K.; Mini, V.; Chandran, N. Coordinated Control of PSS and SSSC using PSO to Improve Power System Stability. In Emerging Technologies for Sustainability; CRC Press: Boca Raton, FL, USA, 2020; pp. 293–302. [Google Scholar]
- Sahu, P.R.; Hota, P.K.; Panda, S. Modified whale optimization algorithm for coordinated design of fuzzy lead-lag structure-based SSSC controller and power system stabilizer. Int. Trans. Electr. Energy Syst.
**2019**, 29, e2797. [Google Scholar] [CrossRef] - Ansari, J.; Abbasi, A.R.; Heydari, M.H.; Avazzadeh, Z. Simultaneous design of fuzzy PSS and fuzzy STATCOM controllers for power system stability enhancement. Alex. Eng. J.
**2022**, 61, 2841–2850. [Google Scholar] [CrossRef] - Esmaili, M.R.; Hooshmand, R.A.; Parastegari, M.; GhaebiPanah, P.; Azizkhani, S. New coordinated design of SVC and PSS for multi-machine power system using BFPSO algorithm. Procedia Technol.
**2013**, 11, 65–74. [Google Scholar] [CrossRef] [Green Version] - Afzalan, E.; Joorabian, M. Analysis of the simultaneous coordinated design of STATCOM-based damping stabilizers and PSS in a multi-machine power system using the seeker optimization algorithm. Int. J. Electr. Power Energy Syst.
**2013**, 53, 1003–1017. [Google Scholar] [CrossRef] - Sahu, P.R.; Hota, P.K.; Panda, S.; Lenka, R.K.; Padmanaban, S.; Blaabjerg, F. Coordinated Design of FACTS Controller with PSS for Stability Enhancement Using a Novel Hybrid Whale Optimization Algorithm–Nelder Mead Approach. Electr. Power Compon. Syst.
**2022**, 1–6. [Google Scholar] [CrossRef] - Rodrigues, F.; Molina, Y.; Silva, C.; Ñaupari, Z. Simultaneous tuning of the AVR and PSS parameters using particle swarm optimization with oscillating exponential decay. Int. J. Electr. Power Energy Syst.
**2021**, 133, 107215. [Google Scholar] [CrossRef] - Fortes, E.V.; Martins, L.F.; Costa, M.V.; Carvalho, L.; Macedo, L.H.; Romero, R. Mayfly Optimization Algorithm Applied to the Design of PSS and SSSC-POD Controllers for Damping Low-Frequency Oscillations in Power Systems. Int. Trans. Electr. Energy Syst.
**2022**, 2022, 5612334. [Google Scholar] [CrossRef] - Saremi, S.; Mirjalili, S.; Lewis, A. Grasshopper optimization algorithm: Theory and application. Adv. Eng. Softw.
**2017**, 105, 30–47. [Google Scholar] [CrossRef] [Green Version] - Panda, S. Multi-objective evolutionary algorithm for SSSC-based controller design. Electr. Power Syst. Res.
**2009**, 79, 937–944. [Google Scholar] [CrossRef] - Panda, S.; Swain, S.C.; Rautray, P.K.; Malik, R.K.; Panda, G. Design and analysis of SSSC based supplementary damping controller. Simul. Model Pr. Theory
**2010**, 18, 1199–1213. [Google Scholar] [CrossRef] - Khuntia, S.R.; Panda, S. ANFIS approach for SSSC controller design for the improvement of transient stability performance. Math. Comput. Model.
**2013**, 57, 289–300. [Google Scholar] [CrossRef] - Panda, S. Differential evolution algorithm for SSSC-based damping controller design considering time delay. J. Frankl. Inst.
**2011**, 348, 1903–1926. [Google Scholar] [CrossRef] - Mudi, K.R.; Pal, R.N. A self-tuning fuzzy PI controller. Fuzzy Sets Syst.
**2000**, 115, 327–388. [Google Scholar] [CrossRef] - Woo, Z.W.; Chung, H.Y.; Lin, J.J. A PID type fuzzy controller with self-tuning scaling factors. Fuzzy Sets Syst.
**2000**, 115, 321–326. [Google Scholar] [CrossRef] - Abdolrasol, M.G.; Hannan, M.A.; Hussain, S.S.; Ustun, T.S. Optimal PI controller based PSO optimization for PV inverter using SPWM techniques. Energy Rep.
**2022**, 8, 1003–1011. [Google Scholar] [CrossRef]

**Table 1.**GOA optimized proposed SSSC and PSS parameters for the SMIB system (i = S for SSSC and i = P for PSS).

Optimization Techniques | Elements/Parameters | K_{Pi} | T_{1}_{i} | T_{2}_{i} | T_{3}_{i} | T_{4}_{i} | K_{1}_{i} | K_{2}_{i} | K_{3}_{i} |
---|---|---|---|---|---|---|---|---|---|

DE | SSSC controller | 22.01 | 0.2923 | 0.3408 | 1.2441 | 1.1502 | 1.7200 | 1.8670 | 1.9664 |

PSS | 3.075 | 1.8607 | 1.4581 | 1.4764 | 0.1360 | 1.7171 | 1.5712 | 1.0303 | |

GA | SSSC controller | 89.44 | 0.2669 | 1.7653 | 1.8048 | 0.0857 | 1.0057 | 0.5662 | 0.6161 |

PSS | 67.48 | 0.4696 | 0.2484 | 1.1000 | 1.8886 | 0.0217 | 0.2992 | 1.3733 | |

WOA | SSSC controller | 65.36 | 1.5746 | 0.7034 | 0.7493 | 1.3192 | 0.5750 | 1.8149 | 0.0263 |

PSS | 15.77 | 1.0111 | 0.9367 | 0.4632 | 0.0102 | 0.8806 | 1.8313 | 0.8059 | |

GOA | SSSC controller | 77.81 | 2.9293 | 1.7299 | 1.9208 | 3.1816 | 3.3687 | 1.4002 | 1.6572 |

PSS | 19.30 | 0.0636 | 1.3818 | 4.1797 | 1.7307 | 1.3187 | 2.2052 | 3.4003 |

Techniques/Cases | DE | GA | WOA | GOA |
---|---|---|---|---|

Case-a (×10^{−4}) | 9.311 | 9.402 | 9.600 | 8.033 |

Case-b (×10^{−4}) | 3.802 | 3.101 | 2.333 | 1.989 |

Case-c (×10^{−4}) | 3.422 | 3.225 | 2.910 | 2.111 |

**Table 3.**SMIB system’s transient response parameters using the proposed controller with DE/GA/WOA/GOA algorithms.

Studied Controller/ Algorithms | Speed Deviation for Case-a | Speed Deviation for Case-b | Speed Deviation for Case-c | ||||||
---|---|---|---|---|---|---|---|---|---|

US (×10^{−3}) | ST | ITAE (×10 ^{−3}) | US (×10 ^{−3}) | ST | ITAE (×10 ^{−3}) | US (×10 ^{−3}) | ST | ITAE (×10 ^{−3}) | |

DE | −8.5 | 3.46 | 9.31 | −2.98 | 3.72 | 3.80 | −2.24 | 4.05 | 3.422 |

GA | −8.1 | 3.42 | 9.40 | −3.04 | 3.44 | 3.10 | −2.27 | 3.40 | 3.225 |

WOA | −8.6 | 3.65 | 9.60 | −2.97 | 3.13 | 2.33 | −1.10 | 3.38 | 2.910 |

GOA | −6.34 | 3.32 | 8.03 | −2.15 | 2.74 | 1.98 | −0.65 | 2.70 | 2.111 |

Optimization Techniques | Elements/Parameters | K_{Pi} | T_{1i} | T_{2i} | T_{3i} | T_{4i} | K_{1i} | K_{2i} | K_{3i} |
---|---|---|---|---|---|---|---|---|---|

DE | SSSC controller | 11.48 | 0.1295 | 0.0161 | 0.1266 | 0.0788 | 0.0289 | 0.1029 | 0.0465 |

PSS-1 | 1.67 | 0.0490 | 0.0378 | 0.0459 | 0.0181 | 0.1305 | 0.0635 | 0.1122 | |

PSS-2 | 7.095 | 0.1047 | 0.1117 | 0.0945 | 0.0335 | 0.1030 | 0.1718 | 0.1758 | |

PSS-3 | 3.065 | 0.0496 | 0.1172 | 0.1315 | 0.0891 | 0.0491 | 0.1899 | 0.0256 | |

GA | SSSC controller | 148.38 | 1.3759 | 0.5413 | 0.7554 | 1.7241 | 3.2915 | 0.5990 | 0.0121 |

PSS-1 | 115.14 | 1.7816 | 1.6899 | 0.2470 | 1.0721 | 1.6739 | 3.7255 | 0.7186 | |

PSS-2 | 5.535 | 1.7971 | 1.6366 | 1.3511 | 0.2691 | 0.3825 | 2.0267 | 1.3590 | |

PSS-3 | 156.38 | 0.2105 | 1.5969 | 1.4985 | 1.3704 | 0.9235 | 1.6272 | 1.7362 | |

WOA | SSSC controller | 18.74 | 0.1421 | 0.0737 | 0.3441 | 0.2203 | 0.0950 | 0.3556 | 0.2218 |

PSS-1 | 18.06 | 0.1225 | 0.3331 | 0.1270 | 0.1575 | 0.3440 | 0.2852 | 0.1094 | |

PSS-2 | 5.145 | 0.0331 | 0.1805 | 0.2334 | 0.1082 | 0.2473 | 0.3476 | 0.0636 | |

PSS-3 | 12.125 | 0.0617 | 0.0344 | 0.0244 | 0.2349 | 0.2944 | 0.2090 | 0.2354 | |

GOA | SSSC controller | 19.475 | 0.2698 | 0.1579 | 0.2650 | 0.3337 | 0.2969 | 0.2245 | 0.0387 |

PSS-1 | 7.82 | 0.1345 | 0.3030 | 0.1274 | 0.0174 | 0.1902 | 0.3474 | 0.0038 | |

PSS-2 | 19.315 | 0.2740 | 1.1771 | 0.3191 | 0.0303 | 0.1175 | 0.3699 | 0.0619 | |

PSS-3 | 8.695 | 0.0508 | 0.1329 | 0.0985 | 0.1961 | 0.2872 | 0.3530 | 0.0338 |

Techniques/Cases | DE | GA | WOA | GOA |
---|---|---|---|---|

Case-a (×10^{−4}) | 2.089 | 2.012 | 1.837 | 1.811 |

Case-b (× 10^{−4}) | 3.311 | 3.150 | 3.142 | 3.021 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sahu, P.R.; Lenka, R.K.; Khadanga, R.K.; Hota, P.K.; Panda, S.; Ustun, T.S.
Power System Stability Improvement of FACTS Controller and PSS Design: A Time-Delay Approach. *Sustainability* **2022**, *14*, 14649.
https://doi.org/10.3390/su142114649

**AMA Style**

Sahu PR, Lenka RK, Khadanga RK, Hota PK, Panda S, Ustun TS.
Power System Stability Improvement of FACTS Controller and PSS Design: A Time-Delay Approach. *Sustainability*. 2022; 14(21):14649.
https://doi.org/10.3390/su142114649

**Chicago/Turabian Style**

Sahu, Preeti Ranjan, Rajesh Kumar Lenka, Rajendra Kumar Khadanga, Prakash Kumar Hota, Sidhartha Panda, and Taha Selim Ustun.
2022. "Power System Stability Improvement of FACTS Controller and PSS Design: A Time-Delay Approach" *Sustainability* 14, no. 21: 14649.
https://doi.org/10.3390/su142114649